EPISTEME - Giano Bifronte

EPISTEME 

Physis e Sophia nel III millennio 

An International Journal 

of Science, History and Philosophy 

N. 6 - 21 dicembre 2002

2 

Redazione (bartocci@dipmat.unipg.it) 

"Episteme" 

c/o Dipartimento di Matematica e Informatica 

Università degli Studi 

Via Vanvitelli - 06100 Perugia 

Direttore Responsabile Euro Roscini (Supplemento semestrale ad: Arte in Foglio, Pubblicazione 

registrata presso il Tribunale di Perugia, N. 36/1991) 

http://www.robotics.it/episteme 

http://www.dipmat.unipg.it/~bartocci 

(per ottenere ~ tenere premuto Alt mentre si compone il numero 126 con i simboli numerici nella parte destra 

della tastiera) 

Numeri arretrati on line: http://itis.volta.alessandria.it/episteme 

PORZI editoriali 

ISSN 1593-3482

PARTE II/ 

SECOND SECTION 

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EPISTEME 

Physis e Sophia nel III millennio/Physis and Sophia in the III millennium 

An International Journal of Science, History and Philosophy 

N. 6 - 21 dicembre 2002 / 21 st Dec. 2002 

[La diffusione via Internet di sezioni della rivista avviene prima della data indicata - Sections of Episteme are 

available in Internet even before the previous date] 

Parte I 

Informazioni editoriali/Editorial Policy 

Pubblicazioni ricevute/Received books and journals 

1 - Lia Mangolini: La vera natura del "magico Shamìr" - A proposito di un'antichissima 

tecnologia per la lavorazione della pietra senza l'uso di strumenti metallici 

2 - Emilio Spedicato: L'Eden riscoperto: geografia, questioni numeriche ed altre storie 

3 - Felice Vinci: L'optimum climatico, il paradiso indoeuropeo e il giardino dell'Eden 

4 - Sabato Scala: Il culto gnostico della Maddalena - Dal mosaico di Otranto alle basiliche 

paleocristiane di Cimitile, attraverso opere letterarie ed architettoniche, fino agli ultimi 

custodi, i Catari ed i Templari 

5 - Arcangelo Papi: La facciata profetica del Duomo di S. Rufino in Assisi 

6 - Prospero Calzolari: Presenza occulta e manifesta dell'Imperatore Federico II nella 

Basilica di San Francesco ad Assisi - Frate Elia e la congiura del silenzio 

7 - Giuseppe Pirazzo, Francesco Vitale: Il mistero degli indiani Mandan 

8 - Ludwik Kostro: When, Where, and How Was Decalogue Created? - Historical Origins 

and Evolution of the Ten Commandments 

9 - Umberto Bartocci: La vera identità di Cristoforo Colombo - Osservazioni e congetture 

10 - Pier Costanzo Brio: Cristoforo Colombo, la nascita - Verità storica e leggenda purista 

11 - Ezio Albrile: Una eresia di luce 

12 - Rosario Vieni: Sul termine greco ανθρωπος … e dintorni 

13 - Oktawian Nawrot: Liberty as a Relation 

14 - Sante Anfiboli: Il canto delle gru - Un racconto iniziatico

15 - Bruno d'Ausser Berrau: Ατοπον − Relazioni spazio-temporali e metafisica tradizionale 

16 - " " " : Solvet saeclum in favilla - In attesa del Dies Irae? 

17 - Umberto Lucia: Il ruolo del trasferimento tecnologico nello sviluppo sostenibile 

Reprints 

Paolo Manzelli, Mariagrazia Costa: Il tempo come coordinata - Gli studi di Giorgio 

Piccardi (1895-1972) 

Omero Speri, Piero Zorzi: Atomo, Energia, Uomo 

Commenti ricevuti/Received Comments 

Sante Anfiboli: A proposito del Vexillum Templi, e altra simbolica templare... 

Alberto Bolognesi: Il Big Bang ha fatto flop? 

Lino Lista: Le tre Grazie - Una chiave per dischiudere il giardino della Primavera 

Arcangelo Papi: Il caso Majorana - L' 

Francesco Pullia: Manlio Farinacci, studioso fuori dal coro 

Recensioni/Reviews 

Luca Bianchini, Anna Trombetta: Goethe, Mozart e Mayr, fratelli illuminati 

Paolo Cortesi: Alla ricerca della Pietra Filosofale - Storia e segreti dell'alchimia 

(Gerardina Cesarano) 

Gianni Grana: L'invenzione di Dio 

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Parte II 

(Sezione speciale, tutta dedicata alla teoria della relatività, e "filiazioni"... - A 

special section, wholly dedicated to the theory of relativity, and "derivations"...) 

- A Letter from the Editor to the Readers 

- Alternative Physics On Line 

1 - Umberto Bartocci: Looking for Special Relativity's Possible Experimental Falsifications 

2 - Christopher Jon Bjerknes: S. Tolver Preston's Explosive Idea - E = mc 2 and the 

Huyghens-Leibnitz Mass/Energy Identity as a Heuristic Principle in the Nineteenth Century 

3 - " " " : Einstein's Irrational Ontology of Redundancy - The Special 

Theory of Relativity and Its Many Fallacies of Petitio Principii 

4 - Alberto Bolognesi: La nuova teoria del cielo - La cosmologia osservativa di Halton Arp 

5 - George Galeczki: Beyond Maxwell-Lorentz Electrodynamics 

6 - Delbert J. Larson: The State of Experimental Evidence for Length Contraction, 2002 

7 - " " : The Most General Fundamental Failures of Modern Physics 

8 - Emidio Laureti: Le basi sperimentali della propulsione non Newtoniana 

9 - Rocco Vittorio Macrì: Neopitagorismo e Relatività 

10 - Jarosław Mrozek: Did Einstein Claim That Nature Has Mathematical Structure? 

11 - Francisco J. Müller: The Problem of Reciprocity and Non-Reciprocity in Relativity 

Theory 

12 - Vladimir Onoochin: On the Impossibility to Describe the Fields of the System of 

Uniformly Moving Charges in the Frame of Special Relativity 

13 - Sabato Scala: Simmetrizzazione delle equazioni di Maxwell con l'introduzione del 

campo gravitazionale, un'idea bizzarra? 

14 - Gianfranco Spavieri, Miguel Rodríguez, Edgar Moreno: Recent Developments in the 

Relativistic Electrodynamics Controversy 

15 - Tuomo Suntola: Dynamic Space Converts Relativity Into Absolute Time and Distance 

16 - Paramahamsa Tewari: Nature of Energy, Light, and Einstein's Light Principle in 

Special Theory of Relativity 

17 - " " : On the Space-Vortex Structure of Cosmic Bodies

18 - Theo Theocharis: Louis T. More, Prophet of the 20th Century 

19 - " " : Ultimate Creative Ignorance 

20 - Tom Van Flandern: What the Global Positioning System Tells Us about the Twin's 

Paradox 

Reprints 

Emilio Almansi: Sulle attrazioni newtoniane di origine idrodinamica 

Stefan Marinov: Annus Horribilis - (The Story of) A Payed Advertisement Published by 

Nature 

N. Moisseiev: Intorno alla legge di resistenza al moto dei corpi in un mezzo pulviscolare 

Carl A. Zapffe: Exodus of Einstein's Special Theory in Seven Simple Steps 

Recensioni/Reviews 

Christopher Jon Bjerknes: Albert Einstein, The Incorrigible Plagiarist 

(Thomas E. Phipps, Jr., from Infinite Energy Magazine, N. 47, 6 October, 2002) 

(A brand new Appendix to the book: A Short History of the Concept of Relative Simultaneity 

in the Special Theory of Relativity) 

Franco Selleri (a cura di): La natura del tempo (Propagazioni super-luminali - Paradosso 

dei gemelli - Teletrasporto) 

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INFORMAZIONI EDITORIALI 

Episteme è soprattutto una rivista "non convenzionale" on-line, reperibile presso i seguenti 

siti: 



(Numeri arretrati: http://itis.volta.alessandria.it/episteme). 

Articoli, commenti e altro materiale sono benvenuti, e possono essere presentati per la 

pubblicazione da parte di ciascuna persona interessata. La spedizione può essere effettuata 

vuoi a mezzo Internet, a: 

bartocci@dipmat.unipg.it 

(inviare eventuali attachments soltanto in formato txt, o doc - si prega di non usare tex! - ed 

eventuali figure, tabelle, etc. in formato jpg), 

vuoi facendo pervenire un dischetto tramite posta ordinaria, all'indirizzo: 

"Episteme" 

Dipartimento di Matematica e Informatica, Università 

06100 Perugia - Italy. 

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rivista. 

EDITORIAL POLICY 

Episteme is mostly an on-line publication, but it does produce even printed copies. In order to 

obtain some of these (15$ each), a request should be sent to the editor, at one of the addresses 

indicated below. 

Episteme is interested in publishing papers which illustrate unconventional points of view - 

that is to say, which do not usually appear in other academic journals - in Science, History 

and Philosophy. 

Since Episteme is thought of as a multi-linguistic journal, papers are accepted and possibly 

published in Deutsch, French, English, Italian, Spanish (etc.?!). 

Episteme will communicate to contributors as soon as possible whether submitted papers are 

in agreement with the journal's criteria, or not. 

Files of the papers, in doc or txt format (please avoid tex!), together with possible illustrations 

in jpg format, should be sent either by attachment, to: 


or by diskette, through ordinary mail, to: 

"Episteme" 

Dipartimento di Matematica e Informatica 

Università, 06100 Perugia - Italy. 

Episteme can be found at the following web sites: 



(Back numbers: http://itis.volta.alessandria.it/episteme). 

- Sections of this journal are available in Internet even before the publication of the printed 

version; afterwards, any modification of the material made available in the web is registered 

in a suitable Errata Corrige. 

- The Internet version of Episteme can sometimes be defective, in presence for instance of 

special characters or symbols. The original file in doc format of the various articles (or of the 

journal's whole issue) will be sent free (as an attachment) from the editorial office to every 

people asking for it. 

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A Letter from the Editor to the Readers 

This special number of Episteme, attached to the ordinary December 2002 issue, is intended 

to celebrate the first three years of the journal (which has grown up more and more from its 

first number, meeting encouraging appreciation from an increasing number of readers), and to 

face - in as "professional" way as possible - one of the greater obstacles to the diffusion of the 

principles of Cartesian rationality. Namely, the assertion that man, conceived as a "young 

animal", and as a recent and still "simple" product of blind evolution and chance from nonliving 

matter, has not (at least in the present moment of his history, but perhaps he will never 

have) an intellect able to make an intuitive image of the real underlying structure of the 

Universe. This is, in our opinion, the answer to the question which Theocharis [a well known 

physicist, who is present in this number of Episteme, as well as in N. 4, Sep. 2002] asks in: 

"Where science has gone wrong"? 1 The turning point could be in fact recognized in the 1859 

publication, and worldwide success, of Darwin's theory 2 , which immediately led to the 1872 

"revolution" in the foundations of mathematics (the voluntary renouncing of intuition in 

favour of a formalistic point of view, which first of all destroyed the foundational rôle of 

euclidean geometry 3 ), and shortly afterwards to the 1905 relativistic revolution (fostered once 

again by mathematicians, those people which one could call the Göttingen men 4 ). As a matter 

of fact, relativity was the first physical theory to introduce the idea that one could not 

anymore interpret all natural phenomena in a "classical way" (the reason for that would be 

that man's intellect does not have experience of the large, and small, scale universe), and thus 

supported the necessity of unconventional mathematics in physics 5 (the famous successive 

Einstein's "qualms of conscience", in front of a physics which had rapidly grown up highly 

counter-intuitive, appear entirely adequate to his "original sin"). 

No more explicit manifesto of this philosophy we could find but in the words of a leading 

XXth Century physicist, the 1965 Nobel prize winner Richard Feynman, who warns that: 

"What I am going to tell you about is what we teach our physics students [...] and you think I'm going 

to explain it to you so you can understand it? No, you are not going to be able to understand it. [...] It 

is my task to convince you not to turn away because you don't understand it. You see, my physics 

students don't understand it either. That is because I don't understand it. Nobody does. [...] It's a 

problem that physicists have learned to deal with: They've larned to realized that whether they like a 

theory or they don't like a theory is not the essential question. Rather, it is whether or not the theory 

gives predictions that agree with experiment. [...] The theory of quantum Electrodynamics describes 

Nature as absurd from the point of view of common sense. And it agrees full with experiment. So I 

hope you can accept Nature as She is - absurd" 6 . 

In front of a Nature which is irreparably "absurd", and can be only manipulated, but not 

understood, a rather nihilistic-irrational 7 drift has spread in "natural philosophy", and from 

physics it has "infected" all fields of science and of Western Weltanschauung. This trend has 

given rise to a sort of epistemological resignation 8 , which has supported the common feeling 

that purely practical satisfaction should be the only consequence of the scientific enterprise. It 

also implies the supremacy of practical-echonomical values (or even simply aesthetical) over 

ethical, as well as metaphysical, ones (regarding as such the pursuit of pure knowledge). And 

this is one of the worst "sins" of our "advanced" civilization, which aims to propose itself - 

sometimes even resorting to the force - as the unique, and the best, for the whole mankind. 

Perhaps, another interesting quotation 9 would be useful in order to realize what kind of 

epistemology is born from such premises.

Constructing a scientific theory means forging a new system of concepts for interpreting the world. 

Such a construction has a great deal in common with the process of creating a fictional world [...] In 

either a work of fiction or a work of science, the task of creation is the same [...] "the boundary line 

between the two is not as clear as is generally believed" [here the author quotes Vladimir Nabokov's 

Lectures in Literature, ed. by Fredson Bowers, Harcourt Brace Jovanovich, New York 1980] [...] 

There is no discontinuity between the thinking processes underlying modern science and the thinking 

represented in the ancient myths. [...] The scientist is a mythopoet who constructs a system of concepts 

for interpreting experience and weaves them into a coherent story. But science adds the discipline of 

prediction, testing, and building upon the results of the others. Science is mythology plus discipline. 

[...] Even physics, the standard of precision for all experimental science, is a mythology created by 

human minds guided by the paradigms of the day. [...] In modern western culture, science has largely 

taken the place of traditional religions [...] Many millennia ago, orally recited myths represented the 

best scientific thought of the time. Today, "objective" science is one of our most widely accepted 

myths. 

The author goes on describing the shock that some students experience when confronted 

with this "truth", and explaining the reason for the "success" of only a few of them. 

Bright students with high scores in mathematical aptitude arrive eager to learn all the wonderful truths 

of science. For the first two years, they really believe it. But in the third year, they study issues in the 

philosophy of science and discover that it is all a myth. It is a myth with high predictive value, and no 

other myth has been found to be more accurate. Yet it is not an Eternal verity, but simply our best 

guess about the universe works. When they come to that realization, many of the students go through a 

profound emotional crisis. Some of them never recover. But the best ones emerge with a deeper 

understanding of science and a better ability to do original research. 

These "skeptical" opinions (which are similar in some sense to those of the well known 

epistemologist Paul K. Feyerabend) are of course in part right, in part wrong, and in part, 

moreover, paradoxical. Yes, even if most of contemporary physics could be well described 

indeed as a work of idealistic "fiction", all the same the aim of any "true" science should 

always be, at the contrary, to try to assemble (as far as it is possible) a rational image of the 

world, which, at least in principle, cannot be but the same for all human beings, since they 

share the same experiences and thought-categories 10 . That is to say, even if a scientist should 

always show himself well aware of the limits of his knowledge, and of its possible 

hypothetical nature, science cannot but reduce the space for arbitrariness of opinions, and a 

"proof" of this is the fact that very often quite independent scientists, coming from all the 

parts of the world, and from absolutely different cultures, elaborate the same kind of scientific 

theories, as this volume shows in some extent. 

The "paradox" arises when one takes note of the existence of a curious factual situation [see 

for instance the paper of Bolognesi about the "big-bang", or the professional experiences 

sketched in Marinov's reprint], namely that, this "liberal" epistemology notwithstanding, 

scientific paradigma are defended by the establishment like dogmas, critical research on the 

"foundations" is discouraged, official journals would not take even in consideration papers 

like most of the ones published here, for instance those which express doubts about relativity, 

under the conviction that this theory is "beyond a shadow of a doubt" 11 , and that only a crank 

would challenge Einstein. Briefly, the paradox is that a self pretended (in words) liberal 

environment, shows itself quite illiberal in the facts! 

It is not difficult to realize how much of this debate is influenced even by politicalsociological 

purposes, since the appreciated value of tolerance would be, in the persuasion of 

many, better favoured by the absence of any "truth", including "scientific" ones. As a matter 

of fact, there are instead effective arguments concerning the possible coexistence of freedom 

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and truth, for instance that there are not too many truths to be afraid of 12 , or that every 

generation has anyway the right, even better the duty, to doubt (this is the Cartesian 

methodological doubt) any opinion received from the previous generation. As Federigo 

Enriques brilliantly says: "For the values of the spirit, as well as for those of economy, a 

degradation law holds: men cannot peacefully enjoy their hereditary possession, but must 

renew and recreate these values, in an effort to understand and to get over them" 13 . 

Carrying on this discussion, we would risk to write down a manifesto of proto-modern 

epistemology, opposed both to modern and post-modern (an example of this is given by the 

quoted Feynman and Sowa), not to say pre-modern!, epistemologies; that is to say, to make 

explicit the general aptitude, and expectations, which inspired the rational work of people like 

Galilei, Descartes, etc., and so we stop here, spending instead a few words in order to make 

understood how the editor (who is a mathematician, and not a physicist!) came to realize the 

unexpected influence of a reductionist materialist philosophy on the "foundations" of 

mathematics and physics, and of the existence of strong (usually overlooked) connections 

between the last two. He used to teach modern formalistic mathematics, telling his students - 

as it is usual under these circumstances - that the highly sophisticated approach they were 

called to follow (since the very foundations), was necessary, due to the "well known" great 

achievements of physical research at the beginning of XXth Century. Most teachers roughly 

satisfy the need of motivations in this way, but the editor decided, at some point of his career, 

to study with more attention the previous statement, in order to be able to persuade better 

(mostly himself!) that the renunciation to intuition, which was demanded by the formalistic 

approach to the "nature" of mathematical objects, was rather justified, and wise - 

notwithstanding his long personal teaching experience, which, quite at the contrary, had 

shown very clearly to him that mathematics could have been taught in a quite simpler way by 

using at the beginning the intuition of ordinary space (euclidean geometry, measuring, real 

numbers) and time (arithmetics, counting, natural numbers, order), instead of abstract 

structures. So he went on studying the physical connection, analysing in some detail the 

famous historical experiments, which led people such as Feynman to claim that "classical" 

explanations were " absolutely impossible". When he started this research he was quite sure 

that he would have found all in perfect order, and that he would have come back to his 

beloved pure mathematics in a very short time: but 20 and more years have elapsed since 

then, and he has found himself more and more sinking into a deep bog, and he was persuaded 

at last that the "magnificence", and the experimental ground, of some theories as relativity, or 

quantum mechanics (in its widespread "irrational" Copenhagen interpretation) was more an 

effect of propaganda, rather than of objective science (namely, a science which is based on 

certain experimental data, and deductions), or of logical "impossibilities". 

This persuasion of the necessity of a new literal re-volution, of the restoration of ordinary 

rationality in Natural Philosophy, appears - we would dare say - a common thread connecting 

the papers collected in this volume, wholly dedicated to criticism and alternative to the pillars 

of XXth Century physics, relativity, relativistic cosmology, etc.. We must admit that we are 

well aware of the fact that some of this criticism could be in its turn criticized, since not 

always the arguments are free of errors, or of misunderstandings. All the same, in our opinion, 

this does not diminish the interest of such attempts for a long overdue renewal of science, 

since we are not in front of mathematics, where a mistake in a line of a proof of a theorem 

usually makes the whole discussion worthless. Matters in physics appear more complex, and 

subtle, and one can take advantage of even "unperfect" papers, which however express good 

ideas 14 . 

We are ending this "foreword" explaining briefly the criteria which inspired the choice of 

the reprints. As Friedwart Winterberg says very keenly, the promising attempts of physics at

the end of XIXth Century, aimed towards a knowledge of the aether's structure, "were brought 

to an abrupt end by Einstein's rejection of the ether and its replacement by his well-known 

postulates" 15 . Both the papers of Almansi and of Moisseiev appeared as a good example of 

this assertion, even if they, especially the second one, were written after the publication, and 

the rather fast acceptance 16 , of Einstein's theory. "Explanation" of gravitation as a possible 

phenomenon of hydrodynamical origin, and the analysis of the resistance to the motion 

through a fluid medium, could have been quite well proposed as studies concerning possible 

properties of "physical space" (pressure, pressure waves, resistance, etc.), supposed either a 

continuous or a powdery (an hypothesis which we personally find more likely) medium. The 

publication of Marinov's "paid advertisement" in Nature, was something due, a tribute to the 

memory of on unforgotten friend, and in most sense a "master". Not all his opinions appear 

acceptable, since he never believed in an "aether", yet he defined himself an "absolutist", a 

situation which led him to statements like: there are no "fields", there is no (finite speed) 

propagation of interaction, there exists energy coming from "nothing", and so on. The same 

applies for the choice of Zapffe's "exodus": a commemoration of a physicist which always 

disputed relativity as a an adequate "model" of physical reality 17 . His magnetospheric theory 

sounds quite attractive, unfortunately one must repeat what has been said in Marinov's case, 

not all his opinions appear acceptable 18 . 

1 - Nature, 1987, 329; Nature, 1988, 333 and 389. 

Notes 

2 - The connection with darwinism is essential in order to understand all the development of Western 

science and culture during the last 150 years. A very interesting virtual book [Adnan Oktar (Harun 

Yahya), The Evolution Deceit] dealing with this matter is freely available at the web page: 

http://www.evolutiondeceit.com/ . Needless to say, this does not mean that everything before was 

quite good, and that were not irrational obstacles interposed against free thought - which is the 

indispensable condition for the progress of any knowledge - but the Darwinistic pessimism and 

aggressiveness had a very bad influence on the field itself of "rationality". 

3 - U. Bartocci and J.P. Wesley eds., Proceedings of the Conference on Foundations of Mathematics 

& Physics in 20th Century: the Renunciation to Intuition, Benjamin Wesley Publ., Blumberg, 

Germany, 1990. 

4 - See for instance the very interesting Lewis Pyenson's book, The Young Einstein - The advent of 

relativity (Adam Hilger Ltd, Bristol and Boston, 1985), in particular Chapter 5: "Physics in the 

shadow of mathematics". 

5 - Ibidem, p. 83. 

6 - QED - The strange theory of light and matter, Princeton University Press, 1985, pp. 9-10. 

Feynman goes over on this opinion at the beginning of his celebrated lectures about Quantum 

Mechanics (The Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965): "We choose to 

examine a phenomen which is impossible, absolutely impossible, to explain in any classical way, and 

which has in it the heart of quantum mechanics. In reality, it contains the only mystery". Of course, 

from an aether-theoretical point of view, all the pretended "impossibilities" are rooted instead on the 

post-relativity disappearance of the concept of aether, as responsible for all quantum phenomena. B.H. 

Lavenda and E. Santamato assert for instance that: "Quantum indeterminism is explainable in terms of 

the random interactions between quantum particles and the underlying medium in which they 

supposedly move" ("The Underlying Brownian Motion of Nonrelativistic Quantum Mechanics", 

Foundations of Physics, Vol. 11, N. 9/10, 1981, p. 654); and elsewhere that: "It might perhaps be 

possible to develop a completely classical formulation of quantum mechanics based upon the irregular 

motion of a single Brownian particle immersed in a suspension of lighter particles" ("Stochastic 

Interpretations of Nonrelativistic Quantum Theory", Int. J. of Th. Physics, Vol. 23, N. 7, 1984). 

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7 - The word "irrational", which could evocatively qualify some contemporary physical theories, is 

introduced just in opposition to "classical physics", namely to physics which makes use only of 

ordinary rationality (that is to say, founded on ordinary space, time, causality), but we must 

explicitely remark that to go beyond this ordinary rationality does not necessarily mean to fall into 

inner contradictions, as some too naif criticism - for instance of relativity - seems to believe. The 

situation is similar to the famous case of non-euclidean geometries. They are logically acceptable 

intellectual constructions, but they do not describe the intuition of ordinary space which is "rooted" in 

man's mind. Exactly as non-euclidean geometries show that there are many possible "models" of space 

which could be thought of, relativity show that it is possible to conceive many abstract mathematical 

models of space-time, and the important question to ask is not whether these counter-intuitive spacetimes 

are "illogical" in themselves (since after all they are mathematical models, and thus they are 

"logical" in the same measure as all mathematics is logical), but if their introduction is really 

necessary in order to describe Nature's laws. 

8 - As it has been called by Franco Selleri, in La causalità impossibile - L'interpretazione realistica 

della fisica dei quanti, Ed. Jaca Book, Milano, 1987, p. 13. 

9 - From the chapter "Science as a Mythology", in John F. Sowa: Conceptual Structures - Information 

Processing in Mind and Machine, Addison Wesley, 1984, pp. 353-356. 

10 - "There can exist but one correct method of viewing any subject or question whatever", see in this 

same Episteme's issue the paper of C.J. Bjerknes dedicated to S. Tolver-Preston. 

11 - From the title of the Chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will, 

Was Einstein right?, Oxford University Press, 1988. No less enthusiastic appears the famous 

mathematician Hermann Weyl (which the author appreciates very much in different contexts), when 

he claims (in Space - Time - Matter, Dover Pub., NY, 1952) that: "Einstein's Theory of Relativity has 

advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us 

from Truth has collapsed" ("Truth" has a capital initial letter in the original English text, but one 

should take into account that in the German original the corresponding term "Wahrheit" had to be 

written with a capital initial by a general rule of that language). Nevertheless, orthodox physicists are 

not so unwise do not acknowledge that any physical theory cannot be a perennial certainty, and that it 

could be shown wrong in certain respects, an approximation of limited validity to reality. For example, 

many physicists would easily accept that the theory of relativity (both special and general) may be 

imprecise when applied in the domain of very small distances, or that it may not be adequate when 

applied to extremely large ones (for instance, of the order of the presumed "size" of the universe). But, 

even if these possible breakdowns would not cause concern, it appears very unlikely that the 

establishment would be willing to recognize that relativity gave a quite misleading image of the 

universe, and that they followed a completely wrong path for more than 100 years. 

12 - We would say, either of a logical-mathematical nature, or of an experimental one, while "general 

theories" do almost always depend on the choice of principles a priori, which as such are obviously 

free. Any discussion acknowledging the different rôles of hypotheses, facts and deductions (or even 

inductions and abductions), should always develop with extreme tolerance, very often establishing not 

one single truth, but just a graph of possibilities, which was the the ideal of Leibniz's calculemus. 

13 - Le matematiche nella storia e nella cultura, Ed. Zanichelli, Bologna, 1936, p. 153. Editor's 

translation, with obvious apologies, here and elsewhere, for the poor English! 

14 - We could add that, in the worst case, some mistakes have the instructive consequence to show 

how a counter-intuitive treatment of physics could lead even educated scholars into intellectual 

bewilderment. 

15 - "The Goal Towards Unified Theory of Elementary Particles and the Ether Hypothesis" (in 

Physical Interpretations of Relativity Theory. Proceedings, London, 1988).

16 - At least from the greatest part of the scientific Western establishment, with some curious 

exceptions, which would not today politically correct to discuss with absolute freedom of opinion and 

expression. 

17 - He was even one of the contributors to the Proceedings of the International Conference "What 

Physics for the Next Century?", Ischia, 1991, Ed. Andromeda, Bologna: "Bradley Aberration and 

Einstein Space-Time", pp. 197-198. 

18 - For instance, as numerous critics of relativity, he falls in the "trap" of the so-called Dingle 

Syllogism, which is unfortunately not so good a weapon against special relativity (it would just 

emphasize that relativity is not completely a "relativistic" theory, since the difference between inertial 

and accelerated motions is an "absolute feature" in Minkowski space-time; see for instance our "Most 

Common Misunderstandings About Special Relativity", at the web page: 

http://www.dipmat.unipg.it/~bartocci/ERRORSVF.htm). 

* * * * * 

The following words, coming from a private communication, seem to be very appropriate to 

put an end to this Introduction. 

Aether as a continuum is the Solution 

Glory to experts in Aether models! While people are wondering how the universe began and 

evolved, The Answer seems to depend upon Aether as the continuum in Fluid Mechanics. 

Hydrodynamics provides an analogy to the physical pictures of simplicity in fundamental 

Nature. In the simplest continuum analogous to vacuum, quantum uncertainty is not yielding 

particles but actually, mini vortices. Vortices are stable, interactive, and able to form particlelike 

patterns. Vortices are actually spinning strings in Superstring Theory. 

The beginning of the Universe is just the quantum fluctuation of Aether or the fabric of space. 

Quantum field is a vacuum continuum. While other physicists are still searching for the 

reality of superstring, aether continuum physicists or fluid mechanics physicists are keen on 

the reality and application of vortices. 

[Wishing a prosperous development and promotion of Aether models], 

Wu Chi Kay - Aether model developer 

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Alternative Physics On Line 

As stated in the previous "Letter to the Readers" which opens this volume, during the second 

half of the last Century (after World War II, and after the worldwide consecration of Albert 

Einstein's "authority"- by the way, due to a doubtful connection between relativity, the famous 

formula E = mc 2 , and the construction of the atomic bomb - as a result of the nuclear 

explosions at Hiroshima and Nagasaki), the publication of papers expressing criticism of or 

alternatives to relativity has almost been banned by "normal" scientific journals (justified by 

the claim that: only a crank would challenge Einstein). This attitude has on the one side 

almost totally discouraged the production of free critical thought, and on the other side has 

crystallized the foundations of established Physics in a system of dogmatic immobility - a 

situation which forced many intellectuals (not only physicists) to understand scientific 

knowledge as a kind of "religion" (a thought system in which beliefs cannot be checked by 

laymen, or not even really "understood" - see for instance, in this same issue of Episteme, 

Marinov's complaints, or Theocharis' contributions). 

Even today, things are continuing in this manner, as far as leading scientific journals are 

concerned, but the increasing diffusion of the Internet has allowed greater freedom of 

expression and communication, and this has supported the acquisition of unconventional news 

and points of view, thus showing that discomfort towards the actual establishment's 

philosophy of Nature and of Science is rather widespread. In this page, we offer some 

interesting examples of this "resistance", which becomes more and more worth of attention, 

the more some investigations could lead to unexpected and very positive practical 

consequences (see for instance Aspden's mention below of an "unseen sea of energy that we 

inhabit in ignorance of its overwhelming power"). 

We are ending this short presentation with an almost obvious consideration: while censorship 

of ideas has become less effective, the web's information content has become so large that 

even a willing reader is at risk of getting lost in a maze of too many inputs, some of which 

must truly be classified in the realm of day dreams, if not of voluntary disinformation... 

[Thanks to Josef Hasslberger, Francisco J. Müller, Delbert Larson, for their valuable support 

and cooperation] 

* * * * * 

"Unconventional" Scientific Journals On Line and General Web Sites 

1) Aetherometry - The Science of the Metrics of the Aether, 

http://www.aetherometry.com/ 

2) Aether Sites, http://www.aethro-kinematics.com/wc_sites.html 

3) Apeiron - Studies in infinite nature, http://redshift.vif.com/ 

4) (Various papers about) Extracting Energy from the Active Vacuum, 

http://jnaudin.free.fr/html/meg.htm 

5) Galilean Electrodynamics, http://www.galileanelectrodynamics.com/

6) Infinite Energy Magazine, http://www.infinite-energy.com 

7) Journal of New Energy, http://www.padrak.com/ine/ 

8) Journal of Theoretics, http://www.journaloftheoretics.com 

9) Astronomy Research - Scientifically viable challenges to mainstream paradigms, 

http://metaresearch.org/ 

Something has gone wrong in the field of astronomy. Many widely held beliefs fly in the face 

of observational evidence. Theories go through such contortions to resolve inconsistencies 

that the ideas can no longer be explained in simple language. Alternative ideas are often 

rejected out of hand simply because they challenge the status quo. The result... many of 

today's theories are unnecessarily complex. Meta Research is dedicated to bringing some 

common sense back to this field. Here we challenge ideas that have consistently failed to 

make successful predictions, examine new paradigms, and advocate the ideas found to be 

most worthy of further consideration and testing. [...] 

10) Modern Scientific Theories of the ancient Aether, 

http://www.magna.com.au/~prfbrown/aetherqr.htm 

11) Natural Philosophy Alliance, http://mywebpages.comcast.net/deneb 

The Natural Philosophy Alliance (NPA) is devoted mainly to broad-ranging, fully openminded 

criticism, at the most fundamental levels, of the often irrational and unrealistic 

doctrines of modern physics and cosmology; and to the ultimate replacement of these 

doctrines by much sounder ideas developed with full respect for evidence, logic, and 

objectivity. Such reforms have long been urgently needed; and yet there is no area of 

scholarship more stubbornly censorial, and more reluctant to reform itself. 

Reigning paradigms in physics and cosmology have for many decades been protected from 

open challenge by extreme intolerance, excluding debate about the most crucial problems 

from major journals and meetings. But the founding of the NPA in 1994 provided those 

struggling against this irrationality and intolerance with the strength, visibility, and credibility 

that comes from numbers and from collaborative, purposeful effort. It has also enabled them 

to share, expand, and refine their individual knowledge through contact with many other 

critical scholars, at NPA general meetings--held at least once per year since 1994--and by 

phone and mail, both postal and electronic. [...] 

12) Sapere Aude, http://www.btinternet.com/~sapere.aude/ 

(from Dec. 2002: http://www.dipmat.unipg.it/~bartocci/fis/sapere_aude.html) 

Reclaiming the common sense foundations of knowledge 

The site seeks to further the debate about the foundations of knowledge by facilitating access 

to the arguments of critics of orthodoxy. Because of the perennially central role the natural 

sciences, critical arguments focus on the presuppositions, concepts and methods of modern 

physics, and especially on the cognitive revolution associated with special relativity ("antirelativity"). 

13) The Subspace Project, http://www.martinelli.org/ 

Why an Aether? Its almost a commonly known fact that the aether was disproven by an 

experiment done almost one hundred years ago, by a couple of physicists whom we know as 

Michelson and Morely (see "Is the Speed of Light Constant" ). Given that, An obvious 

question might be then, "why should we re-visit this idea?". There are a few reasons why we 

should. The first point I should make is that the aether theory that was disproven by the 

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Michelson and Moreley experiment was that conceived by 19th century physicists. This only 

means the first aether conception was wrong, not that there is no aether. 

Furthermore, new scientific research is a process of "turning over stones". We are simply not 

smart enough to know which 'stones to turn' or what we will find underneath. Sometimes we 

can find things of interest , most times not -- but, sometimes you get "spin-offs". 

When it comes to basic research it is unfortunately hard to guess at any kind of a return on 

investment. The Michelson and Morley experiment is one example of an unexpected ROI. 

They were doing basic research - just doing the sweeping - after all the great discoveries had 

finally been made. They were measuring the drift velocity of the earth through the aether. 

Every physicist expected that the Michelson and Morley experiment (because of the 

extremely precise Michelson Interferometer) would give some number for the earth's drift 

velocity through the aether. This number was the expected ROI. Instead they found no drift 

velocity whatsoever. In fact, if we were to use their results to calculate the velocity of the 

earth with respect to the aether we would have to say that the earth is at absolute rest - not 

even orbiting the sun!. This was far more interesting and valuable than the expected ROI. 

They found 'gold' - a new principle - a new physical law. … "the speed of light is constant for 

all frames." With this new law, physics took a very unexpected turn. This find was one of the 

key ingredients to today's modern physics. It gave Einstein the foundation upon which all of 

his work was built. And this gives us another observation… As the turn of the century was 

approaching, physicists believed that physics was nearly done. This turned out to be wrong - 

way wrong. This is a pattern in science history. In fact, it is not too far off to state this as a 

principle, that "established science is often wrong". [...] 

Are There Aether Atoms? Yes, but they are not what you might expect. [...] 

14) Sur la piste de l'Energie Libre, http://quanthomme.free.fr/CHERCHEURS1.htm 

15) 21 st Century Science & Technology, http://www.21stcenturysciencetech.com 

Some Interesting Papers On Line 

1) http://www.energyscience.co.uk/index.html 

Aether Science Papers 

by: Harold Aspden 

This is not a commercial website. It is an educational site operated on a non-profit basis by 

Energy Science Ltd. under the direction of Dr. Harold Aspden, who in his retirement years 

provides the financial support needed to sustain this venture. Dr. Aspden acknowledges his 

gratitude to the Internet facility for providing the means to tell the world about his lifelong 

exploration of the unseen sea of energy that we inhabit in ignorance of its overwhelming 

power. 

The book Aether Science Papers was published in 1996. [...] The 14 papers, reproduced in A4 

format from the scientific periodicals in which they were first published, constitute the main 

section of the book. The front section of the book is a 68 page commentary entitled The 

Creative Vacuum. In view of the importance of making scientists aware of this work, it has 

been decided to publish the opening 68 pages here in these Web pages. 

About the Title: The 'aether' is a word which says that there is no such thing as empty space. 

To say there is no aether is therefore to assert that space can be truly empty, meaning it 

contains nothing of an electrical character, it now being a well established fact that there is 

nothing having a physical existence that lacks electrical properties. If a scientist expresses 

doubt by reference to the 'neutron', I say that the neutron has magnetic properties which are 

seated in the motion of electric charge. Otherwise, you need to explain why it has a magnetic

moment. If that scientist then mentions the 'neutrino', then I say that the 'neutrino' was only a 

notion, a figment of imagination invented as a devious way of declaring that the aether could 

absorb or shed energy and momentum without admitting that the aether exists. If that scientist 

says that the consensus opinion of professors of physics who deny the reality of the aether can 

surely not be discarded, then I ask "Why not?" and can but point to a report on page 12, 6 

May 1996 issue, of The Times newspaper in U.K. Science correspondent Nigel Hawkes wrote 

under a heading 'The possibility of getting something for nothing': "A physicist at Cambridge 

University has produced a new and daring explanation for an old puzzle. If she is right, it 

could be the first convincing evidence that it is possible to get something from nothing. The 

question Claudia Eberlein addresses in a forthcoming issue of Physical Review Letters is that 

of sonoluminescence. If you expose water to a blast of ultrasound, you get a flash of light. 

This is deeply puzzling, because visible light has so much more energy than sound that the 

energy of the sound has somehow to be boosted by a trillionfold. The wavelength of the light 

emitted implies that the source is at a temperature of tens of thousands of degrees C. Ms 

Eberlein suggests that the emission of light is a quantum vacuum effect - energy given off by 

the vacuum. Quantum theory says that there is in reality no such thing as a vacuum and that 

empty space teems with 'virtual particles' including photons which flit in and out of existence. 

The theory is open to test. If it turns out to be right, her explanation will be a major coup, the 

first observable manifestation of quantum vacuum radiaton." 

The energetic vacuum is, therefore, a live issue. The 'aether' is a reality and I believe that it 

can, like a fluid crystal, form structure and dissolve that structure, as it latches onto material 

substance, but if that substance vibrates excessively then even the aether is confounded and, 

in its confusion, it sheds energy! I have, accordingly, chosen the title Aether Science Papers 

with deliberation, knowing that, in the end, the 'aether', per se, will have to be recognized, 

even though that will confound the non-believers who constitute the modern generation of 

physicists. 

2) http://mujweb.cz/veda/babiakjoz/MMX%20New%20view.htm 

Michelson-Morley's Experiment - A New View 

by: Jozef Babiak 

Michelson-Morley's experiment carried out in 1887 should determine absolute velocity of the 

Earth around the Sun in the hypothetical "aether". Negative results of this experiment, why 

the shift of the interference fringes does not appear when rotating the interferometer in the 

angle of 900, explained in 1892 Fitzgerald and independently of him Lorentz with the 

contraction hypothesis. Einstein in 1905 built his Special Theory of Relativity on validity of 

the contraction hypothesis and on the principle of constant velocity of light in vacuum. [...] 

The calculation of the shift of the interference fringes that should appear by absolute velocity 

of the Earth around the Sun, is in literature given as follows: [...] This calculation of the shift 

of the interference fringes in the Michelson - Morley's experiment is incorrect, because it is 

calculated according to the laws of the classic Newton's mechanics - using Galileo's 

transformations. Michelson - Morley's experiment is a physical experiment with light, 

therefore calculation of the shift of the interference fringes should be calculated according to 

the optics' laws. Light in its nature (photons, electromagnetic oscillation) and with its way of 

propagating in the solid environment (Snell's law, Huygens' principle) differentiates with its 

characteristics from solid bodies to that are valid the laws of the Newton's mechanics. Light - 

photons - are atom particles which by interactions with atoms of the solid environment create 

the optics' laws, therefore we can not describe the propagation of the light in the solid 

environment using the laws of the classic Newton's mechanics. Snell's law defines the 

velocity of light beams in the solid environment as c / na , where na is refractive index of light 

in the solid environment. In the calculation of the shift of the interference fringes is the 

velocity of light beams in the interferometer arms stated incorrectly as c, which is the velocity 

of light in vacuum. In the Michelson-Morley's experiment there is no vacuum in the 

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20 

interferometer arms. I present here an argument, that is often presented, that the velocity of 

light in the air is just a few less than in vacuum and has no significant meaning for this 

experiment. The velocity of light beams in the air in the Earth's atmosphere is less by c - c / na 

= 79 km/s than the velocity of light in vacuum c. Michelson's inteferometer can measure he 

change of the velocity of light from the shift of the inteference fringes with the accuracy 1 m/s 

on the length of one meter. Therefore is unavoidable to state the precise value of the velocity 

of light in the arms of the Michelson's interferometer. Huygens' principle of propagation of 

the light in the solid environment defines, that every point to which the oscillation comes, 

becomes the source of the elementary oscillation. Huygens' principle avoids adding the 

velocity of light beams with the velocity of light, because the source of the light oscillation 

becomes each point of the solid environment which the oscillation reaches. Sound is 

propagated in the solid environment using the same principle. Pressure wave - sound is 

propagated in the solid environment progressively from point to point with the velocity given 

by the parameters of the solid environment. We can observe this phenomenon very well and 

graphically on the flying plane. The velocity of the sound coming from the flying plane is not 

added to the velocity of the plane, the sound is propagated from the flying plane in the air 

with the velocity given by the air parameters. The velocity of the movement of the sound 

source has no influence to the velocity of the sound. Only the sound frequency is changing, 

according to the Doppler's principle. Michelson-Morley's experiment has been measured in 

the air, therefore the light beams in both interferometer arms were moving in the air. The air 

in both interferometer arms is at rest with respect to the interferometer, therefore the velocity 

of the light beams with the respect to the interferometer is in both arms c / na . [...] 

3) http://www.paradox-paradigm.com/ 

From Paradox to Paradigm 

by: Johan Bakker 

Foreword: Quantum mechanics and the Relativity Theory are incompatible. Somewhere 

something must be wrong. In 1727 Bradley observed the star y-Draconis and measured the 

stellar aberration. Science concluded unjustly from these measurements that the influential 

ether could not exist. Michelson and Morley proved without doubt, with their famous 

experiment in 1887, that absolute ether could not exist. 

After both ethers were denied the Special Relativity Theory of Einstein was inevitable. The 

propagation of forces and light through vacuum became mysterious and almost 

unexplainable; time and space became relative. 

In the 20th century quantum mechanics developed and gained momentum through the rapid 

development of computer science, mathematics and technological development. The 

mathematical solutions are staggering, though even the greatest scientists admit they do not 

comprehend the physical implications of quantum mechanics totally. In atomic and subatomic 

physics math has taken over. The flaw of quantum mechanics is the lack of physical 

understanding; it's become an empirical science. 

When we consider that science unjustly rejected the hypothesis of the influential ether, in 

theory the possibility of this alternative still exists. Exploring the possibilities of the 

influential ether, it was "easy" to find mathematical and physical explanations for relativistic 

observations and the Lorentz factor. The scientific explanations the ether gives for 

unexplained and mysterious physical phenomena are vast. 

Elementary and atomic particles like electron, positron, proton, neutron, deuteron, photon and 

neutrinos reveal their existence in simple non-relativistic mathematics. The physical 

background of quantum mechanics becomes clear. The dual character of particles and 

uncertainty principle of quantum mechanics coincides with the ether. Nuclear fusion is better 

understood. Even the cause for gravity emerges.

Theoretical physicists are not able to disprove the ether theory. They however, 

understandable, reject the possibility of ether because it differs too much with the present 

scientific perception; their opinion is pre-determined. [...] 

Summary: The concrete indications science should look in depth at the possibilities of the 

ether theory are: 

- In the 19th and 20th century science did not give enough attention to the possibility of the 

influential ether after this medium was denied prematurely. The influential ether describes the 

stellar aberration perfectly and therefore science should admit the ether theory is a possible 

alternative theory. 

- The drag coefficient of Fresnel was confirmed by the experiment of Fizeau. This 

confirmation had no scientific meaning at all, because the drag coefficient was introduced ad 

hoc without a valid physical explanation. It was already certain a "drag factor" would be 

measured after Arago's observations. The perfect match of the experiment of Fizeau with the 

assumption of ether is a different case and should puzzle scientists. 

- The ether theory, described in a simple basic manner in the previous chapters, give all the 

explanations you need to explain relativistic observations. 

- The inert qualities of the ether gives an explanation for the observed, yet unexplained, 

synchrotron radiation. 

Often one hears scientists declare the more simple a theory is the more valid it becomes. The 

ether theory, with only two forms of energy and related forces, is extremely simple and 

explains a lot. Why do scientists reject the ether theory without validated arguments? The 

comfort the ether theory explains the revelation of stable particles from ether should mean 

something to scientists and produce wondering. The, in a simple way, derived radius of the 

neutron combined with the basic equation of the energy of an oscillation eliminates the 

constant of Planck and derives a simple classical non relativistic presentation of the 

mysterious photon. What is the chance this can happen if it is pure coincidence? The strong 

magnetic force, the electrostatic force and the electromagnetic oscillation energy in the 

deuteron, the aligned proton and neutron, gives a basic explanation for the quantum mechanic 

properties of atomic nuclei and particles. The speculative, but yet simple and consistent, 

explanation of gravity emerging from atomic nuclei in matter opens the possibility the ether 

theory becomes "the theory of everything" when science gives it proper attention. 

Measurements on magnetic currents with directed magnetic spin indicate that there might be a 

relation between mass and magnetic energy that exceeds the relation E=Mc 2 . 

These are the arguments I found pro "ether", by assuming there might be ether after all. The 

described ether can explain many othernot mentioned phenomena. For example it is not hard 

to see that it is impossible for a proton to merge with an electron when conditions are not 

extreme dense. The properties of the mysterious neutrino become clear etc. 

Also in favor for the ether theory are contradictions like: 

- The Relativity Theory and quantum mechanics contradict each other. There must be 

something wrong somewhere! 

- The American spacecraft's, the Pioneer 10 and 11 moves through space with a different 

direction than calculated with the Relativity Theory. The differences are small but undeniable 

and unexplained. 

- In astronomy calculations bare large uncertainties. The estimations of the age of the universe 

are between 7 and 20 billion years. Factors of importance in astronomy are speed, distance, 

mass and time. All the astronomic measurements need relativistic corrections, which 

corrections will differ slightly when ether is assumed. Possible the accuracy of these 

calculations increases when astronomic data is corrected, according to ether, in a slightly 

different way? 

- And "last but not least" there are the paradoxes the Relativity Theory and quantum 

mechanics imply. If there is no other explanation, the paradoxes have to be real, but without 

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having to explain the paradoxes, the outcome of science is much clearer and therefore much 

more preferable. 

When I started to write "From Paradox to Paradigm" I just knew in what direction I had to 

look. I was not satisfied with the perception of science of the world we do not experience. 

Science does not yet have all the answers. When you look what science achieved the last 

century you have to be impressed. The information technology and mathematics opened a 

world that was fast explored. Scientists eager to explore the unknown had found the code to 

decrypt the inexplicable. It had to be the truth what they discovered because the math matched 

the experience so well and suddenly what we experienced was no longer valid. Scientists use 

the validated argument that what we see is not necessary correct. But they misuse a similar 

argument when they say that math describes the data and therefore must be true. They forget 

that math is only a tool to describe the events observed and therefore only describes the 

mathematical solution of that part of reality. Quantum mechanics describe the experienced 

atomic and subatomic world very well. The achievement of science in this area is enormous. 

One has to be impressed, but science is also the achievement of men and therefore there is a 

change it overestimates itself: science itself can become arrogant. Science should be aware of 

its limitations. Quantum mechanics describe the behavior of (sub) atomic physics very well, 

this however does not mean that quantum mechanics are the answer to the whole truth. It is 

not, nothing is. It describes only a part, the observed in a mathematical way, and can therefore 

not be absolute. Quantum mechanics are even more limited in its revelations when derived 

relations are extrapolated. The value of extrapolated mathematical solutions is seriously 

limited by the fact that one does not know what the math describes exactly. It is a 

mathematical solution for a limited outcome of part of the process. Quantum mechanics 

describe the mathematical relation between observed data. These mathematical solutions do 

not explain the physical process that takes place. Quantum mechanics has no validation to 

pretend to describe the physical processes completely. 

It would be arrogant to state that the ether is a better way to understand physics, but it is not 

when you state that it might be. As long as science denies the possibilities of the ether without 

valid arguments science is arrogant. In theoretical physics there are many contradictions that 

cannot be resolved, and therefore set aside. The possibilities of the ether theory to combine 

the uncertainty principle and duality of quantum mechanics and the deterministic aspects of 

classical physics are vast. 

The main reason to write "From Paradox to Paradigm" is not be "right" or "wrong". If science 

took a path that is not completely correct, the perception quantum mechanics provides may 

not be totally valid. The consequence will be that we are not able to foresee that some 

interpretations are not entirely correct. We cannot adjust, because the only hold we have is the 

math and math only describes the direct relation of the data in a mathematical way. The ether 

described in this book gives strong indications that nuclear fusion will not be achieved, in an 

economic profitable way, by means of thermal nuclear fusion. The approach according to the 

ether should be totally different. 

When atomic nucleus are captured and guided by strong magnetic fields the uncertainty 

principle can be contained and Controlled Cold Nuclear Fusion (CCNF) becomes 

theoretically possible. No one denies the necessity of abundant and clean nuclear fusion 

energy for our modern society. The high costs, pollution, global warming and limited reserves 

of natural energy resources will become disastrous in due time. And yet science denies society 

to explore this possibility by not taking the ether seriously. 

[The book is accessible and can be printed, free of charge, at the web site above] 

4) http://www.einsteinontrial.com/ 

Einstein on Trial, Or Metaphysical Principles of Natural Philosophy - A collection of 

essays written over a period of a quarter of a century

y: Jorge Céspedes-Curé. 

In 1905, Einstein set the scientific community on an innovative and, at the time, controversial 

course abandoning the Newtonian concept of space and time and upholding the Maxwell- 

Lorentz electrodynamics. Was this a leap forward or has the 20th century followed a 

misleading course? In a thoroughly readable and exhaustively philosophical analysis, backed 

by rigorous mathematical arguments, Jorge C. Curé places Einstein's conceptions on historic 

scrutiny. By unifying the Newtonian and classical relativistic conceptions of nature, he 

establishes a New Physics. A fitting revolution for the new millennium. 

In Chapter 1, the author examines the philosophical knowledge Einstein had about the 

ontological and epistemological foundations of physics. He finds, in this respect, that Einstein 

was one of the few creators of 20th century physics who knew precisely what he was doing in 

the philosophical foundations of physics. In Chapter 2, Curé deduces a generalized Hamilton- 

Jacobi equation (HJ) from Newton's axiom of motion. This generalized HJ equation contains 

an extra term, which Curé calls the "quantum collective potential" (QCP). Curé goes on to 

show the ontological origin of the QCP based on a philosophical consideration when applying 

Newton's axiom of motion. He then shows that Schrödinger's equation is a particular case of 

the generalized HJ equation. In this chapter, Einstein is found not guilty, at all, in accusing 

quantum mechanics for being an incomplete theory. In Chapter 3, a vast collection of 

Electrokinetics (EK) and Electrodynamics (ED), which were scattered in the history of 

physics of the 19th and 20th centuries, are examined. They are classified and also translated to 

a modern vector notation. In Chapter 4, Newton's three principles are extended from three to 

five. Curé accepts Einstein's challenge to deduce "formally and logically" a Newtonian 

Gravitodynamics and Electrodynamics. Then he shows theoretically and experimentally the 

existence of a new ED field proportional to the square of the electric current. He also presents 

the revival of Eddington's model of the neutron as a miniature hydrogen atom. In Chapter 5, 

Curé re-examines the cosmic ether concept, discovering how Einstein himself resuscitated the 

concept in 1920. The author explains the light deflection of remote stars by the solar energy 

field, using the classical phenomenon of refraction. Curé's calculations show a much better 

agreement with Merat's empirical law of solar light deflection, than Einstein's calculations. In 

Chapter 6, Curé demonstrates that Newton provided, in his Principia of 1687, an original 

explanation about the perihelic rotation of planet Mercury. Curé defends General Relativity 

Theory (GRT), in the event that the sun is oblate. Curé uses the measured starlight deflection 

by the energy field of the sun to determine the stellar density of energy. At the end of this 

chapter, the author speculates on an alternative explanation of the starlight redshift. This work 

has profound implications on the Big Bang theory and modern cosmology. In the last Chapter 

7, Curé begins with the analyses of four essays written by Einstein, between 1930 and 1948, 

about "Science and Religion." The author points out that Einstein, through the four essays, 

foresaw the advent of a future scientific theology. Einstein believed that through a "cosmic 

religious experience" man could acquire transrational knowledge by a transcendental 

reconnection with the Supreme Intelligence. In the rest of this chapter, Curé pursues, to its 

finality, the consequences of these initial theological intuitions of Einstein. In this way, Curé 

establishes the foundations of "Cosmotheism" or Scientific Theology. 

5) http://ourworld.compuserve.com/homepages/jlnaudin/html/elecmtr.htm 

Electrogravitics - Experiment With A Motor 

By: Patrick Cornille 

6) http://www.orgonelab.org/miller.htm 

Dayton Miller's Ether-Drift Experiments: A Fresh Look 

by: James DeMeo 

The history of science records the 1887 ether-drift experiment of Albert Michelson and 

Edward Morley as a pivotal turning point, where the energetic ether of space was discarded 

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by mainstream physics. Thereafter, the postulate of "empty space" was embraced, along with 

related concepts which demanded constancy in light-speed, such as Albert Einstein's relativity 

theory. The now famous Michelson-Morley experiment is widely cited, in nearly every 

physics textbook, for its claimed "null" or "negative" results. Less known, however, is the far 

more significant and detailed work of Dayton Miller. 

Dayton Miller's 1933 paper in Reviews of Modern Physics details the positive results from 

over 20 years of experimental research into the question of ether-drift, and remains the most 

definitive body of work on the subject of light-beam interferometry. Other positive etherdetection 

experiments have been undertaken, such as the work of Sagnac (1913) and 

Michelson and Gale (1925), documenting the existence in light-speed variations (c+v > c-v), 

but these were not adequately constructed for detection of a larger cosmological ether-drift, of 

the Earth and Solar System moving through the background of space. Dayton Miller's work 

on ether-drift was so constructed, however, and yielded consistently positive results. 

Miller's work, which ran from 1906 through the mid-1930s, most strongly supports the idea of 

an ether-drift, of the Earth moving through a cosmological medium, with calculations made of 

the actual direction and magnitude of drift. By 1933, Miller concluded that the Earth was 

drifting at a speed of 208 km/sec. towards an apex in the Southern Celestial Hemisphere, 

towards Dorado, the swordfish, right ascension 4 hrs 54 min., declination of -70° 33', in the 

middle of the Great Magellanic Cloud and 7° from the southern pole of the ecliptic. (Miller 

1933, p.234) This is based upon a measured displacement of around 10 km/sec. at the 

interferometer, and assuming the Earth was pushing through a stationary, but Earth-entrained 

ether in that particular direction, which lowered the velocity of the ether from around 200 to 

10 km/sec. at the Earth's surface. Today, however, Miller's work is hardly known or 

mentioned, as is the case with nearly all the experiments which produced positive results for 

an ether in space. Modern physics today points instead to the much earlier and less significant 

1887 work of Michelson-Morley, as having "proved the ether did not exist". [...] 

http://www.orgonelab.org/ 

7) http://www.norbertfeist.de/english.htm#Absatz4 

Ether Theory or Relativity Theory? 

by: Norbert Feist 

The missing aberration of terrestrial sources, a new analysis of the Michelson Experiment and 

analogous acoustic experiments with the result of a new identical propagation equation for 

light and sound call the premises of relativity theory into question. They speak for the 

existence of a luminiferous ether as absolute frame of reference and propagation medium for 

electromagnetic waves. 

8) http://rosarioclub.com/ciencia.htm 

La Aventura del Razonamiento - Ciencia & Descubrimiento 

by: Ricardo Gómez Kenny 

La comunidad cientifica, si bien evoluciona, es cerrada, ciega y sorda. El inesperado 

descubrimiento, anunciado por un argentino hace ya varios años, hoy deja sin respuesta a los 

matemàticos. Entre las opiniones que han podido recibirse - todas con alguna excusa - se 

puede leer "entre lìneas" , algo asì como...".!Ah, yo no fuì! Dirìjase a fulano." Si el error 

puntualizado llama la atenciòn, (por lo simple y razonable), la causa de todo sorprende mucho 

màs aùn. Los equipos de cientìficos, oficialmente reconocidos y que dicen "estar a favor de la 

acciòn interdiciplinaria", nunca quisieron tomar en cuenta la opiniòn racional de los grupos 

llamados comunmente "proyectistas". En sìntesis: Segùn este investigador ... todos los dibujos 

que representan experiencias en los libros de fisica, (En el tema Relatividad), estan mal 

confeccionados. No responden a las reglas preestablecidas para objetos en movimiento. 

Obviamente, la crìtica no se refiere a errores propios del dibujante sino de aquèl que concibiò

dicha forma de representaciòn.¿Tienen validez los razonamientos que le siguen? Podrìamos 

resumir toda esta situaciòn en esta frase: "Un arquitecto moviò la estanterìa. Los matemàticos, 

desconcertados, se reùsan a debatir". [...] 

9) http://www.hasslberger.com/ 

Vortex - The Natural Movement - Considerations on Light, Matter, Gravity And 

Magnetism 

by: Josef Hasslberger 

Physics, the science which should be explaining to us how the universe came about and what 

it consists of, seems to have arrived at the end of a blind alley. Its descriptions of the origin 

and the workings of our universe get more and more complex, less and less agreed-upon and 

they are definitely not going to accompany us into the 21st century. We are at the beginning 

of the space-age. In order to survive in that new age, we need clear and unequivocal 

descriptions of physical phenomena. [...] The trouble is not where physicists commonly look. 

It seems to be more a question of philosophical or religious outlook. Our view of nature was 

conditioned first by the great philosophers of ancient Greece and then, for a long time, by the 

orthodox religions prevalent in current western civilization. Ironically, the physicist who 

denies the action of a creator, just by this very denial limits the scope of his investigations. He 

has become "inversely religious", which to an independent scientific investigation is no less 

limiting than the stand of the dogmatic religionist. So it might be that progress in our time has 

become dependent again on philosophy, on that science of thinking, of looking at basics and 

drawing conclusions that is unencumbered by the specialization so prevalent in the physical 

sciences. The following is a speculative description, in simple terms, of the basic workings of 

the universe. [...] 

10) http://www.dipmat.unipg.it/~bartocci/H&KPaper.htm 

Hafele & Keating Tests; Did They Prove Anything? 

by: A.G. Kelly 

Abstract: The original test results were not published by Hafele & Keating, in their famous 

1972 paper; they published figures that were radically different from the actual test results 

which are here published for the first time. An analysis of the real data shows that no credence 

can be given to the conclusions of Hafele & Keating. 

... A leader in Nature in 1972 [11] said that "the agreement between theory and experiment 

was most satisfactory". ... The Hafele 1971 report said "Most people (myself included) would 

be reluctant to agree that the time gained by any one of these clocks is indicative of anything" 

and "the difference between theory and measurement is disturbing" ... 

11) http://personales.ya.com/carlosla/model/ 

EVE, a model of the aether 

by: Carlos Laborde 

Introduction: The main purpose of this work is to define a model of aether within a given 

description scheme. The description scheme used is considered a matter of free election. This 

election must only be judged "a posteriori" by its power to organize in an economic and 

simple way as much knowledge of the physical world as possible. The description scheme is 

the following classical one: 

- The space/geometry chosen for the description is the Euclidean with three dimensions. 

- The time concept chosen for the description is the Absolute Time. 

Such Space and Time are well defined mathematical concepts that behave according to the 

postulates. This does not necessarily imply that, in the absence of known external forces, 

every material mechanism used in some local context as a clock and that every, so called, 

rigid bar should always behave classically (i.e. remain constant when compared with 

standards). It must be considered satisfactory enough if the experimental behaviour of such 

25

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clocks and rigid rods can be described in a consistent way within the description scheme 

chosen, invoking perhaps some new phenomena. Clocks are used to measure time, not Time, 

and rigid rods are used to measure space, not Space, (in a similar way that gas pressures, 

electric currents, etc, are measured by the corresponding instruments). The Time and Space 

are theoretical bricks of the description that are not measured in the physical world but 

defined in the model world. 

It is considered that the goal of adjusting the physical laws to a classic descriptive scheme 

should not be abandoned since it promises more advantages than the relativistic point of view 

which adjusts the description scheme to some crude experimental observations. First, when 

seeking a global description of the positions and movements of the celestial bodies, the use of 

General Relativity seems condemned to lead to circular arguments due to the fact that the 

metric used in the description is itself altered by the gravitation fields of the bodies that aim to 

be installed in that metric. Second, if succeeding instead to describe the Universe with a 3-D 

Euclidean metric together with an absolute Time, the models so constructed are easily 

understood by our minds (used to treat with these kinds of relations in our everyday life). In 

this case, intuition becomes a powerful tool to suggest new inferences. 

The descriptive point of view defended in this work is the same adopted by the majority of 

physicists before the arrival of Relativity. It is not ignored that the theory of Relativity 

became a safety raft when the efforts made at the beginning of the 20th century failed to 

explain the new experimental facts within the classical description frame. This work may be 

considered just a call to make one more effort in the old line impelled by two new facts: First, 

our knowledge of physical phenomena is now greater (quantum mechanics, vacuum 

fluctuations, existence of a preferred reference frame associated with the dipolar anisotropy of 

cosmic microwave radiation...). Second, today's official description of Physics seems again 

unsatisfactory to an increasing number of physicists. 

Abstract: A very simple aether is postulated. This aether is represented by an ensemble of 

moving point entities (aetherinos) that pervade all space. The aetherinos are not material 

particles. They have no intrinsic material properties (mass, charge, magnetic moment, spin...) 

but are responsible for the appearance of these properties in matter, which is postulated to be 

an ensemble of entities of another kind (Simple Particles). In principle this aether is fully 

described by its aetherino's velocity distribution (which can change in space and in time) and 

by an hypothesis about the effects of the collisions of the aetherinos with matter. (The 

aetherinos do not collide with themselves). 

No attempt is made in this work to deduce the exact local distribution consistent with the 

experimental facts. With the help of a plausible example distribution and a very simplistic 

model of matter it is "shown" nevertheless that many fundamental laws of physics can be 

"explained" instead of just stated. [...] 

Light is considered a space - time modulation in the aetherino's velocity distribution. The 

"spread out" space - time propagation of the disturbance resembles more the idea of light as a 

wave than that of light as a particle (photon). The corpuscular properties of light should then 

be ascribed only to its emission and absorption by matter and explained by its cooperative / 

destructive interaction with the wave-type disturbance. [...] 

12) http://www.dipmat.unipg.it/~bartocci/larson.htm 

A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical 

Aether 

by: Delbert J. Larson 

Abstract: Maxwell's equations are derived from a postulated, mechanical, two-component 

aether. 

[Two more papers by the same author at http://www.dipmat.unipg.it/~bartocci/listafis.htm, 

point N. 20]

13) http://www.geocities.com/hlindner1/Writings/Space/Physics.htm 

Flowing Space 

by: Henry H. Lindner 

Abstract: A simple theory of Cosmic space and motion explains the experimental results, 

unifies our understanding of the effects of motion and of gravity, produces no paradoxes, and 

makes more predictions than Relativity. 

Key words: absolute space, atomic clocks, black holes, entrainment, gravity, inertia, light, 

mass, motion, paradoxes, principle of equivalence, Relativity, space, time. 

http://www.geocities.com/Athens/Atrium/8041/ 

14) http://www.scientificexploration.org/jse/articles/mccausland/toc.html 

Anomalies in the History of Relativity 

by: Ian McCausland 

Abstract: In November 1919 it was announced to the world that observations of a solar 

eclipse that occurred in May 1919 supported Albert Einstein's general theory of relativity. 

That announcement was one of the most influential events of 20th-century science, since 

Einstein's instant rise to enormous fame arose directly from it. In spite of the confidence with 

which the announcement was made, however, it was later realized that the accuracy of the 

observations was insufficient to constitute a reliable confirmation of the phenomenon that was 

predicted. Furthermore, another of the formulas published in the general theory, for the 

variation in the perihelion of the planet Mercury, had already been derived by another 

scientist several years earlier using another method. In spite of the fact that the experimental 

evidence for relativity seems to have been very flimsy in 1919, Einstein's enormous fame has 

remained intact and his theory has ever since been held to be one of the highest achievements 

of human thought. The resulting deification of Einstein has had some unfortunate effects: 

critics of his theory are often dismissed as cranks, and the search for better theories has been 

inhibited. It is suggested that the announcement of the eclipse observations in 1919 was not a 

triumph of science as it is often portrayed, but rather an obstacle to objective consideration of 

alternatives. 

Abstract (first page of article) - Introduction - The General Theory of Relativity - The Eclipse 

Expeditions & their Observations - Announcement of the Eclipse Results - The Perihelion of 

Mercury - The Special Theory of Relativity - Discussion - Acknowledgement - References 

15) http://www.aetherpress.com/ 

Aether and Gyrons 

by: Frank Meno 

Present physical theories are based on numerous postulates for such things as forces, 

momenta, energy, mass, charge, etc., which are not defined in terms of comprehensible 

concepts. For example, a force that causes attraction through empty space is clearly 

impossible to comprehend. Although one can obtain some useful results by manipulating 

mathematical expressions based on such postulates, this approach has neither yielded progress 

in philosophy, nor has it enabled further progress in practice. Common sense tells us that, to 

investigate something effectively, we should know what we are dealing with. As I describe in 

my book [Cats, Atoms, Gyrons, Aether, and the Universe], the ancient Greeks have delineated 

the basic questions, but they failed to develop the required mathematics, and have not 

performed the necessary experiments to verify their hypotheses before their civilization 

collapsed. Nevertheless, the Greek philosophers came to the correct conclusion that there 

exists a fundamental substance which must be atomistic. This means that the ultimate 

constituent parts of this substance must not be further divisible. Furthermore, since the 

observed physical reality is changing, these fundamental entities, which they called atomos, 

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must be in perpetual motion. The issue that was not effectively resolved regards the shape and 

size of these 'atoms' (gyrons). [...] 

Aether Gyron 

Each gyron moves in a straight line while at the same time rotating around its center. These 

gyrons, colliding with each other, comprise the gas called aether. Gyrons are very small on 

our scale, their length probably corresponds to the Planck length, which is 1.6 x10^-35 m. In 

comparison, the diameter of a proton is 1.5 x10^-15 m. The gyrons are spread throughout the 

universe, and the majority of them are undergoing random collisions with each other. In this 

condition they are comprising what we call the vacuum. Thus, vacuum is not empty, it 

contains the random moving gyrons whose motion represents the potential energy. The 

average gyron speed corresponds to the speed of light, while some of them move slower, and 

some faster. 

Like in material substances, if the equilibrium condition is disturbed, waves can propagate in 

the aether. The most commonly observed aether waves are called electromagnetic waves, to 

which belongs light. In these waves the gyrons move as a group in a non-random spiral 

pattern which is called a photon. The intensity of light depends on the number of photons 

moving together. If the spiral trajectories of the participating photons move in unison, then the 

light is termed coherent. Coherent light is generated in lasers, while incoherent light comes 

from the sun and common illumination. 

As in material fluids, there can also exist vortices in the aether. In an aether vortex the gyrons 

move non-randomly in a closed circular pattern. The simplest aether vortex is called electron. 

Since there are possible only right-handed, and left-handed rotations, we have also only two 

kinds of electrical charge. The charge is conserved because the rotation in the vortex is 

conserved. However, if a right-handed, and a left-handed vortex meet, the rotation cancels, 

and charge disappears. This is termed annihilation of matter with anti-matter. The disturbance 

associated with such an event causes the generation of photons. The images below show the 

organized trajectories of gyrons manifested as photons, and electrons. [...] 

16) http://mywebpages.comcast.net/deneb/muller.htm 

An Experimental Disproof of Special Relativity Theory (Unipolar Induction) 

by: Francisco J. Müller 

Here is an experiment that invalidates Relativistic Electrodynamics. To facilitate 

understanding it will be presented in two parts, each one in turn subdivided into a rotational 

case and a translational one. [...] 

17) http://jnaudin.free.fr/html/troutnbl.htm 

A Successful Trouton-Noble experiment 

by: Jean-Louis Naudin and Patrick Cornille 

18) http://www.ece.drexel.edu/ECE/AR/Aether_Model.pdf 

An Aether Model of the Universe 

by: Allen Rothwarf 

Abstract: An aether model based upon a degenerate Fermion fluid, composed primarily of 

electrons and positrons in a negative energy state relative to the null state or true vacuum, is 

proposed and its consequences are explored for physics and cosmology. The model provides 

both insight and quantitative results for a large number of phenomena for which conventional 

theory provides no answers or unsatisfactory answers. Among the concepts treated are: waveparticle 

duality, the nature of spin (a vortex in the aether), the derivation of HubbleÕs law; 

electric fields (polarization of the aether); Zitterbewegung (a bare particle orbiting within a 

vortex core); inflation in cosmology; the arrow of time; the Pauli exclusion principle 

(repulsion between parallel spin vortices); the nature of the photon (a region of rotating 

polarized aether propagating with a screw-like motion); neutrinos (a spin vortex with no

particle in its core); redshifts; g-ray bursters; and a number of other topics. A key assumption 

is that the speed of light is the Fermi velocity of the degenerate electron-positron plasma that 

dominates the aether. As a consequence the speed of light decreases with time on the scale of 

the age of the universe. 

Keywords: Aether, Quantum Mechanics, Cosmology, Relativity, red-shift, Hubble's law, 

speed of light, vortices, wave-particle duality. 

1. Introduction 

We live in a universe of interacting fluids. While oceans in which gases are dissolved, and an 

oxygen-nitrogen atmosphere with water vapor and other trace gases are readily accepted, the 

third fluid, the aether, which penetrates everything is ridiculed as a relic of a bygone era in 

science. Yet, while rejecting an aether, the science establishment has no problems swallowing 

waves in vacuum, mysterious probability waves, ad hoc cosmological constants, vacuum 

fluctuations that can generate anything, and time and space expanding and shrinking. To the 

true believer, the fact that they work is the only justification for the major theories in physics; 

Maxwell's equations, the Schrodinger equation, and Relativity, and is used as evidence that 

we know everything, that Science is Dead, and humanity's brightest should move on to more 

challenging tasks. Some of us, however, are heretics. We would actually like to understand 

the physics, rather than just use it as a magic wand to create technology. In this pursuit of 

understanding, which is also ridiculed by the establishment as asking meaningless questions, 

we have found that the aether is not only a useful concept, but that it is a real substance with 

an origin that coincides with the birth of our universe and whose properties determine the 

speed of light, the other physical constants, and the missing insight lacking in present 

theories. 

Before expounding upon the aether and how it explains so many phenomena in a simple way, 

let me point out that contrary to popular belief, science is not logically based. Instead, it, like 

all human activity is based upon chance and trial and error. [...] 

http://www.ece.drexel.edu/ECE/AR/Rothwarf_home.html 

19) http://get.ilja-schmelzer.net/ 

General Lorentz Ether Theory 

By: Ilya Schmelzer 

An old and seemingly discredited notion of ether has found its new incarnation in a "metric 

theory of gravity" by I. Schmelzer, who managed to find for his new ether a consistent and 

instructive interpretation in terms of condensed matter physics. (Prof.V.A. Petrov) 

General Lorentz ether theory (GLET) is a metric theory of gravity with a predefined 

Newtonian framework with preferred coordinates Xi, T. It generalizes Lorentz-Poincare Ether 

Theory to Gravity. The ether has density, velocity and stress tensor, and fulfills the classical 

conservation laws [...] 

20) http://www.journaloftheoretics.com/Links/Papers/Seto.pdf 

Unification of Physics 

By: Ken H. Seto 

Abstract: In the final days of his life, Einstein tried in vain to unite gravity with the 

electromagnetic force. The reason for his failure was due to his incomplete understanding of 

the physical space. A new description of physical space along with a new understanding of 

matter was formulated. This new model of the current universe gives rise to a new theory of 

gravity and at the same time it unite gravity with the electromagnetic force naturally. Also this 

new model predicts the existence of a new fifth force - called the CRE force. In addition, the 

unification of all physics is within the scope of this model. 

http://www.erinet.com/kenseto/ 

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[The author is already known to Episteme's readers for his article "The Resurrection of the 

Light Conducting Medium for Modern Physics" which appeared in the issue N. 3, April 2001] 

21) http://metaresearch.org/cosmology/speed_of_gravity.asp 

The Speed of Gravity - What the Experiments Say 

By: Tom Van Flandern 

Abstract: Standard experimental techniques exist to determine the propagation speed of 

forces. When we apply these techniques to gravity, they all yield propagation speeds too great 

to measure, substantially faster than light speed. This is because gravity, in contrast to light, 

has no detectable aberration or propagation delay for its action, even for cases (such as binary 

pulsars) where sources of gravity accelerate significantly during the light time from source to 

target By contrast, the finite propagation speed of light causes radiation pressure forces to 

have a non-radial component causing orbits to decay (the "Poynting-Robertson effect"); but 

gravity has no counterpart force proportional to v/c to first order. General relativity (GR) 

explains these features by suggesting that gravitation (unlike electromagnetic forces) is a pure 

geometric effect of curved space-time, not a force of nature that propagates. [...] 

* * * * * 

Call for papers for a book of essays 

The Editors of a proposed book on classical electrodynamics to be published 

by Rinton Press, Inc. (USA) invite submission of papers. 

The name of the compilation will be 

Has the last word been said on classical electrodynamics? 

(Classical electrodynamics: new horizons) 

All papers to be submitted by e-mail 

to dr. Andrew E. Chubykalo (preferable) 

andrew_chubykalo@terra.com.mx 

or to Dr. Vladimir Onoochin 

a33am@dol.ru 

or to Dr. Roman Smirnov-Rueda 

Roman_Smirnov@Mat.UCM.Es 

or to Dr. Augusto Espinoza 

drespinozag@terra.com.mx 

in LaTeX, LaTeX- 

"\documentstyle" format is preferable (i.e. not "\documentclass"!). 

Figures for papers should be presented in eps-format (encapsulated postscript 

format). Page size should not be more than 22.86 x 15.24 см. Papers should be 

approximately 15 pages in length and must not exceed 20 pages (except special 

cases agreed with the Editors). 

All received papers will be evaluated by independent referees.

Deadline is 1st of June, 2003 

After publication of the book all contributors receive two printouts of their 

contributions. 

EDITORIAL AIMS AND OBJECTIVES 

In the last decade, it is observed an emergence of revived interests towards classical 

electrodynamics. While the conventional Maxwell's theory remains one of the few cornerstones 

of modern physics and cradle of Einstein's relativity, an throughout study on it may 

lead us to a better and deeper understanding on electromagnetism which has a nearly two 

century history and may bring us nice surprises. In spite of all its visible successes, there are 

still reasons to believe that either Maxwell's equations or the conceptual background of 

electromagnetism needs to be modified. 

There are also attempts in these directions. R. Feynman was one of these who had 

some doubts on the completeness of classical electrodynamics, and he once commented: "… 

this tremendous edifice (classical electrodynamics), which is such a beautiful success in 

explaining so many phenomena, ultimately falls on its face. When you follow any of our 

physics too far, you find that it always gets into some kind of trouble. …the failure of the 

classical electromagnetic theory. Classical mechanics is a mathematically consistent theory; it 

just doesn't agree with experience. It is interesting, though, that the classical theory of 

electromagnetism is unsatisfactory theory all by itself. There are difficulties associated with 

the ideas of Maxwell's theory which are not solved by and not directly associated with 

quantum mechanics…". 

Many unresolved and forbidden problems of classical electrodynamics seem to be 

more serious in view of frustrated intentions to make fully compatible Einstein's relativity 

(based mainly on Maxwell's equations) with quantum mechanics. According to Bohm, this 

significant incommensurability has to lead to discover an entirely new order to physics at a 

fundamental level with all its implications for classical theory. It will be helpful if there is a 

forum where arguments of both for and against modification of standard Maxwell's approach 

are presented, and thus, an objective discussion of all possible alternative views logically 

sound and based on a rigorous mathematical ground is conducted. 

This review volume as entitled above will provide such a forum. The editors would 

call scientists who are actively working in electromagnetic theory to send in your review or 

research papers on classical electrodynamics, especially these on unsolved and annoying 

problems. 

The Editors: 

Dr. Andrew E. Chubykalo (Mexico) 

Dr. Augusto Espinoza (Mexico) 

Dr. Vladimir Onoochin (Russia) 

Dr. Roman Smirnov-Rueda (Spain) 

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1 - Introduction 

Looking for Special Relativity's 

Possible Experimental Falsifications 

(Umberto Bartocci) 

We already had the opportunity to describe, in the Letter... which opens this special number 

of Episteme, the fundamental reasons which should inspire a general criticism of relativity, or, 

better, of the "philosophy" which was (and is) the ground of Einstein's success. This paper is 

an attempt to analyse the strictly physical (phenomenological) situation, in order to give a 

suggestion where to look for possible experimental falsifications of the theory (from now on 

SR, special relativity 1 ), in the conviction that this is the only possible manner to show that the 

main assumption of "abstract physics" supporters is wrong: namely, that the renouncing to 

ordinary space, time, causality, was not a "nihilistic caprice", but a necessity forced by facts 2 . 

This analysis is not so easy as it could appear, since to decide whether a given experiment, 

or phenomenon (two paradigmatic examples: annual stellar aberration, Sagnac's experiment), 

could be explained in a relativistic manner or not (or else, from the other side, that it could 

not be explained in a "classical" way), is an engagement which can be pursued only with a 

great care, and a good knowledge of the theory one is aiming to prove or to disprove 3 . 

Our main points will be that: 

I - There are not so many convincing (direct) experimental arguments in favour or SR, as it is 

vice versa usually emphasized by "orthodox" physicists - which sometimes add, on these 

premises, that a pretended phenomenon possibly disproving SR would be like a vox clamantis 

in deserto, and that this justifies the cautious establishment's response in front of such claims. 

II - Moreover, there is not even a crowd of experimental data against Einstein's physics. In 

simple words, we do not have until now enough evidence in favour of neither a point of view, 

which shows that it would be rather unwise, at least for the moment, to dismiss all attempts 

aiming to provide a "rational" description of how Nature works. 

1.A Cartesian Physics vs Special Relativity 

In order to achieve our goal, let us give a sketch of what relativity essentially is. First of all, 

it is a theory which, contrarily to the common opinion, should be considered more 

conservative than revolutionary in its essence. In order to explain this assertion, we must go 

back to the very beginning of physics as a science, and to the opposition between Cartesian 

conception of space as a plenum, and Newtonian contrary point of view 4 , an empty space not 

endowed of any physical objective, measurable, property. Of course, from this quite simple 

starting point 5 , divergences grow up in an increasing complexity, but the substance of all 

conflict is there. After the success of Newton on Descartes, the image of the empty space - in 

which a mysterious action at a distance ruled the trajectories of all celestial bodies, and in 

which movement could only be relative, according to Galileo's famous ship's argument 6 - 

dominated the scene of science for more than one Century. The conception of a space acting 

as an indispensable medium for all physical interactions, came back during electromagnetic 

studies in XIX Century: Ampère, Oersted, Faraday, Neumann, the great Maxwell's Treatise, 

etc.. At the end of that Century the situation in theoretical physics was indeed an

uncomfortable one. There was the image of the world given by Newtonian mechanics, which 

marked, even in a symbolical way, the "victory" of science over the supporters of darkness 

and superstition. But there was an aether too, which was clearly "seen" for instance in the 

lines of force surrounding a magnet. When Einstein appears on the stage 7 , a solution was 

really needed, and there were only two possible way out. Either to accept the evidence for an 

electromagnetic aether, to refuse the principle of relativity (from now on PR), and to frankly 

acknowledge that Newton's party was wrong; or, at the contrary, to maintain the foundation of 

Newton's physics 8 , even in a quite different space-time set up, really undreamed of until 

Einstein's age (and this would be the "revolution"). 

It is obvious that, from our point of view, the really true courage would have been to choose 

the first option, while Enstein did exactly the opposite. He maintained Newton's empty space, 

proposing PR as one of the essential Nature's laws, and at the same time "borrowed" from 

aether's physics concepts like the independence of light's speed from the speed of the source, 

the finiteness of the speed of propagation of all aether's "disturbances" (fields), etc.. He 

showed in such a way that it was possible to assemble a general theory, but he was forced, 

however, to give up ordinary space and time conceptions. Thus, it is not a "paradox" to assert 

that Einstein followed rather closely Newton's tracks 9 , and that its only true opponent is 

Cartesian fluid-dynamical physics 10 . One could as well assert that SR is similar to a proof ab 

absurdo: the only way to keep together the abstract RP, and the experimental 

electromagnetism, is to abandon ordinary space-time, and since this is absurd, we must 

choose between the principle and the facts. Needless to say which should have been, in our 

opinion, the right choice. 

1.B Special Relativity's True "Heart" 

As we have mentioned, SR is made up of two postulates (Voraussetzungen), RP plus LSP 

(Light's Speed Principle) 11 . In an empty space RP is "acceptable", because of a kind of 

insufficient reason principle: there is no reason why an inertial observer 12 should experience a 

physics different from another one, seeing that there exists nothing which could decide which 

one is really moving, or still. In an aether theory, and in a wave theoretical approach to the 

nature of light (perhaps not the only possible one), LSP is acceptable (even in a stronger 

form, see the next section 4). So, from the point of view of a critic of SR, this is 50% correct, 

and it is not LSP the assertion which should require a careful scrutiny, but SR's true 

foundation, that is to say PR 13 . Indeed, it is PR which, added to LSP, makes LSP quite 

counter-intuitive, and such that all the attention of people goes to the very qell known strange 

features of relativistic speeds, but, we repeat it, LSP has nothing wrong in itself, and it 

becomes "bad" when one changes the independence from the speed of the source with the 

independence from the speed of the observer! 

At this point, the fundamental question is: which are the direct experimental arguments in 

favour of PR? 

We believe that an "honest" answer should be, at least for the moment being, that there are 

not. The greatest part of the pretended experiments in favour of SR - whose correctness one 

could even accept, mostly if he is not a professional physicist, like the present writer - could 

be, first of all, easily re-interpreted in an aether theory, finding in fact in such a context their 

better (proper) "explanation" (the "increasing" of the inertial mass as a phenomenon of 

"resistance"; the finiteness of the speed of propagation of interactions, perhaps equal for many 

different phenomena, the consequent "retardation", etc., obvious; for the so-called "time 

dilation", see the next section 3; and so on, we must confess that we find most of all worth of 

some attention the claims about the experimental validity od the so-called transverse Doppler 

effect). Second, that part of experiments which seem to validate PR, have only used the 

33

34 

hypothetical motion of the Earth through the aether 14 , thus showing that theoretical physics 

has not made, in this field, a great progress since XVII Century! The possibility that this 

motion does not exist at all - or that it is too small to be detected 15 - is seldom taken into 

consideration in popular divulgations of Einstein's theory, while Descartes-Leibniz's vortex 

theory 16 implies exactly this inexistence. Only experiments performed in reciprocally moving 

laboratories would give some evidence in favour of the one or of the other conflicting points 

of view, and these experiments have been almost never done 17 ! In 20 years study of this 

problem, and innumerable discussions with colleagues (usually worried to avert a friend from 

bad companies), the author has never heard of such experiments, while at the contrary 

everybody claimed that it was practically impossible to reach those speeds which could have 

been significant in order to test RP. Moreover, they added that the required accuracy of 

measures would have been irreparably disturbed by the forced movement (see even Marinov's 

remarks, in the next section 2.A). 

And so then? Why one should believe in something which has not yet been proved beyond a 

shadow of a doubt 18 ?? 

It is at this point unavoidable the doubt that the motivations of Einstein's followers are not 

of a strictly scientific nature (mathematicians for instance greeted with enthusiasm the "birth" 

of SR, since it showed that their sophisticated tools would have shown their practical utility 

too 19 ), and we feel obliged to carry on a long research work like the present one. 

1.C The Theory of the "Dragging Aether" 

It is clear from the above that the general theory which we feel the most trustworthy opponent 

of SR is the so-called theory of the dragged aether 20 , a denomination which shows 

nevertheless an implicit relativistic conditioning. If we consider a physically active aether, 

why should we accept - in obedience to the opinion that any motion could not be but relative - 

that it would be the same thing to say either that the aether is dragged, or that the aether is 

dragging, as it is quite more likely? This misunderstanding is not only of a linguistic nature, 

since it is at the origin of a pretended "proof" against the theory we are aiming to propose as 

the possibly "true" one. As a matter of fact, most text-books recall the famous Fizeau's 

experiment as a "crucial" one proving that the aether is not (at least completely) dragged by 

moving bodies (in this case water, forced to move in a pipe), but this has really nothing to do 

with Descartes-Leibniz's theory 21 ! 

At this point one could ask whether there are other arguments against the dragging aether 

(the usual name for an hypothesis of this kind is Stokes theory, but we believe, as we have 

said, that we are in front of similar but different theories), and one would be perhaps surprised 

acknowledging that, according to the well known Resnick's book 22 , only Fizeau's experiment 

and annual stellar aberration are quoted as such "proofs". Of the first one we have just said, 

the other one appears as a possible new great misunderstanding, one of the many which affect 

theoretical physics, which the author, not accustomed to this kind of situation in mathematics, 

discovered with great amazement 23 . As a matter of fact, it has been shown very clearly by 

Giancarlo Cavalleri et al. 24 : "Some special relativity textbooks assert, without giving a 

detailed history of the question of aberration, that Stokes theory is wrong [...] their argument 

is grounded on a misunderstanding: precisely, the aether which they consider is not 

irrotational". Moreover, we feel that is not even impossible to explain Bradley's aberration 

introducing a "model" similar to the local magnetosphere (quite compatible with the general 

theory of the dragging aether) discussed in the reprint of Zapffe's paper in this same volume, 

namely, that this question is still well open.

This is the general conceptual frame 25 in which one should fit the observations and 

proposals below, which represent a kind of Summa, trying to collect the "best" acquired in 

many years research and frequentation of "alternative physicists", to whom all (dead or 

alive) go the author's warmest thanks. 

2 - Does RP Hold in Electromagnetism? 

We begin our analysis restating the fundamental question in more specific words: does 

electromagnetic phenomenology really allows physicists to propose RP as one of the most 

fundamental Nature's "laws"? 

It is obvious that, from the point of view of the "Cartesian physics" sketched in the previous 

section, the expected answer of Nature should be a clear and strong not, and not only in 

electromagnetism, but in principle even in mechanics, with the only difference that it is very 

likely that mankind has not been able to observe until now significant mechanical violations 

of RP, as men have been confined in their small planet, and in the realm of "low velocities". 

It is rather instructive to quote at the opposite the words of a physicist (taken from an 

Internet group discussion), who claims that: 

The experimental evidence confirming the principle of relativity is actually overwhelming, in 

the sense that in no field has one ever discovered any dependence of the forms of the laws of 

physics on the velocity of the reference frame. 

Is this an opinion, or objective science (as far as science can be objective in the limits of our 

present knowledge)? The fact is that exactly Maxwell's Electrodynamics (from now on ME), 

the supposed pillar of Einstein's SR 26 , provides a mathematical set-up which can have 

different interpretations as a physical theory (which is a mathematical theory, plus a set of 

more or less explicit, and formalized, assumptions, rules of codification and decodification, 

from the reality to the abstract intellectual "model", and conversely, which are not so rigid), 

some of which interpretations do not satisfy RP. 

To this question the author has dedicated a paper 27 , in which it is shown that the 

phenomenon of the electromagnetic induction, the only one which Einstein choosed as a 

motivation for his proposal of a complete symmetry between "inertial frames", is indeed a 

good example (internal to ME) of a symmetrical interaction 28 , but it should have been 

regarded as an exception (which has to do with the circumstance that we are in this case in 

front of closed circuits) in classically interpreted ME, and not as a rule. As a matter of fact, 

general Maxwell's treatment (which is "aether-based") suggests instead that we are possibly 

in front of an asymmetrical phenomenology, in which velocities with respect to a priviliged 

frame make a great difference. One must admit, of course, that SR show how it is possible to 

interpret ME even in a conceptually symmetrical framework, but one should admit too that 

we are indeed in front of two different physical theories, even if they are "sharing" the same 

equations. Which one is "true", we actually do not really know. Physics is believed to be 

above all an experimental science, but the most meaningful and widespread convictions 

appear to be more theoretical in essence (we do not want to say: ideological) than 

experimental, and it was really a surprise to realize that some endless discussions could have 

been put to an end with experiments that nobody has ever properly done (but almost every 

physicist thinks, and acts, as if they had been done!). 

35

36 

2.A The Direct and the Inverse Rowland Experiments 

It seems convenient, for many reasons, to start with an "experiment" which could be thought 

of as the possible key for understanding the nature of the eventual electromagnetic 

asymmetries we are talking about. The dear unforgotten friend Stefan Marinov explains the 

situation is his Divine Electromagnetism (1993), pp. 169-173, and we quote below some of 

his very clear words. 

Rowland [Rowland H.A., Sitzungsberichte der K. Akademie der Wiss. zu Berlin, p. 211 (1876)] carried 

out in 1876 the following experiment: A disk was charged with positive (or negative) electricity. There 

was a magnetic needle in the neighbourhood of the disk. When the disk was set in rotation, the needle 

experienced a torque due to the magnetic action produced by the convection current of the charges 

rotating with the disk. I call this the DIRECT ROWLAND EXPERIMENT. 

According to the principle of relativity, if the disk will be kept at rest and the needle will be set in 

rotation, the same torque has to act on it. Such an experiment is called by me the INVERSE 

ROWLAND EXPERIMENT. 

[...] The above two experiments can be called ROTATIONAL Rowland experiments. It is easy to 

transform them into INERTIAL experiments. So if we charge a conveyer belt and set it in action, the 

motion of the charges can be considered as inertial (i.e., with a velocity constant in value and in

direction) over a considerable length of the belt and we shall realize thus the inertial direct Rowland 

experiment. 

[...] As far as I know nobody has carried out either the rotational nor the inertial inverse Rowland 

experiments. 

Now I shall show that, contrary to the prediction of the princople of relativity, the inverse Rowland 

experiment must be null, i.e., a magnet moving with respect to charges at rest does not experience 

torque. 

[...] I carried out the rotational direct and inverse Rowland experiments. [...] Of course, because of the 

mechanical vibrations and the Earth's magnetism, it was pretty difficult to establish such a null effect 

and my experiment, naturally, needs confirmation carried out in a first class laboratory. According to 

me, the inverse Rowland experiment has been not carried until now not because of technical 

difficulties but because of a fear that the result will be null [...] 

Marinov's words describe a situation which we will face later on in other conceptually 

similar contexts, but we wish to remark since now that, apart from possible theoretical and 

experimental questions arised by the "Rowland case" 29 , they testify our same experience: 

direct fundamental experiments, the only ones which should allow Einstein's enthusiasts to 

assert that SR is really beyond a shadow of a doubt, have never been performed 30 ! 

2.B Some Theoretical Remarks About ME 

Before going on, it is convenient to be more precise about ME as a mathematical theory. By 

this we mean the system of the four Maxwell's equations (expressed in standard differential 

notation, in the MKSQ unit system): 

(1) curl(E) = - ∂ B 

∂ t 

(2) curl(B) = μ0 (ε0 ∂ E 

∂ t 

(3) div(E) = ρ 

ε 0 

(4) div(B) = 0 , 

+ j) 

which can be reduced to the two D'Alembert wave equations for the electric and magnetic 

potentials Φ , A : 

(5) Φ = - ρ 

, 

ε 0 

(6) A = -μ0 j , 

where appear the charge density ρ(x,y,z,t) and the density current j(x,y,z,t) (which satisfy 

∂ ρ 

the charge continuity equation div(j) = - ). 

∂ t 

The potentials Φ , A are connected by the Lorentz gauge condition: 

(7) div(A) = -c -2 

∂ Φ 

∂ t 

(where: c -2 = ε0μ0 ) . 

37

38 

The electric and magnetic fields E, B are expressed in terms of the potentials by the 

equations: 

∂ A 

(8) E = -∇Φ - 

∂ t 

(9) B = curl(A) , 

and the force acting on a charge q , movin with velocity v , is the Lorentz force: 

(10) F = q (-∇Φ - 

∂ A 

∂ t 

+ v×curl(A)) = q E + q v × B . 

There is indeed in the theory a further assumption, which can be viewed as a restriction on 

the way fields originate from sources31 : we assume that for a given ρ and j, (5) and (6) have a 

unique solution which is physically relevant, namely the one given by the so called Liénard- 

Wiechert retarded potentials: 

(11) Φ(x,y,z,t) = 

(12) A(x,y,z,t) = 

1 

4π 

ε 

μ 

4π 

0 

ρ (x', 

y', 

z', 

t - 

∫ ∫ ∫ r 

0 ∫ ∫ ∫ r 

r 

) dx'dy' dz' 

c 

r 

j (x', 

y', 

z', 

t - ) dx'dy' 

dz' 

c 

where r'(x,y,z;x',y',z') is the ordinary distance [(x - x') 

+ 

integration is made on the whole space (one gets smooth solutions if one starts from smooth 

data for ρ and j ). 

, 

, 

2 

2 

2 

+ (y - y') 

(z - z') 

, and the 

The previous formulae (11) and (12) are in truth not so simple to understand. Their 

"physical" meaning is that the contribution of a point (x',y',z') to the integrals is not given for 

instance by the charge which is in this point at the time t , but only by the charge which was 

r 

in (x',y',z') at the retarded time t - , that is to say by the charge which is seen from (x,y,z) 

c 

in the point (x',y',z') at the time t . 

The equations introduced above must be thought of - in ME's classical interpretation - as 

valid only in a set of privileged reference frames K , the so-called aether frames (in principle 

they are unique up to spatial rotations and translations, and up to a time homothety, but do not 

forget what has been said in footnote 25), where the ordinary concepts of classical mechanics 

can be used. In their relativistic interpretation, one must add an additional hypothesis, which 

ensures the validity of the theory in all inertial reference frames K' , namely the ones moving 

with a uniform velocity with respect to K (connected to K by means of a Lorentz-Poincaré 

transformation): 

(13) (j,ρc) and (cA,Φ) are 4-vectors of the Minkowski space-time. 

Only this assumption enables to write the Maxwell's equations in a covariant form, but one 

must remark that (13) is a genuine new physical assumption, which is logically independent 

of the previous ones, and that it is perfectly legitimate to use ME in a "classical" space-time 

theory without any connection at all with relativity. We shall show now some of the

differences which can arise between different physical interpretations of the same 

mathematical theory. 

2.C Trouton-Noble Type Experiments 

Let us study more carefully the different previsions which a Cartesian and an Einsteinian 

physicists (from now on: C and E ), can do with the same mathematical theory. 

Let K(x,y,z,t) be an inertial coordinate system of the space-time. K will mean for C a 

(possibly local) rest-frame in the aether (or even an aether-frame). Measures of space and 

time (for instance, synchronizations of remote clocks) can be made exactly as Einstein 

requires, so that even E can accept K as one of his inertial coordinate system. Until this 

moment, the only difference is that C would not accept as a "good" coordinate system any 

other similar system K' which would "move" with respect to K with a uniform velocity, and 

most of all that C would not accept the method that E could indeed use (rightly, from his 

point of view) in order to simplify the effort to give an answer to some theoretical questions. 

Namely, to change the coordinate system, choosing another one K' more "suitable" with 

respect to the physical situation under discussion; make computations in K' ; then go back to 

K using some coordinate transformation (in the present case, Lorentz-Poincaré 

transformations). In other words, C cannot use sometimes of the facilities of E , but it does 

not really matter, since they agree at least in the choice of K , and most of all in the system of 

equations that they have in order to describe electromagnetic phenomenology. 

Let us think of an electric charge Q moving in K with some uniform velocity 

v = (v,0,0) along the x-axis (let us even suppose that x = vt , y = z = 0 , are the equations of 

the motion of Q ), and let us ask, to both C and E : which are the electric and magnetic 

potentials associated with Q ? 

The question is such that both C and E will give the same answer 32 : 

(14) ΦQ = 

(15) AQ = μ 

1 

4π ε 0 

0 

π 

v 

(where, as usual, β = ). 

c 

4 

Q 

2 

( x − vt) 

+ ( 1 − β 

Q v 

2 

)( y 

2 2 2 2 

( x − vt) + ( 1 − β )( y + z ) 

2 

+ 

The coincidence of these potentials both for C and E , which could be extended to any 

system of a finite number of charges (since we are in front of a linear theory), could make 

believe that C and E would share even the same "physics", at least in the electromagnetic 

field, but this is not true, as we should immediately understand, now and later in the next 

section. 

Let us in fact introduce another charge q , in the (xy)-plane, which in the instant t = 0 has 

coordinates (Rcos(θ),Rsin(θ),0) , as in the following picture, and let us ask which is the total 

electromagnetic force acting on q in virtue of Q in the case q is supposed to move with 

velocity w = (w,0,0) parallel to v (in particular, comoving with Q with the same velocity v 

, or standing still in K , case w = 0 ) : 

z 

2 

) 

, 

39

40 

∂ AQ Starting from (10), namely, in our case, Fq = q (-∇ΦQ - + w×curl(AQ)) , 

∂ t 

straightforward computations give the following values for the three terms in the right hand 

side of the previous expression of the required force: 

-∇ΦQ = 

∂ 

- 

AQ ∂ t 

1 

4π ε 0 

= - μ 

curl(AQ) = μ 

0 

π 

Q 

3 

2 

2 2 2 

[ ( x − vt) 

+ ( 1 − β )( y + z ) ] 

Q v 

4 [ ] 3 

2 

2 2 2 

0 

π 

w×curl(AQ)) = μ 

( x − vt) 

+ ( 1 − β )( y + z 

Q v 

4 [ ] 3 

2 

2 2 2 

0 

π 

( x − vt) 

+ ( 1 − β )( y + z 

Q v w 

) 

) 

(x-vt,(1-β 2 )y, (1-β 2 )z) 

v(x-vt) 

4 [ ] 3 

2 

2 2 2 

( x − vt) 

+ ( 1 − β )( y + z 

and so, remembering that μ 0 

4 π 

= 1 1 

2 

4π 

ε 0 c 

(16) Fq = 

- 

1 

4π ε 0 

1 

4π ε 0 

1 

+ 2 

4π 

ε 0 c 

= 

1 

4π ε 0 

qQ 

3 

2 2 

2 2 2 

[ R cos ( θ ) + ( 1 − β ) R sin ( θ ) ] 

qQ 

3 

2 2 

2 2 2 

[ R cos ( θ ) + ( 1 − β ) R sin ( θ ) ] 

vw 

R 

2 

: 

qQ 

(1-β 2 ) (0,-z,y) 

3 

2 2 

2 2 2 

[ R cos ( θ ) + ( 1 − β ) R sin ( θ ) ] 

qQ 

[ ] 3 

2 2 

1 − β sin ( θ ) 

) 

(1-β 2 ) (0,-y,-z) 

(Rcos(θ),(1-β 2 )Rsin(θ),0) + 

β 2 Rcos(θ) ix + 

(1-β 2 ) (0,-Rsin(θ),0) = 

(1-β2 vw 

) [ (cos(θ),sin(θ),0) - 2 sin(θ) iy ] = 

c

= 

1 

4π ε 0 

qQ 

2 

R 

( 1 

− 

β 

3 

2 2 

[ 1 − β sin ( θ ) ] 

2 

) 

vw 

[ u - 2 sin(θ) iy ] , 

c 

where ix , iy are the unit vectors of x and y , and u is the unit vector of the vector Qq in the 

instant t = 0 . 

This formula gives the exact expression of the required interaction in ME , with no 

difference whatsoever whether we are following a classical point of view or a relativistic one. 

1 

It is in fact rather instructive, since it is made up of two terms. The first one, namely 

4π ε 0 

qQ 

2 

R 

( 1 

− 

β 

[ ] 3 

2 2 

1 − β sin ( θ ) 

2 

) 

u , does represent the complete force acting on q when the velocity of 

q is equal to 0 , or even when the velocity of Q is equal to 0 , no matter which is w . When 

both v = w = 0 , this term is equal precisely to the well known Coulomb's law for the 

interaction of static electric charges. 

For any v , different from 0 or not, this "partial" (if w is not zero) force is "almost" equal 

- that is to say, up to second order in β - to Coulomb's force, and if we think of a "rigid rod" 

which connects the two charges Q and q , this term is annihilated by the reaction of the rod. 

For our purposes, the interesting term is the other one, which in the comoving case 

1 

( w = v and not zero) becomes: - 

4π ε 0 

qQ 

2 

R 

2 

β ( 1 − β 

[ ] 3 

2 2 

1 − β sin ( θ ) 

2 

) 

sin(θ) iy . 

This force is not directed along u , so it is not annihilated by the reaction of the rod. Up to 

second order in β , the projection of this force along the vector 

u' = (-sin(θ),cos(θ),0) , namely the unit vector orthogonal to u such that the pair (u,u') has 

the same orientation as (ix,iy) , is equal to: 

1 

(17) - 

4π ε 0 

qQ 

2 

R 

β 2 sin(θ) cos(θ) u' . 

The "symmetric" computation of the force acting on Q by means of q , always in the 

comoving case, gives a similar force, but with opposite sign, which implies that we are in the 

presence of a couple of forces, having linear momentum equal to: 

1 

(18) M = - 

4π ε 0 

qQ 

R 

β2 1 

sin(θ) cos(θ) iz = - 

4π ε 0 

qQ 

2R 

β 2 sin(2θ) iz . 

A very "small" momentum indeed, but enough, from the point of view of C , to let him 

predict that the rod would turn clockwise (if we suppose the two charges of the same sign) 

with respect to z , in order to reach the equilibrium position parallel to v (for θ = 0 the 

π 

). 

momentum vanishes, but it vanishes even if θ = 2 

This is indeed a violation of the Newton's action-reaction principle, a violation which 

appears not only in classical electromagnetism, but even in SR (see footnote 29). It appears 

indeed quite "understandable" in an aether theory, since it would be due to the retardation due 

to the finite speed of propagation of the electromagnetic interaction. But why have we said: 

"from the point of view of C ", if we have even asserted that C and E agree with their 

computation? Because E , the previous formula notwithstanding, is forced to predict that the 

41

42 

rod would not rotate! As a matter of fact, C has no other means to ground his prevision of a 

rotation, while E could argue in the following way too. If I think of an observer X on the 

rigid rod, then from the point of view of X the rod is standing still, and since X is a "good" 

observer as I am, then the forces acting on the two charges at the extremities of the rod would 

be for X exactly equal and opposite, directed along the direction of the rod, as they are for 

me when v = w = 0 . Since this reference frame K' which I could think of, comoving with 

the rod, is physically quite equivalent to the one, K , in which I am standing still, and since in 

K' there should be no rotation (in SR, the action-reaction principle holds in the "proper 

frame" of the given physical situation), then a rotation should there be not even in K ! 

This analysis of E is in fact rather easy, but it is not so trivial to understand why E would 

conclude that, even if the previous momentum in K is indeed different from zero for him too, 

then the rod would remain nevertheless still. This is why the two forces acting on q and Q 

at the same instant t in K (we have supposed t = 0 , but it could be any other instant) are not 

acting in the same instant in K' . That is to say, E thinks that from K we see only an 

"apparent" momentum, due to the fact that the two forces "appear" to act simultaneously in K 

, while in the proper system K' , comoving with the rod , the two forces which are "really" 

simultaneous do not produce a momentum. In conclusion, E would claim that C's 

prediction is wrong, since he is trying to estimate physical quantities standing far away from 

the moving object. C could easily object that it is E which is wrong, because when he is 

thinking of an "observer" E' comoving with the rod, E' would be in motion with respect to 

the aether ("absolute" motion), and so the Einstein's synchronization of clocks performed by 

E' is uncorrect. This is the reason why E' believes that the two forces acting simultaneously 

with respect to him on q and Q do not produce momentum, while they do 33 . 

We have proved that, even starting from the same equations, and making the same 

computations, there is not a physical agreement between C and E . But who is really right 

(perhaps no one of the two!)? Thought of a true rod like the previous one, uniformly moving 

with respect to a frame which one has some right to consider "inertial" (with a "good 

approximation"), does this rod rotate or not?? An experiment inspired to the situation above 

was indeed attempted by Trouton and Noble in 1903, and it is one of the few truly 

electromagnetic experiments aimed to prove the consistence of SR. Unfortunately, Trouton 

and Noble tried, as usual, to make in evidence a pretended motion of the Earth through the 

aether, which as we have said very likely does not exist 34 . To people who are influenced by 

the rôle of the famous Michelson-Morley optical experiment as one of the principal 

motivation for the birth of SR, we say that experiments of the previous kind, at the same 

manner that the one proposed in the next section, aimed to put in evidence the possible 

electromagnetic effects of the "aether wind" due to an absolute motion, should be regarded as 

electromagnetic "Michelson-Morley experiments", and that they should be performed for 

instance in a "train" like the one of the Buys-Ballot's test (see footnote 17). 

2.D The Cardone-Mignani Experiment 

We have seen in section 2.C that it is not enough to share the same mathematical equations in 

order to have the same physics. Moreover, even if C and E have a common starting point in 

Maxwell's equations, to compute the same expressions for the potentials (and for the fields), 

is not the general rule. We have analysed before a very simple case, in which potentials are 

indeed equal for C and E , but this agreement does not exist anymore when they are in front 

of non-uniform motions, like the ones which appear for instance in the case of a circular 

current. 

As an example of this, we suggest to compute (in a given aether-frame K as before; 

remember what has been said on the "agreement" of C and K about this frame) the force

which does act at the instant t = 0 on a test-charge q placed in the center of a circular circuit 

S , as the effect of a stationary current I flowing in S , when the circuit and the charge are 

comoving with a uniform speed v = (v,0,0) as in the previous section. 

The situation is described in the following picture (the current is supposed to flow in the 

anticlockwise direction from x to y with respect to z), and so by the parametric motion's 

equations (both for C and E ): 

x = Rcos(θ) + vt , y = Rsin(θ) , z = 0 , 0 ≤ θ ≤ 2π , 

while the motion's equations of q are obviously: 

x = vt , y= 0 , z = 0 : 

The author did extensively deal with this not simple computation (which requires a direct 

integration of Maxwell's equations) in the paper quoted in footnote 27, and the result is that 

the force acting on q , from the point of view of C , is equal to (up to second order effects in 

β ): 

(19) F = - 

μ 0 

qI 

v 

4R 

iy . 

Thus, C would expect a force which is not equal to zero, and which does depend both on 

the intensity and on the direction of the current. 

From the point of view of E , at the contrary, the prediction is quite different, and he will 

not agree at all with (19). As a matter of fact, in the proper reference frame K' , comoving 

with the circuit ( S will be no more circular in K' , but this does not really matter), the 3force 

acting on q must obviously be equal to zero ( E maintains the validity of Clausius' 

postulate in K' ), and this implies that it must be zero even in K . 

So the important question is: in which point E , which is using the same Maxwell's 

equations as C , do not forget it, will differ by the formula (19) when doing his computations 

in K ? 

Here they are, in order to answer precisely to this question, the exact expressions of the 

potentials of the circuit S computed by C 35 : 

(20) ΦS = 0 

43

44 

(21) AS = μ 0 

π 

2π 

4 IR ( − sin( 

θ ), cos( θ ), 0) 

∫ 

dθ 

2 

2 

2 2 

( x − vt − Rcos( 

θ )) + ( 1 − β )[( y − Rsin( 

θ )) + z ] 

0 

and now the expressions of the same quantities as computed by E : 

v Ax 

' 

(20') Φ*S = 2 

1 − β 

(where Ax' is the first component of the magnetic vector potential in the proper frame K' of 

S ; we are using the simplest possible case of a Lorentz transformation) 

(21') A*S = μ 0 

4π IR 2π 

2 

( − sin( 

θ ), 1 − β cos( θ ), 0) 

∫ 

dθ 

2 

2 

2 

2 2 

0 ( x − vt − R 1 − β cos( θ )) + ( 1 − β )[( y − Rsin( 

θ )) + z ] 

The great difference between (20), (21) and the corresponding (20'), (21'), is that Clausius' 

postulate (see footnote 35) does hold in SR only in the proper frame of S , while it is no more 

valid in K , according to the transformation rules (which are consequences of (13)): 

Φ '+ 

v Ax 

' 

Φ*S = 2 

1 − β 

ρ*S = 

v 

ρ '+ 

2 

c 

1 − β 

j 

x 

2 

' 

v A 

x' 

= 2 

v 

= 2 

c 

1 − β 

j 

x 

' 

1 − β 

(where the apices designate quantities computed in K' ). 

2 

These equations imply that the moving circuit "appears" to have a non-zero density charge 

in K , and so a non-vanishing electric potential. In classically interpreted ME, at the contrary, 

the expression for ρS is simply given by the general formula: 

ρ(x,y,z,t) = ρ0(x-vt,y,z,t) = 0 , 

where ρ0 represents the density charge in the case v = 0 . 

An analogous "classical" formula describes the relation between the density current terms 36 : 

j(x,y,z,t) = j0(x-vt,y,z,t) + ρ0(x,y,z,t) , 

while the same equation, from the point of view of SR, is given instead by: 

j 

x' 

+ vρ 

' 

jx(x,y,z,t) = 2 

1 − β 

j 

x' 

= 2 

1 − β 

(the other two components of j remains unchanged in the passage from K' to K ). 

, 

.

This shows 37 that Maxwell's equations have relativistic solutions only when relativistic 

treatment of charges and currents is introduced, while they can have equally good "classical" 

solutions when these terms are defined in a classical way. 

Let us remark too that the difference between AS and A*S is "very small", since the two 

potentials are indeed equal up to second order in β , but that it is not so small to be neglected 

(see footnote 32), since, in force of (7), one must have (and one has): 

div(AS) = - c-2 ∂ Φ S 

∂ t 

div(A * S) = - c-2 ∂ Φ * 

∂ t 

S 

, 

, 

and these formulae show that the small difference becomes essential in the second case, when 

a small term (the divergence of the magnetic potential) is multiplied by c 2 , and thus it gives a 

meaningful non-zero time-variation of the electric potential, a potential which cannot vanish 

(in the first case, instead, the divergence of the magnetic potential is exactly equal to zero). 

In conclusion, we should ask once again: who is really (that is to say: experimentally) right, 

C or E ? The aforesaid divergence can be elaborated in view of the proposal of a new 

gedankenexperiment aimed to discriminate between classical and relativistic interpretations of 

ME . One could either try to perform direct measures of the force acting on the charge q , or 

better of the electric potential difference across a thin linear conductor T placed along a radius 

with an extremity in the centre of C and the other one close to the current wire, as in the 

following picture: 

We could attempt to make in evidence a possible Earth's absolute velocity (and this is why 

the sensor and the circuit's plane have been projected to be able to rotate, since this velocity is 

unknown), but, as we already said many times, the apparatus should be put in a real motion 

with respect to an ordinary Earth's laboratory, before saying that this test has given all 

possible information. 

The fact that the force predicted by C does depend both on the intensity and on the 

direction of the current, should make it possible to separate a non-zero effect from other 

possible "disturbances" (due for instance to the electromagnetic fields existing in the 

terrestrial reference frame, and to other sources of systematic errors, or even to the possible 

45

46 

non-validity of Clausius' postulate - see footnote 35). Moreover, by increasing I and/or q , 

one might be able to observe an effect even if the velocity of the moving laboratory is very 

small, as presumably it has to be, compared with c . 

We show below another picture, showing the experimental apparatus which we 38 have tried 

to use in an amateurish way (in Foligno, near Perugia, in 1990): 

An experiment of this kind has been in fact performed in a professional way by Cardone- 

Mignani 39 , with results which are difficult to interpret. Anyway, their apparatus was still in an 

Earth's laboratory, and so it could have possibly put in evidence only an unlikely "absolute" 

Earth's velocity. 

In conclusion, we want to repeat it once again that: 

* - Apart the fact that the most conspicuous phenomena alleged in favour of SR (namely the 

increasing of the inertial mass and the mean-life of speedy particles) appear rather more 

compatible with an "absolute theory", than conversely (in absence of any evidence about a 

symmetry of these phenomena), it is possible to predict from ME physical effects which 

would depend from an absolute velocity, and this shows that the observation at the beginninf 

of section 2 - in no field has one ever discovered any dependence of the forms of the laws of 

physics on the velocity of the reference frame - is wrong (at least from a theoretical point of 

view, but the assertion appears to be theoretical, and not experimental). 

** - Electrodynamical experiments (charges-and-currents) to test SR have been 

undeservedly neglected, to our actual knowledge, in favour of optical ones, and they 

moreover (of both kinds) have never (or seldom) been performed in moving laboratories with 

respect to the Earth. 

These statements should "prove" our assertion that SR has not been tested so much as it is 

usual to claim, by those physicists who appear anxious to persuade their audience that 

Einstein was the greatest scientist of all times, and that a doubt about SR would be the same 

as a doubt about the Copernican system 40 . 

3 - An (Impossible?!) Gedankenexperiment with Moving Clocks 

There is little doubt that one of the most impressive, and counter-intuitive, consequences of 

SR, is the so called time dilation, which could be roughly 41 expressed as (from the same 

Internet group discussion quoted before, in section 2): 

The lengthening of the period of a moving clock in the ratio γ = 

1 

1 − β 

2 

.

It would be quite better to say that, for any observer Ω , the time interval Δτ which has 

elapsed for Ω between two events E , F in its life is equal to: 

(22) Δτ = 1 2 

− ds 

c 

F 

∫ 

E 

(where ds 2 is the pseudo-metrics of Minkowski space-time), 

and that, when expressed in any Lorentz coordinate system K(x,y,z,t) , then (22) becomes: 

F 

∫ = 

E 

1 F 

2 2 

− + 

c E 

(23) Δτ = 1 2 2 2 

− dS + c dt 

c 

∫ v c dt = ∫ 1 − β 

F 

E 

2 

dt , 

since now ds2 = dx2 + dy2 + dz2 - c2dt2 = dS2 - c2dt2 , and where v = dS 

dt 

observer Ω with respect to K , and as usual β = v 

c . 

is the speed of the 

Of course, if this speed is a constant, for instance when Ω is an inertial observer, then we 

can write: 

2 

(24) Δτ = 1 − β ∫ dt 

or even: 

(25) Δt = γ Δτ , 

F 

E 

2 

2 

= 1 − β [t(F) - t(E)] = 1 − β Δt , 

which means that the coordinate time which has elapsed between the two events E , F is γ 

times the so-called proper time which has elapsed between the same two events with respect 

to Ω . 

This is all, as far as the mathematical theory of "relativistic time" is concerned. Thereafter it 

is the moment of phenomena, which go from the observed increasing of the mean-life of 

speedy particles (with respect to an Earth's laboratory), to the so called twin-paradox, which 

seems to have been experimentally confirmed by the famous Hafele-Keating clocks' travel 

around the world (an effect which is more complicated by the presence of a theoretical time 

dilation due to the gravitational potential, which must be taken into account by people which 

are confident in relativity, either special or general). 

Well, as far as this last experiment is concerned, we share the strong doubts which are 

illustrated in the very important paper by A.G. Kelly listed at the point N. 17 in the chapter 

dedicated to "Alternative Physics on Line" in this same volume of Episteme, and so we 

propose a similar test, remarking that, at least in principle, this "twin effect" could be checked 

also by comparing the time elapsed for a rotating clock (with constant speed, which makes the 

formula (24), or (25), applicable, even if we are not in front of an "inertial" clock) with a 

reference clock, which remains still in an Earth's laboratory: 

47

48 

One cannot of course hope to be able to reach very high speeds v of C' , but one could 

think to take advantage from the fact that C' could be rotated for a long period of time. If for 

instance we take for the radius R of the rotating platform R = 1 m , and an angular speed ω 

= 2πν which is corresponding to a frequency of ν = 50 Hz, then v is just about 300 m sec - 

1 , which is almost exactly the Earth's rotation speed. From the formula (24) we have Δτ = 

1 β 

2 

− Δt , which is almost equal (namely, once again, up to second order in β ) to: 

1 1 2 2 (26) Δτ ~ (1 - β ) Δt = Δt - β Δt . 

2 

2 

1 2 This last equation shows that the rotating clock C' should loose β Δt sec for each 

2 

second which is measured by the reference clock C , and since actually: 

2 v 3x10 

β = = 8 c 3x10 

= 10-6 1 1 2 -12 , β = 10 , 

2 2 

then we have that in an hour time the rotating clock should theoretically (according to SR) 

loose 18 x 10 -10 sec , which is about 2 nano-seconds, a value perhaps great enough to be 

detected (even in the Hafele-Keating test quoted above the "game" is played around a few 

nano-seconds). 

Going on with our pure theoretical (pre-experimental) speculations, what could we expect, 

from a qualitative point of view, from such an experiment? 

Well, according to SR, one should observe not only the expected time retardation, but even 

that all kind of clocks should show exactly the same slowing down. From an aethertheoretical 

point of view, instead, a time retardation is not strictly necessary; moreover, if 

there is one, then it should be explained by some "absolute" effect, namely a real physical 

effect due to the interaction of the moving clock with the aether. Along this path of thought, a 

Cartesian physicist should expect that different clocks (atomic, mechanical, etc.) could 

experience different time dilations (and, why not?, even contractions), at different rates. 

The author can hear "orthodox" physicists saying: "this experiment has to do with one of the 

phenomena which we observe every day in our particle accelerators", but we object that the 

increasing of the mean-life of a particle (and let us even accept that the corresponding rate is 

exactly the one predicted by SR, and moreover equal for all particles) is not exactly the same 

thing proposed before. As an example of a physical cause (coherent with the hypothesis of a 

dragging aether) which one could think of, in order to explain the increasing of this mean-life, 

let us give the following one, which comes from an analogy (analogies are methodologically

fundamental in Cartesian philosophy). Let us imagine an ordinary cartesian orthogonal 

reference frame, with an origin O and three axes Ox, Oy, Oz , and a rain falling down along zaxis 

with intensity s (for instance millimeters of rain for time unity: so s has the physical 

dimension of a speed). This means that, if we take a container (a tea-cup!) in form of a 

paralleliped (suppose that it has a vertex in the origin, and the three sides coming out from 

this vertex along the three axes of the given reference frame being such that the length along 

x-axis is L , along y-axis L' , along z-axis L'' ; so the volume is V = LL'L'' ), then, after a 

period of time T , we will find a volume of water inside the container which is equal to 

LL'sT . Suppose now to rotate the cup along the y-axis of an angle θ , less than 90°, and then 

ask the same question: what will be the volume of water inside the cup after a time T ? It is 

clear that the answer will be LL'sTcos(θ) , and so far so good. Suppose now that the cup - 

with sides parallel to the three axes - is moving along x-axis with a velocity v = (v,0,0) , and 

then ask once again the same question: after the same time T , what will be the volume of 

water inside the cup? It is rather clear that, from the point of view of an observer moving with 

the cup at the same velocity v , the rain will not fall anymore along the perpendicular to the 

"base" of the cup, since one must take in account a kind of "composition of velocities" 

(classical aberration, see next section!), and that the rain will fall for him along the direction 

s 

(v,0,s) , "aberrated" of an angle θ , with respect to z-axis, such that: cos(θ) = 2 2 . 

This obviously means that the case we are studying now is exactly the same as before, as if 

the cup was simply rotated along y-axis of the same angle θ , and then the answer will be 

once again: 

LL'sTcos(θ) = LL'T 

s 

2 

s 

2 

+ 

v 

2 

= LL'T 

1 

v 

1 + 

s 

2 

2 

When comparing this value with the value LL'sT found at the beginning, we find, as it was 

obvious to expect, that the water inside the moving cup is less than the water inside the 

standing cup, and, pushing further our analogy, if T = U/LL's is the time required for getting 

a given volume U of water in the standing cup, then this same time will be equal to: 

(27) T(v) = 

U 

LL' 

s 

v 

1 

s 

v 

1 

s 

2 

2 

+ 2 = T + 2 

in the case of a moving cup, a time which is bigger than T . 

Of course, we claim that we could possibly be in front of a "similar" phenomenon in the 

case we wished to "explain". Let us call T the mean-life, for instance of a muon, in a 

terrestrial laboratory: then this T will be, presumably, a function of the given particle and of 

its interaction with the "surrounding aether". Then we know that a speedy particle will appear 

to have, from the point of view of the terrestrial laboratory, a bigger mean-life, equal to: 

(28) T(v) = γT = 2 

1 − β 

T 

. 

1 2 ~ T(1+ β ) (up to second order in β ), 

2 

which is the value predicted by SR, and which we admit agrees with the experimented value. 

But let us now compare (28) and (26), by putting in the first equation, as it would be quite 

"natural", s = c . Then, up to second order in β , the two equations appear to be identical! In 

conclusion, could we be quite sure that the "true" physical reason of the discussed 

s 

+ 

v 

49

50 

phenomenon is not of the kind of the "moving cup" model, at least in absence of any evidence 

of symmetry, which would be essential for the relativistic explanation? 

Coming back to the argument of different clocks, and in view of the possible objection of 

relativity's supporters (if the proposed experiment would fail their expectations), that the 

"failing" clocks are not "good" ones, the question which must receive a clear answer is: but 

which is a "good" clock for SR? (remember that at Einstein's times atomic clocks were not 

available, not even in theoretical speculations). As a matter of fact, the answer is not difficult, 

since the only one clock which is good for relativity is the light-clock, which is described in 

the following figure (which we take, with the description below, from Marinov's book: 

Classical Physics, Part III, High-Velocity Mechanics, 1981, p. 7): 

A short light pulse (i.e., a group of photons) is generated at a given initial moment. The pulse flies ... 

to mirror B, ... it returns to A, where it puts a counter ... showing the number "1" and generates (after 

amplification) a second pulse which flies to mirror B again; after the return of the second pulse the 

counter will show the number "2"... 

It is rather clear why this the ideal, perfect clock in SR, and it is curious to remark42 that 

even from an aether-theoretical point of view a light-clock would experience some time 

dilation when in (absolute) motion through the aether. If we suppose that the absolute velocity 

is (v,0,0) along the horizontal arm of the clock43 (say that its length is L , in such a way that 

the period of the clock44 2 L 

is T = ), then the moving period would be: 

c 

(29) T(v) = 

L 

c − v 

+ 

L 

c + v 

2Lc 

c − v 

= 2 2 

= 

2L 

c( 

1 − β 

2 

) 

= T 

( 1 

1 

2 

− β 

NT 

which implies that, if one measures some time interval Δt as N = ticks with respect to 

T 

an aether-rest light-clock, then the same time interval will be measured with N' ticks with 

respect to the (absolutely) moving light-clock, in such a way that: 

(30) N' = 

NT 2 = N (1 - β ) . 

T (v) 

The previous formula can be interpreted as a time dilation effect due to the absolute velocity 

1 

v , and when compared with (26) one realizes that only a factor is missing (of course, the 

2 

same is true for (29) and (28)). If one introduces a "real" length contraction too, again due to a 

possible interaction with the aether, then one would get exactly the same factor of the 

relativistic time dilation. But since we do not have enough information whether this length 

contraction must be conjectured or not (see in this same Episteme's volume the first Larson's 

paper), we prefer to leave (30) as it is, because it gives, after all, an instructive example of 

other possible time dilations factors, not necessarily equal to the unique one predicted by SR. 

) 

,

In other words, if for instance from an aether-theoretical point of view, the previous tea-cup 

model would be able to predict a time dilation for moving atomic clocks equal to the 

relativistic time dilation, for light-clocks this dilation could be different, and so on, so on... 

In conclusion, let us repeat it, even if it was true - at least in some measure - that absolute 

speed effects are such that to imply a perfect quantitative identity with SR predictions, then all 

the same this would not mean that we are in front of identical physical theories (or of 

equivalent physical theories, as many physicists like to say), since the proper time should be 

interpreted, from the point of view of the aether physics, only as an apparent time, while the 

true time would always be only the coordinate time measured in an (absolute) aether-frame 45 . 

4 - On Relativistic Light's Aberration 

We end this paper by proposing at last an optical experiment, but not a test like the usual 

ones, aimed to measure speeds, or speeds' differences. Rather, we feel that a very important 

consequence of relativity is the so-called light's aberration, which could easily been explained 

as follows. 

Think, in a coordinate system K of Minkowski space-time as above, of a photon emitted at 

the time t = 0 along the y-axis by a light source S standing still in K , say for instance at the 

L 

, the photon will arrive in the spatial "origin" of K , the 

point (0,L,0) . Then, at the time c 

point (0,0,0) . Suppose instead that the source is moving with respect to K with some 

velocity v = (v,0,0) , and suppose to introduce a proper system K'(x',y',z',t') comoving with 

S (with spatial axes "parallel" to x, y and z). Then the photon will go along a straight line in 

L 

(now it appears, as it must in SR, the 

K' , but not in K , which implies that, at the time γ c 

time dilation factor!), the photon will meet the x-axis in the point (βγL,0,0) , and not in the 

point (0,0,0) as before. 

So, the aberration angle θ is given (in K ) by: 

β γ L 

(31) tg(θ) = 

L 

= βγ , 

or even, up to second order in β : 

v 

(32) tg(θ) ~ β = , 

c 

which is the classical formula for astronomical aberration 46 . 

A few mathematics would perhaps describe better the situation. 

Motion's equations of the photon in K , when the source is still in K : 

x = 0 , y = L - ct , z = 0 ; 3-velocity of the photon in K (0,-c,0) ; speed = c . 

Motion's equations of the photon in K' , source moving in K : 

x' = 0 , y = L - ct' , z' = 0 ; 3-velocity of the photon in K' (0,-c,0) ; speed = c . 

Motion's equations of the photon in K , source moving in K : 

v 

x' = x - vt = 0 , y = L - c(t - γ 2 ) , z = 0 

c 

51

52 

x = vt , y = L - γct + βγvt = L - γct(1 - β 2 ) = L - ct 

arrival of the photon at y = 0 : L - ct 

3-velocity of the photon in K : (v,-c 

1 β 

1 β 

2 

− = 0 , t = γ 

c 

1 β 

2 

− , z = 0 

L 

2 

− ,0) ; speed2 = v2 + c2 (1 - β2 ) = c2 . 

This relativistic analysis of aberration shows that, if it is true, according to SR, that the 

light's speed c does not depend from the source's motion (in our case from v ), then the 

light's vector velocity can depend from v . As a matter of fact, in the 3-velocity (in K ) of 

the photon the quantity v does appear explicitely, even if it disappears in the formula which 

gives the speed. 

Well, from a possibly strict aether-theoretical point of view, when supposing the 

independence of light's propagation from the "source's movement", we could think that the 

whole vector velocity would not depend from the source, and not only the speed. That is to 

say, there is possibly in this point a divergence between aether-grounded previsions and the 

corresponding relativistic previsions. So, is it possible to compare relativistic predictions with 

analogous aether-theoretical ones, outside from the realm of astronomical observations? In 

other words, is it possible to test the relativistic aberration of light in an Earth's laboratory?? 

We suggest to use a circular platform P like in the following picture: 

First suppose that P is at rest, and place a mono-directional (the most possible point-like!) 

photon's source S in the rim of the platform, near to a "fixed" point p in the laboratory. 

Direct the source towards the centre of P , in such a way that a "fixed" light's detector S* 

(once again, the most possible point-like), placed near the "antipodal" point p* of p , can 

detect the arrival of the photons emitted by S . Then, we can make the platform rotate, and 

arrange things in such a way that, in "stationary" conditions for the angular velocity of P , S 

does emit photons only when it is in front of p . The goal is to check whether S* will 

continue to detect these photons, as an aether theory would foresee, or not, as relativity would 

instead predict. That is to say, one could test whether light is really "dragged" by the velocity 

of the source, or not. 

One could even think to take both detector S* and source S fixed in the laboratory, and to 

use as a moving source a mirror M (almost possibly point-like, as before!), placed in the rim 

of P . S does emit photons directed towards the centre A of P , and these photons are 

reflected only when M passes in front of A (that is to say, with a period equal to 2πR/v = 

2π/ω - of course, from relativity's point of view, one must specify that this is the period with 

respect to the laboratory coordinate system). The trace of the backwards photons can be 

detected by a fixed screen-detector S* . 

In order to avoid S and S* to be too much close one to the other, one could think to place 

a semi-transparent mirror M' at some inessential distance from S , orthogonal to the photon 

beam, and at a distance L1 from A , in such a way that the emitted photons can pass through

M' . One could then place S* at some distance L2 from A , in order to detect the backwards 

photons reflected by the "other" face of M' , like in the following picture: 

One could even think to increase the expected effect by repeated reflections, introducing 

another "mirror" placed between the platform and the detector S* . 

It is easy to give quantitative evaluations for this Gedankenexperiment. For a given radius 

R , and a given angular speed ω , then the distance between the impact point A° of the 

inwards non-aberrated photons, and the impact point A 1 of possibly aberrated backwards 

photons would be equal, in force of (32), to: 

(33) δx = δx' + δx" = (L1+R)tg(θ) + (L1+L2)tg(θ) = (2L1+R+L2)tg(θ) , 

which is almost equal (up to second order in β ) to: 

ω R 

(34) δx ~ (2L1+R+L2)β = (2L1+R+L2) 

c 

This identity shows, first of all, that the described test would be called to measure a first 

order effect in β . For 1 meter radius, a distance L1 = L2 equal to 25 meters, an angular speed 

ω once again corresponding to 50 Herz, then, according to SR, one should have a "shifting 

effect", after just one reflection, of: 

2 

3x10 

76 x 8 

3x10 

= 76 x 10 -6 m , 

namely an effect of a few microns, which is perhaps not so small to start with. This effect 

could afterwards be emphasized - as we have suggested - and finally detected. 

It would perhaps be even better, from practical purposes, to replace the rotating platform 

with a "very sly" vertical spinning rotor - as in the following picture - in order to get always 

an angle of 90° between the inwards beam, and the reflecting mirror M : 

In such a way, the proposed "experiment" would rather be similar to the famous Fizeau 

cog-wheel experiment. Summing up, the light emitted by S is periodically reflected by M . 

. 

53

54 

Then, after a new reflection by M' , the beam hits the mirror-detector S* , from which it is 

once again reflected to M' , and so on. If SR is correct, then one should be able to appreciate 

an increasing displacement of the trace of the reflected photons, compared with the original 

one, corresponding to photons which have not been reflected (and hence are not aberrated). At 

the contrary, if the aether-theoretical prevision is correct, then one should not observe any 

displacement. The qualitative side of this last experiment could be perhaps one of its most 

attractive features 47 . 

Notes 

1 - "Special" refers to the first 1905 Einstein's theory, which did not yet include a treatment of 

gravitation (Newtonian gravitation was irremiadably out of the requested relativistic "covariance"). 

After the building of general relativity (GR), we could say that SR is the theory of a flat space-time (a 

4-dimensional connected time-oriented Lorentz manifold; in truth, to the property of flatness, one has 

to add simply connectedness and completeness in order to get the characteristic properties of 

Minkowski space-time), namely that part of relativity which does neglect gravitational effects due to 

the presence of the space-time curvature induced by matter. In this sense, SR deals only with 

electrodynamics in Minkowski's space-time. 

2 - One should perhaps emphasize that any "relativistic space-time" in GR, must be be regarded as a 

purely logical admissible construction, whose only "fault" is that it does not describe the "space" and 

"time" thought-categories which are rooted in the human mind (a statement this one with which even 

relativity supporters generally agree). Hence one can just discuss whether these new space-time (or 

others, there is no limit to abstract mathematical constructions) do correspond in some extent to 

reality, or not. This remark implies that attempts to prove that relativity is "logically inconsistent" 

(contradictory in itself) are worst than useless as arguments against relativity (one case for all, the socalled 

Dingle syllogism, see section 5 in our "Most Common Misunderstandings...", quoted in footnote 

18 in the quoted Letter...). This does not exclude, of course, that such attempts could teach, in any 

case, something interesting (see footnote 14 in that same Letter...). 

3 - We say that in the conviction that some of the usual criticism against relativity is, unfortunately, 

ineffective (see the paper mentioned in the previous footnote). 

4 - We must acknowledge that, during his many years of activity, Newton did not always push his 

criticism against Descartes up to the point to completely refuse the aether. Anyway, what does really 

matters in this discussion, is the manner in which Newton's ideas have been interpreted - and 

developed - by his followers, and not which was his original, authentic, thought about this, or others, 

argument (if there ever was such a "thought", since it could have changed from an age of life to the 

other, or could have been uncertain, undecided). The historical fact is that the hypothesis of the aether 

was dismissed after Newton in the conviction that the conception of a "plenum space" was 

incompatible with the gravitation's law which ruled the the movement of celestial bodies (see also 

footnote 10), and this is enough for our "judgement". Of course, the two conflicting options influenced 

the conjectures about the nature of the light too, which was thought of as made up of "corpuscules" in 

one case, or conceived as a "wave" (perturbation of the medium) in the other (Huyghens). 

5 - Which grounds in something like an "antinomy of the pure reason". The conception of an empty 

space does in fact correspond to the mental space of euclidean-intuitive geometry, the "space" 

regarded as a "transcendental form" of the human intellect, and it should not by any means be 

confused with the space of physical reality. 

6 - Besides, a rather old argument, expressed for instance almost in the same words by Nicholas of 

Cusa and Giordano Bruno (traces of its influence can be found even in Copernic). It was at that time 

needed in order to rebate the objection: "why the pretended Earth's movement around the Sun is not 

detected by Earth's inhabitants?". This shows that the chief argument which opposes relativity to the 

aether's physics was already fully active not only at the beginning of XVII Century, but at an earlier

date too. As we shall see, the most popular experiments alleged in favour of relativity show only that 

this pretended movement (the famous aether's wind) cannot be detected in a terrestrial laboratory. 

7 - By the way, there were already important studies about the question which gave only to him an 

unprecedented fame, see Bjerknes' book reviewed in this same volume. 

8 - Which - and this could be thought of as a "paradox" - does not include Newton's gravitation's 

theory itself, since, as it is well known, this was the first victim of the requirement that all physics' 

laws should be expressed in a covariant form. Of course, people seeing this much beloved theory 

disappear, together with the "classical" space-time which Newton too used in his work (as everybody 

else until the beginning of XXth Century!), fall in the mental trap of identifying classical physics with 

Newtonian physics, and do not realize the importance of the fact that the conception of "physical 

space" is identical in Newton's and Einstein's approach. 

9 - Even the introduction of the term "inertial" (by no means an easy concept to understand: Einstein 

in fact did not make any attempt of explanation, and just used the language of "ordinary" Newtonian 

mechanics), show the asserted conservative side of SR. 

10 - We feel dutiful a reference to the "unknown" Italian physicist Marco Todeschini, who studied 

deeply this argument, and advanced the question to investigate Newton's objections to Descartes' 

"gravitational theory", in order to realize whether they are, at the light of advanced physical and 

mathematical knowledge, still well-founded or not. See for instance some information about this 

scientist in: http://www.dipmat.unipg.it/~bartocci/todes.html (in Italian only). 

11 - And many other "implicit" assumptions, see footnote 9. 

12 - This restriction to inertial observers appears indeed a conceptual weak point of SR, since a fully 

relativistic approach should perhaps make no difference at all between "states of motion" with respect 

to nothing (see even the footnote 18 mentioned in the previous footnote 2). 

13 - One should not forget that, if Maxwell's theory is "correct" (an assertion, however, which should 

be investigated with more care: see for instance, both in this same volume, Galeczki's article, or the 

"Call for papers": Has the last word been said on classical electrodynamics?), then LSP would be a 

direct consequence of RP, since there is nothing in that theory which connects the speed of an 

electromagnetic wave to the speed of its source. 

14 - Not to say of their "accuracy", either theoretical or instrumental. Flaws appear sometimes 

unintentional, sometimes more suspicious (see for instance Kelly's paper mentioned in section 3). One 

of the most interesting examples of this situation, is the analysis of Michelson-Morley's experiment 

made in: Marco Mamone Capria, Fernanda Pambianco, "On the Michelson-Morley Experiment" 

(Foundations of Physics, 24, 6, 1994), or the refusal of subsequent Miller's results - obtained during 

many repetitions of this same experiment - which is discussed in DeMeo's paper listed at the point N. 

6 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. We 

consider worth of attention under this point of view many papers by the (well known as a critic of 

relativity) Italian physicist Roberto Monti, in particular his "Theory of Relativity: A Critical 

Analysis", Physics Essays, Vol. 9, N. 2, 1996, pp. 238-260 (see also his papers published in Episteme 

N. 3 and N. 4). 

15 - The Earth's revolution speed is about 30 km/sec , and it was not detected for instance by 

Michelson and Morley, Trouton and Noble (see section 2.C), and many others. The Earth's rotation 

speed in the 24 hours is a more likely candidate for this detection, and it is about 300 m/sec , so an 

hundred of times less than the previous one, which implies that, for experiments of-second order in β, 

the factor β 2 = v 2 /c 2 becomes 10.000 times less. We believe that this could be the reason for the 

experimental "anomalies" pointed out for instance in Van Flandern's paper about GPS (see this same 

volume of Episteme), but the trouble is that the "detection" of this speed (already realized by 

Michelson-Gale's experiment, or by variations of Sagnac-kind experiments) would easily be 

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56 

considered uninfluential to our purposes by relativity's supporters, since it does concern non-uniform 

motions! 

16 - See for instance Alessandro Moretti: "L'universo intellegibile, ovvero, la gravità descritta da 

Leibniz", in Episteme N. 3 (2001) (in Italian only). 

17 - One of the very rare exceptions is the experiment that the Dutch meteorologist Buys-Ballot (1817- 

1890) "conducted in order to confirm the Doppler shift. "He put a group of 

musicians on a train and took up his position on a station platform. He asked the train driver to rush 

past him as fast as he could while the musicians played and held a constant note, and was able to 

detect the Doppler shift (as a change in pitch) as the train passed him (D. Filkin, S. Hawking: Stephen 

Hawking's Universe: The Cosmos Explained, BasicBooks, New York:, 1997, p. 65)". From: 

http://scienceworld.wolfram.com/physics/DopplerEffect.html . 

18 - From the title of the chapter: "Special relativity: Beyond a Shadow of a Doubt", in: Clifford Will, 

Was Einstein right?, Oxford University Press, 1988 - quoted also in the Letter... which opens this 

volume. 

19 - See for instance Pyenson's book, quoted in the aforesaid Letter... (previous footnote). 

20 - We repeat that it seems necessary to accept as a fact the failure of too many experiments aimed to 

detect an "appreciable" aether's wind in a terrestrial laboratory, and so we confess to have some 

suspicion towards those people who claim for instance to have proven the existence of an Earth's 

absolute movement of almost the same amount of the famous speed with respect to the background 

radiation (and of course these numerical evaluations have been given only a posteriori). 

21 - See for instance: Giuseppe Antoni, Umberto Bartocci, "A Simple 'Classical' Interpretation of 

Fizeau's Experiment", Apeiron, Vol. 8, N. 3, July 2001 (available on line at: 

http://www.dipmat.unipg.it/~bartocci/fizhoek.html ). 

22 - Robert Resnick, Introduction to Special Relativity, Wiley, New York, 1968. 

23 - It is very famous the alleged Hilbert's remark: "Physics is too important to be left to physicists" 

(see for instance Pyenson's book quoted in footnote 19, p. 183). Unfortunately, from one side it is true 

that theoretical physics should always be carried on with all the logical exactitude which 

mathematicians display in their researches. For instance, it is surprising to see how often physicists 

assert that something cannot be done, giving as only proof the fact that they did not succeed in doing 

that, when it is well known that any assertion of this kind in mathematics is very difficult to prove (a 

good example: Paul Cohen's 1963 proof of the independence of the so-called "continuum's hypothesis" 

from the Zermelo-Fraenkel-Skolem axioms for a set theory; or perhaps, even better known, Galois' 

proof that it was not possible to give a "general" formula for the solutions of an algebraic equation 

with degree greater than 4, it would have been certainly not enough to claim this impossibility on the 

basis that mathematicians did try for some time to find this formula, and that they did not find it!). But 

from the other side, it is even true that mathematicians have in many recent circumstances shown 

themselves perhaps worst, with their propensity to aesthetical canons, formalistic abstractness, etc., 

and that these propensions are one of the not minor causes of the physical "philosophy" we are 

criticizing (see again Pyenson's book in footnote 19, or, of the present author: "'Cattivi maestri', 

ovvero, a proposito di un morbus mathematicorum (ma non solo!) recens", at the web page: 

http://www.dipmat.unipg.it/~bartocci/st/goedel6.htm - in Italian only). 

24 - G. Cavalleri, L. Galgani, G. Spavieri, G. Spinelli, "Esperimenti di ottica classica ed etere - 

Experiments of classical optics and aether", Scientia, Vol. 111, 1976, pp. 667-673. 

25 - We should perhaps explicitely remark that in this theory could even happen that observers in 

effective relative motion could be both in absolute rest, a situation which implies that all aetherframes, 

or rest-frames, should be considered only as local ones.

26 - "The special theory of relativity grew out of the Maxwell electromagnetic equations. So it came 

about that even in the derivation of the mechanical concepts and their relations the consideration of 

those of the electromagnetic field has played an essential role" (A. Einstein, "Elementary Derivation of 

the equivalence of Mass and Energy", Bulletin of the American Mathematical Society, 41, 1935). See 

the second Bjerknes' paper in this same volume of Episteme. 

27 - "Symmetries and Asymmetries in Classical and Relativistic Electrodynamics", with Marco 

Mamone Capria, Foundations of Physics, 21, 7, 1991; availabe on line at: 

http://www.dipmat.unipg.it/~bartocci/symm.html . 

28 - Einstein's source was very likely Alfred Föppl's: Einführung in die Maxwell'sche Theorie der 

Elektricität, 1894, but this case was well known to Maxwell himself (A Treatise on Electricity and 

Magnetism, 3rd edition, 1892, p. 601). 

29 - See for instance: G. Cavalleri, G. Spavieri, G.Spinelli: "On the Action and Reaction Principle in 

Special Relativity", Nuovo Cimento B, 5, 1988; G. Spavieri: "Proposal for Experiments to Detect the 

Missing Torque in Special Relativity", Found. of Phys. Lett., 3, 1990. 

30 - Some people question whether even Marinov did really perform all the experiments he claimed to 

have done, or whether they were "professionally" performed, which is perhaps true, at least to some 

extent. But this could be so only because Marinov, after his exile from Bulgaria, was a poor man, and 

did everything with his own money and enthusiasm, not having access to public funds, often not used 

in the best way by luckier establishment's physicists. As far as the strictly experimental situation is 

concerned, we should perhaps add that Marinov did not use an electric coil, or a magnetic needle, in 

order to try to detect the torque which was, at last, missing, and that he claims to have used an Hall 

detector. 

31 - The solution below gives the "right" behaviour of fields E and B at infinity, and excludes the 

so-called advanced potentials as having no possible physical meaning. We could perhaps point out 

that Roberto Monti (see footnote 14) remarks that in equation (2) it should be added a term σ0E , 

where σ0 is the possible vacuum conductivity, and that the conventional present-day choice of 

putting σ0 = 0 is not experimentally so well established as it should be. Even if this observation, in 

case it was experimentally confirmed, would destroy all pretended covariance of Maxwell's 

electrodynamics, one must acknowledge that in non-cosmological contexts (such as the ones we shall 

be dealing with) σ0 seems to be really negligible. In other words, that this would be one of those 

possible violations of SR on a large scale which would not worry relativity's supporters (see also 

footnote 11 in the often mentioned Letter...). 

32 - See for instance the celebrated Feynman Lectures on Physics, Addison-Wesley Publ. Co., 1965, 

"Electromagnetism and Matter". The author warns (21-5) that it is not so trivial to get (14) and (15) 

from (11) and (12), since at first sight "almost everyone" would claim that after integration it should 

appear, in the denominator of the fractions, the retarded distance (namely, the distance from the point 

in which the charge is seen at the time t), which is not the case. We could perhaps emphasize that the 

distance which appears in (14) and (15), and the "ordinary" distance , differ only up to second order 

in β , but their difference - which a physicist willing to uncautiously approximate computations since 

the beginning, and not only at the end, would risk to neglect! - is essential to further developments. 

33 - One should perhaps meditate about the circumstance that this possible factual divergence between 

classically interpreted and relativistic Maxwell's electrodynamics is in principle meaningful even for a 

small length of the rod, or for a "low" absolute speed v . 

34 - But see also the analysis and the experimental results mentioned in the paper listed at the point N. 

17 in the chapter dedicated to "Alternative Physics on Line" in this same volume of Episteme. As far 

as Trouton-Noble's type experiments is concerned, see also the paper by G. Spavieri, et al., again in 

this same volume. 

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58 

35 - In the calculation which leads to formula (20) we did use the fact that Φ = 0 , and then ∇Φ = 0 . 

This is the so-called Clausius' postulate: "For a circuit in which is flowing a stationary current, the 

charge density is zero" (another electromagnetic "principle" which is not explicitely stated in ME). 

Recent reports (for instance: O. Jefimenko, "Demonstration of the Electric Fields of Current-Carrying 

Conductors", Am. J. of Phys., 30, 1962; T. Ivezic, "The 'relativistic' electric fields produced by steady 

currents: comparison with experiments", Phys. Lett. A, 156, 1-2, 1991; A.K.T. Assis, W.A. Rodrigues, 

A.J. Mania, "The Electric Field Outside a Stationary Resistive Wire Carrying a Constant Current", 

Foundations of Physics, 29, 1999), both experimental and theoretical, have questioned its validity, but 

this would not change the essence of the present discussion. As a matter of fact, both classical and 

relativistic Maxwell's electrodynamics should take into account the same modification, and moreover 

a charge situated right in the centre of a circular circuit should not be affected by the force arising 

from this nonzero electric potential, apart from "asymmetries" in the circuit (not to say of the fact that 

the special features of the force (19) could be, at least in principle, allow its detection between other 

forces). 

36 - It is perhaps useful to remark that the charge continuity equation does hold for these classical 

values of the density charge and of the density current, as well as it does hold for the corresponding 

relativistic values. 

37 - By the way, as one should always expect: mathematics can never give explicitely at the end 

anything more than it had in itself implicitly, in the original assumptions one started from! 

38 - Umberto Bartocci, Marco Mamone Capria, Luigi Mantovani; see Umberto Bartocci: "On a 

Possible Experimental Discrimination Between Classical and Relativistic Electrodynamics", 

Proceedings of the International Conference "What Physics for the Next Century?", Ischia, 1991, Ed. 

Andromeda, Bologna, pp. 88-94. 

39 - Umberto Bartocci, Fabio Cardone, Roberto Mignani: "New electromagnetic test of breakdown of 

local Lorentz invariance: Theory and experimental results", Foundations of Physics, Vol. 14, N. 1, 

2001 (see point N. 10 in: http://www.dipmat.unipg.it/~bartocci/listafis.htm, with figures). 

40 - Tullio Regge, Cronache dell'Universo , Ed. Boringhieri, Torino, 1981. 

41 - This is indeed a popular description of time dilation, but we find it misleading - that is to say, a 

source for possible misunderstandings - to speak of a "moving clock", since in Minkowski's spacetime 

nothing is really "moving" (space and time are "tied" together, and can be untied only in 

particular coordinate systems), and so the period of a clock remains always unchanged. 

42 - As it is curious to remark that the ideal clock of SR (which, as far as our actual knowledge, has 

never been realized in practice!) cannot be thought of as point-like, since a length is necessarily 

required (one could object that any real clock cannot be thought of as point-like, but here the question 

is different, since the light-clock has even a privileged direction). This shows that, at least in principle, 

it is not possible to think of a light-clock in an accelerated frame (for instance in the "rotating 

platform" of Sagnac's experiment: see section 3 in "Most Common Misunderstandings...", quoted in 

footnote 2), without meeting serious conceptual troubles. This observation refers for instance to the 

well known difficulties of SR when one wishes to introduce in it some "simple" physical concepts, 

like for instance the concept of rigid body. 

43 - Not fortuitously we have decided to neglect to analyse any "transversal" motion of the lightclock's 

behaviour from the point of view of an aether theory! It is clear that to discuss this question 

would be exactly as to discuss the Michelson-Morley experiment, and we have serious doubts about 

the correctness of its usual theoretical descriptions (see for instance the paper by Mamone Capria and 

Pambianco quoted in footnote 14). It is obvious that, at least in the case of high absolute speeds, a 

light-clock should in general simply cease to work. 

44 - This period of time is quite suggestive, since it would imply that, thought of a minimum possible 

length (an hypothesis rather natural in the fluid-dynamical conception of space), call it for instance a

metron, then one would have as a consequence a minimum possible time, call it for instance a cronon: 

1 cronon = 1 metron / c . Just to give an idea of the possible quantitative size of these units, if we 

conjecture that a metron has something to do with the so-called Planck length, whose magnitude is 

about 10 -35 m , then the cronon would be about 10 -43 sec . 

45 - About the supposed equivalence of different physical theories (would the pretended equivalence 

mean that all possibly conceivable experiments should give the same result? Or that this would be true 

for only some of them??), it is rather instructive the reading of: Gianfranco Spavieri, "Nonequivalence 

of Ether Theories and Special Relativity", Physical Review A, 34, 1986. 

46 - This light's relativistic aberration was studied by Einstein since his first 1905 paper, since he had 

to explain the known phenomenon of the annual stellar aberration, discovered by James Bradley in 

1728. As a matter of fact, this phenomenon could have thought of, at first sight at least, a physical fact 

contrary to relativity's principle. We have to admit that Einstein seems to have succeeded in his 

purpose, and that annual stellar aberration has a good relativistic explanation too - that is to say, one 

must even admit that this phenomenon has - and it had before Einstein - other "classical" explanations. 

In truth, this is a rather controversial argument, and are numerous the Einstein's critics which assert 

instead that SR cannot provide a good explanation for astronomical aberration (see for instance: 

Thomas E. Phipps Jr., "Relativity and Aberration", Am. J. Phys., 57 (6), June 1989). The point is that, 

according to SR, only the relative speed between the Earth and the moving star should be the reason 

for the observed phenomenon, while all stars appear equipped with the same aberration, which does 

depend only from the Earth's revolution speed v around the Sun. This is of course wholly correct, but 

the point is that, always according to SR, the phenomenon does depend from a comparison between 

two positions of the same star in a 6 months interval, when the Earth should be thought of in an 

(approximatively) inertial frame K' different from the one K in which it was 6 months early ( K' is 

then moving with respect to K with a speed 2v ). If this argument appears able to "save" SR, at least 

on this question, and in general, one could object that the indispensable hypothesis for the relativistic 

explanation of stellar annual aberration is that the relative speed Earth-star does not change 

significatively in this 6 months time, and that this could not be always the case, for instance when 

dealing with binary stars, which have a revolution period comparable with that of the Earth, but show 

the same aberration of all other stars. At this point, relativity's supporters find another ad hoc 

explanation for these stars, etc., and the question does not appear settled once for all (but see the 

chapter dedicated to aberration in Reflections on Relativity, http://www.mathpages.com/rr/s2-05/2- 

05.htm). 

47 - For instance one could think to invert the rotation of the platform, or of the wheel, and to see what 

happens: that is to say, whether there is "symmetry" in the observed patterns (the case in favour of the 

aether hypothesis), or not (which would be the case in favour of SR). Needless to say, one should 

discuss many more practical details of this "experiment", such as the necessity to provide for a 

suitable photon source, since a "real" laser beam is much more similar to a divergent cone, rather than 

to a cylinder, as one should instead need in the actual case. These practical imperfections 

notwithstanding, a SR supporter should yet predict that one would truly find an asymmetry in the trace 

of the photons in S* , depending on the direction of rotation. 

- - - - - 

[A presentation of the author can be found in Episteme N. 1] 


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60 

S. Tolver Preston's Explosive Idea 

E = mc 2 and the Huyghens-Leibnitz Mass/Energy Identity as a 

Heuristic Principle in the Nineteenth Century 

(Christopher Jon Bjerknes) 

Abstract. In 1875, S. Tolver Preston published a prophetic treatise, which set forth his 

arguments for the existence of an aethereal medium in space. The title of this work is Physics 

of the Ether. Its purpose is to discredit the spiritualistic concept of "action at a distance" and 

to evince the irrationality of the principle of "potential energy", and replace these mythologies 

with "physical causes capable of rational appreciation." Among the many achievements of 

this heuristic masterpiece are Preston's arguments for atomic energy, the atomic bomb, a 

luminal speed for the propagation of gravity, and the heuristic principle that E = mc 2 . 

Introduction 

Samuel Tolver Preston [b. 1844, was the son of Daniel Bloom Preston (b. 1807) and Mary 

Susannah Tolver] set forth arguments in the nineteenth century, which were to condition life 

in the twentieth century, and beyond. In an early attempt to apply Herbert Spencer's "Social 

Darwinism" in a constructive way (as opposed to the horrific racism it furthered), Preston 

argued for the collegiate education of females, on the grounds that it would strengthen the 

genetic stock of males and generally increase the intelligence of human beings.[1] This 

opposed the longstanding tradition that the Church is the bride of Christ, and is obedient; and, 

therefore, a woman must obey her husband and shun professional work. In a letter to Darwin, 

Preston professed rationalistic words to the effect of, "self-interest as a motive for conduct is a 

thing to be commended - and it certainly [is] I think ... the only conceivable rational motive of 

conduct: and always is the tacitly recognized motive in all rational actions."[2] Preston's 

equally pragmatic aether theories led him into diverse fields. For example, Preston speculated 

on the nature of "Free Will" and brain dynamics - another of his scientific challenges to the 

religious ontology and traditions pervasive in his time.[3] 

Preston's profound physical insights were the result of a rational analysis of 

phenomena he conducted in the refined language and images of the eighteenth century 

homme d'esprit George-Louis Le Sage. Preston's work was in part a self-described scientific 

reaction to contemporary "theories of a vague nature" which proposed "phantom agencies" to 

account for known phenomena. His Physics of the Ether [4] is a scientific synthesis derived 

from the hypotheses that aether is rarified mass, mass, concentrated aether; and that aether 

particles must be in motion and this motion is conserved. For Preston, as for many of his 

contemporaries, all things are modes of motion. These premises evolve subtly into a 

definition of terms, identities, and mathematical expressions described in compelling prose, 

which assert, among other things, that energy is proportional to mass times the speed of light 

squared, yielding incredibly potent kinetic effects, 

"165. To give an idea, first, of the enormous intensity of the store of energy attainable by 

means of that extensive state of subdivision of matter which renders a high normal speed practicable, 

it may be computed that a quantity of matter representing a total mass of only one grain, and 

possessing the normal velocity of the ether particles (that of a wave of light), encloses a store of 

energy represented by upwards of one thousand millions of foot-tons, or the mass of one single grain 

contains an energy not less than that possessed by a mass of forty thousand tons, moving at the speed 

of a cannon ball (1200 feet per second); or other wise, a quantity of matter representing a mass of one

grain endued with the velocity of the ether particles, encloses an amount of energy which, if entirely 

utilized, would be competent to project a weight of one hundred thousand tons to a height of nearly 

two miles (1.9 miles)." 

Towards a Comprehensive Theory of Dynamics Based on Motion as a 

Unifying and Vivifying Cause 

Preston set a high standard for his work, which many today would consider naïve, 

"there can exist but one correct method of viewing any subject or question whatever." Before 

we can come to understand Preston and evaluate the nature of his conclusions and determine 

his method for arriving at them, we should first explore the historical context, which led him 

to question the mythologies prevalent in his day, and to propose alternative points of view 

based on a Le Sagian materialism, which originally arose as a materialistic exposition on the 

Epicurean theory of "universal attraction".[5] 

Le Sage argued that if space were to contain an extremely fine particulate aether of 

"ultramundane particles" moving at light speed in all directions, these particles would 

bombard bodies. In the case of a comparatively isolated body, the bombardment would, 

statistically, be even on all sides, and a sort of equilibrium pressure would result. However, 

bodies would cast "shadows" on other bodies by blocking out those "ultramundane" aether 

particles which strike them. This proposed shadowing effect would cause a net force of 

attraction between bodies, in conformity with Newton's inverse square law. 

In Preston's day, as today, there was a lingering religious opposition to any such 

mechanistic exposition on the cause of gravity, which would obviate the governance and 

active intervention of God as the cause of gravity. Many, Roger Cotes, Richard Bentley and 

Voltaire, among them, considered the idea of "universal attraction" to be a scientific proof of 

the existence and active governance of God. Just as the Church had opposed any refutation of 

Aristotle's Physics and Metaphysics, religious extremists opposed and oppose any mechanistic 

exposition on a proposed cause of "mutual attraction". This corrupt attitude toward pure 

science, which is an offense against religious freedom, not an expression of it (Descartes, 

Huyghens and Leibnitz, who were vocal advocates of aethereal gravitational theories, were 

deeply religious men), is exemplified by Bentley's A Confutation of Atheism from the Origin 

and Frame of the World, written pursuant to Newton's letters,[6] 

"And first as to that ordinary Cant of illiterate and puny Atheists [***] That such a mutual 

Gravitation or spontaneous Attraction can neither be inherent and essential to Matter; nor even 

supervene to it, unless impress'd and infused into it by a Divine Power. (3.) That though we should 

allow such attraction to be natural and essential to all Matter; yet the Atoms of Chaos could never so 

convene by it, as to form the present System: or if they could form it, it could neither acquire such 

motions, nor continue permanent in this state, without the power and Providence of a Divine 

Being."[7] 

This religious persecution had a chilling effect on research into the physical causes of 

gravity and magnetism. The subject became and remained largely taboo, with a few notable 

exceptions. Colin Maclaurin's writings evince how lightly one had (has) to tread when 

proposing a physical theory of gravity. He was a diplomatic apologist for such an approach: 

"14. As we cannot but conceive the universe, as depending on the first cause and chief mover, 

whom it would be absurd, not to say impious, to exclude from acting in it; so we have some hints of 

the manner in which he operates in nature, from the laws which we find established in it. Tho' he is the 

source of all efficacy, yet we find that place is left for second causes to act in subordination to him; 

and mechanism has its share in carrying on the great scheme of nature. The establishing the equality of 

action and reaction, even in those powers which seem to surpass mechanism, and to be more 

immediately derived from him, seems to be an indication that those powers, while they derive their 

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62 

efficacy from him, are however, in a certain degree, circumscribed and regulated in their operations by 

mechanical principles; and that they are not to be considered as mere immediate volitions of his (as 

they are often represented) but rather as instruments made by him, to perform the purposes for which 

he intended them. If, for example, the most noble phaenomena in nature be produced by a rare elastic 

aetherial medium, as Sir Isaac Newton conjectured, the whole efficacy of this medium must be 

resolved into his power and will, who is the supreme cause. This, however, does not hinder, but that 

the same medium may be subject to the like laws as other elastic fluids, in its actions and vibrations; 

and that, if its nature was better known to us, we might make curious and useful discoveries 

concerning its effects, from those laws. It is easy to see that this conjecture no way derogates from the 

government and influences of the Deity; while it leaves us at liberty to pursue our enquires concerning 

the nature and operations of such a medium. Whereas they who hastily resolve those powers into 

immediate volitions of the supreme cause, without admitting any intermediate instruments, put an end 

to our enquires at once; and deprive us of what is probably the most sublime part of philosophy, by 

representing it as imaginary and fictitious: by which means, as we observed above, they hurt those 

very interests which they appear so sanguine to promote; for the higher we rise in the scale of nature, 

towards the supreme cause, the views we have from philosophy appear more beautiful and extensive. 

Nor is there any thing extraordinary in what is here represented concerning the manner in which the 

Supreme Cause acts in the universe, by employing subordinate instruments and agents, which are 

allowed to have their proper force and efficacy; for this we know is the case in the common course of 

nature; where we find gravity, attraction, repulsion, &c. constantly combined and compounded with 

the principles of mechanism: and we see no reason why it should not likewise take place in the more 

subtile and abstruse phaenomena and motions of the system."[8] 

Preston courageously and unapologetically confronted the religious bias and dogma 

against mechanistic theories of gravitation. He cautions us to not "attach two ideas to [a] 

fundamental conception[.]" Motion is the sole cause, for Preston. He also notes, regarding 

theories of a vague nature, "that their very vagueness, in which their real weakness consists, is 

employed as a defence against argument: hence the long life of such theories." This is a 

reaction against the vague and "spiritualistic" notion of "action at a distance" as a "cause". 

The cause of gravity is to this day considered by some a divine mystery not meant to be 

understood by humankind. 

Consider Cotes' preface to Newton's Principia, where he intimates that the search for a 

physical cause for gravity, as opposed to a blind faith in (mythological and numerological) 

theological forces, is heresy. Cotes, seemingly together with Newton, asserts that induction 

resolves gravity to the will of God as the ultimate cause of the phenomenon, 

"Without all doubt this World, so diversified with that variety of forms and motions we find in 

it, could arise from nothing but the perfectly free will of God directing and presiding over all. [***] 

All sound and true philosophy is founded on the appearance of things; which if they draw us never so 

much against our wills, to such principles as most clearly manifest to us the most excellent counsel 

and supreme dominion of the All-wise and Almighty Being; those principles are not therefore to be 

laid aside, because some men may perhaps dislike them. They may call them, if they please, miracles 

or occult qualities; but names maliciously given ought not to be a disadvantage to the things 

themselves; unless they will say at last, that all philosophy ought to be founded in atheism. [***] He 

must be blind who from the most wise and excellent contrivances of things cannot see the infinite 

Wisdom and Goodness of their Almighty Creator, and he must be mad and senseless who refuses to 

acknowledge them.[9] Newton's distinguished work will be the safest protection against the attacks of 

atheists, and nowhere more surely than from this quiver can one draw forth missiles against a band of 

godless men."[10] 

Voltaire, also, threatened those who would attempt a Cartesian exposition on gravity, 

"The cause of this cause is among the Arcana of the Almighty. 'Procedes huc, et non amplius.' 

(Thus far shalt thou go, and no farther.)"[11]

Preston's fundamental conception is that all things transform as modes of motion 

through the impact of particles. These hypothetical particles bear the measurable properties of 

inertia, momentum and energy, and "fill" an otherwise void cosmic "empty space". There is a 

tacit monadism lurking in Preston's ideas, which he leaves largely unexplored. He argues 

through induction that the gaseous nature of his aether filling "space" is self-evident and need 

not be explained in terms of frames of reference, or contained volumes, other than as 

ontological absolutes. It is this absolutism, which ultimately leads him to predict that E = mc 2 , 

as an absolute store of energy contained in material bodies, which can be put to work. 

For Preston, as for Huyghens and Leibnitz, the identity between mass and energy is 

the mode of motion. He argues that "action at a distance" is an impossibility, which requires 

the "absurd postulate of an infinite velocity[.]" He further argues that the concept of "potential 

energy" is devoid of meaning, because it asserts energy without motion, and confuses terms 

by equating, in name only, one state with a completely different state. A living person can 

potentially die, and become a dead person, but such a fact does not render a living person, 

dead. The state of a mass in a field of force is not the same as the state of a mass in motion, in 

terms of the ability to do work. Should a field of force composed of a shower of aether 

particles impart motion to a body, then it is this conserved motion which is cause, not spiritual 

"potential" which is cause. 

Preston substitutes the action of an intervening medium for the two myths of "action at 

a distance" and "potential energy", which he finds feed off of one another, the fall of one 

necessarily toppling the other. He attempts to logically prove that the conservation of energy 

is only satisfied by supposing that the aether is a gas of particles in linear motion, which 

expand to fill any contained volume. The "forces" of Nature result from contact with these 

moving particles of aether. The velocity of these particles cannot be infinite, for if it were, 

then the aether particle which causes the phenomena of gravity and magnetism would have to 

concurrently occupy the beginning, middle and end of its journey, an impossibility. 

Preston induces the elasticity and speed of aether particles, which of logical and 

experimental necessity (by analogy to an aeriform medium) must be in motion, from the 

speed of light. He does not delve into the metaphysics of why his proposed aether particles 

move at light speed, but instead infers this speed as a logical necessity, his necessary singular 

exposition of the known phenomena, his ultimate generalization arrived at through induction 

from known experimental results. 

We see here many of the elements of the theory of relativity, stated in scientific terms, 

as opposed to the metaphysics, which later replaced the scientific hypotheses of this aether 

theory. "Action at a distance" must occupy time, due to the fact it is through the action of an 

intervening medium that the effects known as "action at a distance" arise. This speed is the 

normal speed of aether particles, known through induction to approximate the speed of light - 

gravity propagates at the speed of light, a speed which nothing can exceed, for speed depends 

upon the size of a particle and an aether particle is perhaps the smallest fathomable 

subdivision of matter, and the fastest motion. Preston induces these Le Sagian ideas from the 

properties of light propagation. Le Sage simply wrote, "we assume for the [gravitational] 

corpuscles the velocity of light[.]" 

From these basic inductions to general principles, Preston begins to synthesize these 

generalizations into fantastic and useful conclusions, 

"The above deduction, as to the high speed of the ether particles in their normal state, throws 

at once a light upon the existence of a vast store of energy in space of a very intense character, 

competent to produce the most forcible observed molecular motions, such as the phenomena of 

chemical action, combustion, the explosion of gunpowder, and other remarkable cases of the 

development of motion or work, all such effects finding their explanation in an interchange of motion 

between the ether and the molecules of matter under special conditions[.]" 

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The bombardment of aether particles flying about in space, each with great energy due 

to their high velocity, produces an enormous pressure in space. Taking note of the fact that the 

tensile strength of steel wire is enormous and again appealing to reason, Preston holds that 

matter cannot cohere with the immense force it does if it is simply composed of isolated 

masses suspended in empty space. There must be a "material agent" which causes this effect, 

which effect Preston attributes to a pressure differential, as a logical necessity, 

"As to the precise physical process by which a reduction of the pressure of the intervening 

medium can take place in the presence of vibrating matter, we shall reserve the consideration of this 

point for the present; but it may be noted that the inference is none the less essential, that a reduction 

of the ether pressure does take place in the presence of the opposed vibrating molecules of the wire, 

since there remains no other conceivable means of explaining in a realizable manner why these 

portions of matter (molecules), already completely disconnected from each other in the normal state of 

the wire, should require this enormous force to shift their positions in the act of breaking the wire, 

unless in this act there were something further to be accomplished than merely to change the positions 

of molecules in space. [A change in position of the wire itself, without breaking it, requires no such 

powerful force.]" 

Preston goes on to attribute the pressure differential to a rarefaction of the aether 

between vibrating bodies caused by "stationary waves" between them, "We have observed 

that a vibratory movement of matter, under such conditions that the waves are reflected and 

thereby stationary vibrations are formed in the medium, is well qualified to disturb the 

equilibrium of pressure of the medium," and makes clear that he does not see cohesion as the 

ultimate pressure differential between normal volume elements of aether and of vacuum; and 

he gives the example of chemical bonds as a state of pressure differential far exceeding the 

force of cohesion. His inferences again and again produce an increase in force commensurate 

with a reduction in scale. The subdivision results in the attenuation of matter into aether 

particles, as a limit. He sets a figure of, "500 tons per square inch as a limiting value for the 

ether pressure". 

Again, there is no metaphysical attempt to delve into the cause of the normal velocity 

of aether particles, but Preston does tacitly and ontologically assume a quite vaguely defined 

frame of reference for this velocity. This ontological belief, and Preston's attitudes toward 

mechanics, truth, and his epistemological agenda, would today be considered by many to be 

naïve and circularly reasoned; but they nevertheless produced predictions which have been 

borne out by technological advances in the twentieth century; and one seriously doubts that 

these predictions would have arisen in relativity theory, other than as a thinly veiled repetition 

(without attribution) of the conclusions drawn by Preston, Olinto De Pretto [Editor's note: see 

for instance Umberto Bartocci, Albert Einstein e Olinto De Pretto: la vera storia della 

formula più famosa del mondo, Ed. Andromeda, Bologna, 1999; information on line: 

http://www.dipmat.unipg.it/~bartocci/listast.htm, points 9 and C] and others, through 

relativity theory's more complicated ontological fictions, which have no inductive 

justification, and which reify purely abstract conceptualizations of dimension. In contrast to 

relativity theory, Preston's ideas are based on quantifiable measurements, on measurable 

relations, ultimately resolved into the most scientific expressions of our empirical sensual 

experience, the sense of resistance to touch, which is "pressure" and "matter", as a measurable 

thing; and the separation of distance through time, which velocity constitutes a measurable 

relation. Preston proposes a dynamic "material agency", the aether. 

Preston derives the density of the aether. This is quite significant to his later 

derivations of the store of energy contained in the density of matter, and the powerful effects 

which he predicts will occur should matter be subdivided into aether particles, 

"In connection with this subject, it may be of great interest to contemplate the possibility of 

the following as a physical problem. If we suppose a given mass of matter and a given volume of

space, the volume of the space being supposed vastly greater than that of the mass of matter. Then it 

becomes possible, by the subdivision of the this mass of matter (which may be readily conceived to 

carried out to any extent), to pervade the entire volume of the space with matter, or there is no limit to 

the degree of close proximity into which the particles of matter pervading this space may be brought 

by continuous subdivision, the approach of the particles going on continuously without limit as the 

subdivision progresses. Thus, with a given mass of matter there is no limit to the extent of space that 

may be pervaded by matter by continued subdivision, or there may be no appreciable portion of the 

vast volume of space but what contains myriads of particles of matter. The normal state of this finely 

subdivided matter may be conceived to be a state of motion or a state of rest; if a state of motion, then 

we may observe the physical possibility of the existence of a store of energy of an extreme intensity, 

and which, from the minuteness and small length of path of the moving particles, must be concealed; 

this motion being also necessarily attended by the production of an intense and at the same time 

evenly balanced pressure, the smoothness and uniformity of the pressure, and the consequent 

concealment of its existence from the senses, being more and more complete as the subdivision 

progresses." 

Preston concludes that the aether is made up of subdivided particles of matter, which 

conclusion is happily in agreement with the velocity and properties of light propagation. He 

infers a posteriori a relation between the subdivision of matter and an increase in the speed of 

particles, which ultimately results through the subdivision of mass in aether particles moving 

at or slightly above light speed. In a statement of the working principle of the atomic bomb, 

Preston avows, 

"If now we imagine, merely for illustration, each of these air molecules to be subdivided into a 

million parts, and that the speed of each component part has been increased a thousand times. The 

presence of the ether within the receiver may be left out of account for the present. Then by this 

imaginary process of subdivision, the mean distance of these parts of matter (which we shall term 

'particles') would be so reduced as to bring these particles into closer proximity than the molecules of 

air outside the receiver (the mean distance of the particles of the subdivided matter being inversely as 

the cube root of the their number). The pressure against the interior of the receiver, which is as the 

square of the speed of the particles, would now be increased a million-fold; and yet this result is 

attained without any increase in the absolute value of the energy of each particle, for the energy has, 

by the reduction of mass, remained precisely the same for each particle as before, although the total 

energy has become vastly greater, this energy being now subdivided among a large number of 

particles, and the pressure maintained by a greatly increased number of moving particles. 

We might imagine this process of subdivision, or this reduction of mass combined with 

increase of speed, to go on progressively, and thus the total energy would be continually increasing, 

and the mean distance and mean length of path of these small moving masses or particles would be 

continually diminishing, and therefore the concealment of this motion from the senses would be more 

and more complete. The pressure would continually rise in intensity, and at the same time become 

more even and perfectly balanced as the number of particles increased. 

We might thus imagine this process to go on progressively, until at length the dimensions, 

mean distance, and speed of the ether particles themselves had been reached; or its possible thus step 

by step to arrive at a just conception of the wonderful intensity of the store of energy that is rendered 

physically practicable, and the high static value of the pressure that may be reached, under the simple 

mechanical conditions of an extensive subdivision of matter combined with a high speed." 

The "speed of the ether particles" is that of a wave of light, and the "absolute value of 

the energy of each particle" when reduced to aether is mc 2 , which is described in Preston's 

prose in section 165 of his book, as quoted here above in the introduction. S. Tolver Preston 

provided a qualitative and quantitative theory, which set in motion the search for atomic 

energy and weaponry, a search which was ultimately successful. His contributions to science 

deserve far greater mention. Preston was indeed a man of science, who did not flinch when 

opposing the religious zealotry he confronted. We would do well to follow his example and 

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oppose "theories of a vague nature" which propose "phantom agencies" like "space-time" and 

replace them with "physical causes capable of rational appreciation." 

Notes 

[1] S. T. Preston, "Evolution and Female Education", Nature, (23 September 1880), pp. 485-486; 

Revised, Original essays. I. On the social relations of the sexes. II. Science and sectarian religion. III. 

On the scientific basis of personal responsibility, with a reprint from an essay on "Evolution and 

female education," revised from Nature, September 23, 1880, Williams and Norgate, London, 

Edinburgh, (1884). 

[2] S. T. Preston paraphrased in F. Darwin & A.C. Seward, Editors, More letters of Charles Darwin, 

Volume 2, Chapter 8, John Murray, London, (1903), p. 52, Letter 421. 

[3] S. T. Preston, "On a Point Relating to Brain Dynamics", Nature, (13 May 1880), pp. 29-30; 

Responses by G. Romanes, Nature, Volume 22, p. 75, and W. C. Ley, Nature, Volume 22, (10 June 

1880), p. 121; Reply by Preston, Nature, (10 June 1880), p. 121. 

[4] S. T. Preston, Physics of the Ether, E. & F. N. Spon, London, (1875). 

[5] G. L. Le Sage, read by P. Prevost to the Berlin Academy in 1782, "Lucrèce Neutonien", Nouveaux 

Mémoires de l'Académie royale des Sciences et Belles-Lettres de Berlin,Year 1782, (Berlin, 1784), pp. 

404-427; reprinted in Notice de la Vie et des Écrits de George-Louis Le Sage, Chez J. J. Paschoud, 

Genève, (1805), pp. 561-604; English translation by C. G. Abbot with an introduction by S. P. 

Langley appears in: "The Le Sage Theory of Gravitation", Annual Report of the Board of Regents of 

the Smithsonian Institution Showing the Operations, Expenditures, and Condition of the Institution for 

the Year Ending June 30, 1898,(U.S.) Government Printing Office, Washington, (1899), pp. 139-160. 

W. Thomson, S. Tolver Preston, H. A. Lorentz, and J. J. Thomson, among many others, pursued Le 

Sage's shadow theory of ultramundane particles. Maxwell and Poincaré opposed it, on the basis that it 

would result in excessive heat accumulation. 

[6] I. Newton, Four Letters from Sir Isaac Newton to Doctor Bentley containing Some Arguments in 

Proof of a Deity, London, (1756) [Editor's note: see also Episteme N. 5, March 2002]. Edward B. 

Davis has presented significant scholarship on Newton's religious views: "Newton's Rejection of the 

'Newtonian World View': The Role of Divine Will in Newton's Natural Philosophy", Fides et Historia, 

Volume 22, Number 2, (Summer 1990), pp. 6-20; reprinted Science and Christian Belief, Volume 3, 

Number 1, (1991), pp. 103-117; reprinted with additions Facets of Faith and Science, Volume 3, 

University Press of America, Lanham, Maryland, (1996), pp. 75-96. 

[7] R. Bentley, A Confutation of Atheism from the Origin and Frame of the World, Part 3, Phoenix, 

London, (1693), pp. 4, 20-21. 

[8] C. Maclaurin, "Of the Supreme Author and Governor of the universe, the True and Living God", 

An Account of Sir Isaac Newton's Philosophical Discoveries, Book 4, Chapter 9, Patrick Murdoch, 

London, (1748), pp. 388-390. 

[9] R. Cotes, in I. Newton, The Mathematical Principles of Natural Philosophy, London, (1729), from 

"THE PREFACE OF Mr. Roger Cotes", not paginated. 

[10] R. Cotes, Cote's preface to the second edition of Newton's Principia. Sir Isaac Newton's 

Mathematical Principles of Natural Philosophy and his System of the World, University of California 

Press, Berkeley, Los Angeles, London, (1962), p. XXXIII. 

[11] F. M. A. Voltaire, "On Attraction", Letters on England, Letter 15. 

* * * * *

[We believe it worthwhile to add an ending section about the important 

question: vis viva versus kinetic energy] 

Clash of Leibnitz and Newton Space as Meta-Aether 

There was in Preston's day an emerging rejection of the Newtonian ideas of mystical "force" 

as a cause of phenomena among "empty space". Fechner stated, 

"All that is given is what can be seen and felt, movement and the laws of movement. How 

then can we speak of force here? For physics, force is nothing but an auxiliary expression for 

presenting the laws of equilibrium and of motion; and every clear interpretation of physical force 

brings us back to this. We speak of laws of force; but when we look at the matter more closely, we 

find that they are merely laws of equilibrium and movement which hold for matter in the presence of 

matter. To say that the sun and the earth exercise an attraction upon one another, simply means that the 

sun and earth behave in relation to one another in accordance with definite laws. To the physicist, 

force is but a law, and in no other way does he know how to describe it. . . All that the physicist 

deduces from his forces is merely an inference from laws, through the instrumentality of the auxiliary 

word 'force'." [12] 

T. H. Pasley, in 1835, averred, 

"Of the nature of matter the knowledge is limited to the principle of inertia. Matter being inert 

it can do nothing and bodies formed of inert matter are incapable of acting in any manner: the want of 

power cannot originate power: hence cause must consist in means independent of action by matter. 

Matter consisting in unorganized molecules, it appeared nothing out of reason to conclude that the 

whole and all things they go to form are inert. For if a body be broken its parts are inactive, and the 

body itself to be in an acting state requires to be impelled by means such as itself does not possess. 

The inertia of matter therefore is evident. Matter being inert it cannot either attract or repel. But then, 

how is universal gravitation, acknowledged by all the most learned of the world and demonstrated 

mathematically, to be set aside, and wherein is cause of it and attraction be rejected. The difficulty is 

as great as the Authorities who make no difficulty of supporting these principles and causes are 

exalted in fame. The greatest difficulty however lies in reconciling them with the Inert nature of 

Matter. Matter has no acting properties as it is essentially inert. Acting implies being in motion; 

motion requires physical impulse foreign to that which is made to act, and from the atoms of matter 

being unalterable, by nothing but physical impulse can they be affected, nor can the effect be other 

than motion. Wherefore, gravitating, and repelling are not properties of either matter or bodies. [***] 

In moral philosophy inertia means inferior ability and ability sluggishly exerted; in Physics it signifies 

no ability or power whatever. Making inertia a 'passive power' amounts to no power; power implies 

acting, passive power not acting or that can act, but power is never passive. Inertia being an 'inert 

force' is the same as force without force: 'vis inertiae' is the force of inactivity, the power of inability. 

All bodies are convertible into powers, but are such only while being made to act. To say a body 

'resists' by means of its inertia, is making nothing a physical force. Who can conceive force at rest. 

Inertia causing 'an endeavour and perserverance in a body to continue in motion or at rest' is a 

contradiction in terms [***] Inertia is no cause, it is nothing active or passive. The resistance of a 

ponderable body at rest is caused by that which makes it ponderable. Inertia being nothing is 

productive of nothing; it may be said to be the zero of cause." [13] 

Pasley identified many of the fatal flaws in the Epicurean mythologies, for example, 

"[W]itness the Newtonian Theory of Gravitation, Attraction and Repulsion, which, it is said 

'Newton has proved to the whole world direct and regulate the System.' But as gravitating, attracting 

and repelling cannot belong to inert bodies, formed as all are of inert matter, the adopted theory, in 

these respects, is utterly fallacious and untrue. Gravitating by the Planets of their own accord is as 

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movement in the lifeless; attraction as the will of the dead; and repulsion as antipathy possessed by a 

stone. The whole of these and all such monstrocities have origin solely in the theory of Perception 

being rejected where most applicable, and in coupling Activity with Inertia." [14] 

Preston wanted to replace these myths with a physical agent, which obeyed the 

principle of the conservation of energy. Perhaps the most famous name associated with the 

principle of the conservation of energy, the foundation of Preston's natural philosophy, is 

Julius Robert Mayer. He sought a meaningful definition of the concept of "force" and this is 

likely why Preston, in working out the energy store in bodies through Joule's and Clausius' 

methods, deduced Leibnitz' vis viva, as opposed to kinetic energy,[16] as the absolute store of 

energy contained in mass. In 1807, Thomas Young defined "energy" in English as, 

"The term energy may be applied, with great propriety, to the product of the mass or weight of 

a body, into the square of the number expressing its velocity."[17] 

Mayer stated, in 1852, in an effort to provide a "generic conception of 'force,'" 

"On the other hand, the product of the pressure into the space through which it acts, or, again, 

the product - or half-product - of the mass into the square of the velocity, is named 'force.' In order that 

motion may actually occur, it is in fact necessary that the mass, whatever it may be, should under the 

influence of a pressure, and, in the direction of that pressure, traverse a certain space, 'the effective 

space' (Wirkungsraum): and in this case a magnitude which is proportional to the 'pushing force' and 

to the effective space, likewise receives the name 'force;' but to distinguish it from the mere pushing 

force, by which alone motion is never actually brought about, it is also called the 'vis viva of motion,' 

or 'moving force.' With the generic conception of 'force,' the higher mechanics, as an essentially 

analytic science, is not concerned. In order to arrive at it, we must, according to the general rule, 

collect together the characters possessed in common by the several species. As is well known, the 

definition so obtained runs thus - 'Force is every thing which brings about or tends to bring about, 

alters or tends to alter motion'. This definition, however, it is easy to see, is tautological; for the last 

fourteen words of it might be omitted, and the sense would be still the same. [***] If a mass M, 

originally at rest, while traversing the effective space s, under the influence and in the direction of the 

pressure p, acquires the velocity c, we have ps = Mc 2 . Since, however, every production of motion 

implies the existence of a pressure (or of a pull) and an effective space, and also the exhaustion of one 

at least of these factors, the effective space, it follows that motion can never come into existence 

except at the cost of this product, ps = Mc 2 . And this it is which for shortness I call 'force.'"[18] 

Preston focused on the notion of aethereal pressure (as opposed to mystical "forces" of 

gravitation and magnetism exerted upon a mass by a mass via "action at a distance") again 

and again in opting for the formulation of the absolute store of energy as E = mc 2 , as opposed 

to E = ½ mv 2 . This is perhaps due to the fact that most of the writings on the principle of the 

conservation of force from the 1840's focused on Galilean-Leibnitzian style experiments with 

falling masses. Leibnitz' arguments for a conserved vis viva against Descartes' momentum 

were initially a posteriori and depended upon experiments of gravitation on the Earth. 

However, by 1875 it was an anomaly for Preston to not see the "transference of work" done 

by a body thrown upwards against the "resistance" of "gravity" as ½ mv 2 . Preston wrote, 

"26. In considering the high normal velocity of the ether particles, it is to be expected 

beforehand that this agent must exert an extremely forcible pressure upon the molecules of matter, 

even if every allowance be made for the extreme low density of the agent; for it is important to note 

that the pressure exerted is as the square of the speed of the particles of the agent, and therefore the 

pressure rises in a very rapid ratio as the speed increases; so that taking into account this fact, in 

conjunction with the high velocity of the particles, we must be prepared to find this pressure will have 

a very high value. In looking to physical phenomena for an indication of this pressure, and also with 

the object, if possible, of arriving at a limiting value for its intensity, or the value which this pressure

must at least attain on the lowest computation, we will consider one observed fact. [***] 53. Secondly, 

it may be shown that an excess of energy is imparted to the surrounding medium by a vibrating mass 

or molecule, due to a second separate physical cause, which we shall now consider. We have observed 

that the speciality of a vibrating movement is to affect the normal velocity of the component particles 

of the medium in such a way that equal increments and decrements of velocity are experienced. But it 

is an important principle to observe, that when masses of matter experience equal increments and 

decrements of velocity so that the mean velocity remains unaltered, that, nevertheless, the energy 

being as the square of the velocity, the value for the energy does not remain unaltered. Thus, if we take 

the case of two equal masses having equal velocities, which we may express by V, the energy in each 

case being expressed by V 2 , and the total energy therefore by 2V 2 . If now we suppose one of the 

masses to receive an increment of velocity v, its velocity therefore becoming V + v, the other mass 

experiencing an equal decrement of velocity, its velocity becoming V - v; then although the mean 

value for velocity has remained unchanged, yet the value for energy has by no means remained 

unchanged, for the energy of each mass being as the square of its velocity, the total energy now 

becomes (V + v) 2 + (V - v) 2 = 2V 2 + 2 v 2 . Now the value for the total energy before this change of 

velocity took place was only 2V 2 . The total energy has therefore, by merely changing the velocities by 

equal amounts (so as not to affect the mean velocity), received a notable increase represented by the 

amount 2v 2 . This is an important point, on account of the direct and practical bearing which it has on 

the phenomena of vibratory motion; the above indicating that the change of the velocities of the 

component particles of the medium by equal amounts, which it is the special function of a vibratory 

motion of matter to effect, is itself a direct cause whereby a certain excess or surplus of energy is 

communicated to the medium. [***] 98. Important Influence of Subdivision. - One of the most 

important practical consequences following from the extensive state of subdivision, which is the 

characteristic of the molecular condition of matter, is the vast extent of surface which is thereby 

brought under the action of the ether pressure. This is a fact of importance, by a due appreciation of 

which the great energy of the action of the ether upon molecules will appear no longer discordant or 

inconsistent, but the fact may be brought into harmony with ordinary mechanical principles, this vast 

extent of surface being the fitting mechanical condition for the production of static and dynamic 

effects of extreme intensity. [***] [114] III. High Normal Speed of Component Particles. - This 

physical quality is absolutely essential to constitute a powerful dynamic agent, for without this high 

speed dynamic effects of a high intensity cannot be produced. Second, this high normal speed of the 

particles is the sole condition on which the loss of motion sustained by the ether can be replenished 

with that degree of speed which is essential to render a continuous dynamic effect of a high intensity 

possible to the ether. Third, this high speed of the component particles is the sole quality by which the 

loss of motion sustained by the ether in producing a given dynamic effect can be subdivided or 

distributed over a large volume of the ether, whereby a notable local disturbance of the equilibrium of 

the ether is prevented. Fourth, this quality is essential for the rapid interchange of motion between 

masses and molecules of matter at a distance from each other, the rapidity of intercommunication or 

exchange of motion being strictly limited by the normal speed of the particles of the intervening agent. 

Fifth, this high speed of the component particles is necessary to render possible the existence of a store 

of energy of a high value, without the encumbrance of a large quantity of matter in space. Sixth, the 

high normal velocity of the ether particles is the necessary mechanical condition to enable an intense 

pressure to be exerted by the ether upon the molecules of matter, without the movements of these 

molecules and masses being obstructed by the agent exerting the pressure. For, in the first place, by 

this high speed of the component particles an intense pressure is attainable (more especially as the 

pressure rises as the square of the speed) without the necessity for the agent being dense, by which the 

free passage of masses of matter through the agent would be obstructed. In the second place, the high 

speed of the component particles enables masses of matter to pass through the agent with the least 

disturbance of its equilibrium, or with a minimum of resistance from this cause, the agent becoming 

almost impalpable; the exertion of an intense pressure by the agent being itself the necessary condition 

to render the agent adapted to control forcibly the molecules of matter in stable equilibrium, as 

exhibited in the general phenomena of 'cohesion,' or the aggregation of the molecules of matter 

generally. The above may serve as a general summary of the special physical qualities of the ether; 

and it may be noted that if the attempt were made beforehand, as a mechanical problem or speculation, 

to devise or scheme out what special physical qualities an agent should possess in order to be 

mechanically fitted to produce the varied physical effects of the character observed, then the scheme 

of the ether would be found to constitute the only possible solution of which the mechanical problem 

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admits; or the ether may be contemplated as a piece of mechanism specially adapted to its work. [***] 

128. We shall now proceed to consider more closely the mode or general principle upon which 

physical processes effect themselves, and it will be our endeavour to show that these processes 

resemble one another in a second fundamental aspect, viz. that all these processes are cyclical, i. e. 

consist in a transference of motion from the ether through matter to the ether, or consist in a 

transference of motion from and to the same source; and therefore that all physical processes, however 

diverse and varied, are identical in this fundamental respect; or that every observed motion whatever 

came from the ether at one time, and will return to the ether at some subsequent time. This theorem 

may be shown to be a necessary consequence resulting from the fundamental principle of 

conservation. The normal state of the ether is a state of motion, or the component particles of the ether 

transfer their motions among themselves, and this motion is of necessity permanently maintained. The 

ether, therefore, constitutes a source of motion. A mass or molecule of matter, on the other hand, 

cannot possibly be in motion without continually giving up some of its motion to the surrounding 

ether, which motion is rapidly carried off to a distance in the form of waves; so that matter cannot 

possibly remain in motion, unless the motion be renewed by the ether as rapidly as it is being 

dissipated in the ether, which would constitute a cyclical process. Since, therefore, the motion of 

matter is being continually dissipated in the ether, the ether constitutes the receptacle of all the 

motions of matter. The ether therefore must, in accordance with the principle of conservation, be the 

source of all the motions of matter, for matter cannot evolve motion out of itself. Also, since matter 

cannot retain its motion, but must be always dependent on the ether for any supply of motion, matter 

therefore cannot in any case constitute a source of motion. The ether therefore constitutes both the 

source and the receptacle of all the motions of matter, or this would constitute the theorem that all 

physical processes are cyclical, or consist in a transference of motion from and to the same source, and 

accordingly that all physical processes are correlated in this fundamental respect. [***] 135. Amount 

of energy being dependent on the quantity of matter in motion and on the square of the velocity of 

motion, and since motion cannot come into existence spontaneously, or go out of existence 

spontaneously, but in accordance with the principle of conservation, the sum of energy must remain 

constant; it follows, therefore, that whenever there is a loss of motion by matter, there must be a 

simultaneous gain of motion by matter, or the loss and gain of motion must be simultaneous, for a loss 

of motion without a simultaneous gain of motion would involve for an interval of time an annihilation 

of energy. It follows, therefore, as a necessary consequence from this, that the energy expended in any 

physical process whatever can be solely dependent on and due to motion simultaneously imparted, i. e. 

imparted at the time of the expenditure of the energy; for unless motion be imparted at the time, 

energy cannot be expended at all, for to expend motion without imparting motion would be to 

annihilate energy; indeed, the motion imparted is itself the measure of that expended, and is the sole 

cause of its expenditure, i. e. motion can only be expended in the communication of motion, and in 

that fact lies apparent the principle of the Indestructibility of Motion. [***] 163. Absolute Quantity of 

Energy in the Unit Volume of Space. - We shall now consider more particularly the energy enclosed by 

the ether, with the endeavour to give some idea of the absolute value of the energy represented by the 

motion of the ether particles contained within a given portion of space, with the object, if possible, to 

fix upon a limiting value for this energy, or the lowest value consistent with what physical facts would 

require. The conditions required in order to determine the amount of energy enclosed in the unit 

volume of space are clearly, first, a knowledge of the quantity of matter in the form of ether contained 

in the unit volume of space (i. e. the density of the ether); and secondly, the normal velocity of the 

ether particles. Now, although we do not know the density of the ether independently, nevertheless 

since density is determined by pressure and velocity of component particles, if, therefore, by a known 

limiting value for the velocity of the ether particles, a limiting value for the ether pressure can also be 

fixed upon, then a limiting value for the ether density is thereby given. The limiting value for the 

velocity of the ether particles is given by the measured velocity of a wave of light. As regards the 

value for pressure, we take the estimate already fixed upon: that this amounts to 500 tons per square 

inch as the lowest limiting value. There are valid grounds for inferring that this value for pressure has 

been under-estimated; for we assumed the total ether pressure as a small multiple of the observed 

difference of pressure in the case of 'cohesion,' whereas, as before remarked, it is a known fact that the 

force required to separate chemically combined molecules must be many times greater, this indicating 

the high intensity of the controlling ether pressure, and showing that an estimate of this pressure from 

the case of 'cohesion' must be but an inadequate representation of the reality. The tremendous energy 

developed in explosives, which is the very energy of the ether itself, is a direct indication of the

intensity of the ether pressure, which is the necessary accompaniment of this energy. That this value 

for pressure has been under-estimated, a bare consideration of the dependent value for density would 

almost show, for the ether density corresponding to this pressure (1/5264800 of the atmospheric 

density) represents a density so insignificant as to be less than that of the best gaseous vacua." 

Additional Notes 

[12] Fechner quoted in H. Vaihinger's, Philosophy of the 'As if', Barnes & Noble, Inc., New York, 

(1966), p. 215; translated by C. K. Ogden. 

[13] T.H. Pasley, A Theory of Natural Philosophy, on Mechanical Principles, Divested of All 

Immaterial Chymical Properties, Showing for the First Time the Physical Cause of Continuous 

Motion, Whittaker & Co., London, (1836), Preface and pp. 145-146. 

[14] Pasley, ibid. xcii. 

[15] See for example the many works of Marc Seguin and M. F. de Boucheporn, Cf. The Correlation 

and Conservation of Forces, D. Appleton, New York, (1867), pp. 4, 76-82; W. B. Taylor, "Kinetic 

Theories of Gravitation", Annual Report of the Board of Regents of the Smithsonian Institution, U. S. 

Government Printing Office, Washington, (1877), pp. 205-282. Another good example is A. 

Anderssohn, Die Mechanik der Gravitation, Breslau, (1874); and Zur Loesung des Problems ueber 

Sitz und Wesen der Anziehung, Breslau, (1874); and Physikalische Prinzipien der Naturlehre, G. 

Schwetschke, Halle, (1894). See also: G. Hoffmann, Die Anderssohn'sche Drucktheorie und ihre 

Bedeutung für die einheitliche Erklärung der physischen Erscheinung, G. Schwetschke, Halle, (1892). 

For some, the aether become their embodiment of the Tertullian-Newtonian pantheistic God and Holy 

Wind. See, for instance, Philipp Spiller, Die Urkraft des Weltalls nach ihrem Wesen und Wirken auf 

allen Naturgebieten, Verlag der Stuhr'schen Buchhandlung (S. Gerstmann), Berlin, (1876). 

[16] G. G. Coriolis, Du calcul de l'effet des machines, ou Considérations sur l'emploi des moteurs, 

Paris, (1829). Coriolis used the term "force vive". First use of the term "kinetic energy" in English is 

perhaps by Thomson and Tait, Good Words, (October, 1862). 

[17] T. Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts, Volume 

1,Taylor and Walton, London, (1845), p. 59. 

[18] J. R. Mayer, translated by J. C. Foster, "Remarks on the Mechanical Equivalent of Heat", The 

Correlation and Conservation of Forces, D. Appleton, New York, (1867), pp. 331, 336. 

- - - - - 

Christopher Jon Bjerknes is an American historian of science, who has 

authored six books and numerous articles on the theory of relativity and on 

Albert Einstein. His most recent book, Albert Einstein - The Incorrigible 

Plagiarist, is reviewed in this same volume of Episteme. 

cbjerknes@attbi.com 

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Einstein's Irrational Ontology of Redundancy 

The Special Theory of Relativity 

and Its Many Fallacies of Petitio Principii 


Abstract. Albert Einstein's arguments were almost always fallacies of Petitio Principii. He argued 

well-known experimental results as if a priori first principles. Einstein would then induce, as if 

deducing, the well-known hypotheses of others, and deduce from these plagiarized hypotheses the 

same experimental results as conclusions, which he had first stated as premises. This was Einstein's 

modus operandi for plagiarism. In the special theory of relativity, Einstein argued light speed 

invariance, a well-known (supposed) experimental result at the time, as if an a priori first principle, 

which an empirical measurement cannot be, to then induce through analysis, as if deducing in 

synthesis, the "Lorentz Transformation" hypotheses. Einstein then used the "Lorentz Transformation", 

the true set of hypotheses of the special theory of relativity, to deduce light speed invariance as a 

conclusion, a conclusion which Einstein had already presumed as a premise. Einstein employed the 

same fallacious method in the general theory of relativity. Einstein irrationally asserted the wellknown 

experimental gravitational-inertial mass equivalence of Bessel and Eötvös as if an "a priori" 

postulate, which an experimental result cannot be, only to arrive at it as an ultimate conclusion, a 

conclusion redundant to the premise. The quasi-postivistic analyses Einstein presented by turning the 

synthetic scientific theories of his predecessors on their heads have been applauded, ridiculed and 

often misrepresented as synthetic, which they are not. 

Method 

In 1905, Mileva Einstein-Marity and Albert Einstein [1] coauthored a paper on the 

"electrodynamics of moving bodies". Fallacies of begging the question emerge even in the 

very introduction to the work. The Einsteins acknowledge in their introduction, that light 

speed invariance and the symmetry of electrodynamic phenomena were well-established 

phenomena. Well-known specific phenomena are not, by definition, "a priori" general 

concepts. However, the Einsteins asked us to abandon reason and assert specific experimental 

results and empirical observations, as if a priori general principles. In other words, the 

Einsteins engaged in an analysis of the problems of invariant light speed, and of the symmetry 

of electrodynamic phenomena in alleged violation of Maxwell's theory, which problems faced 

physicists at the end of the nineteenth century; and the Einsteins irrationally pretended that 

these two problems were solutions of themselves. 

1 Henry August Rowland stated the two main problems facing the physicists of his day, 

on October 28 th , 1899, and I have italicized that which the Einsteins would later call "two 

assumptions", or "postulates": 

"And yet, however wonderful [the ether] may be, its laws are far more simple than those of 

matter. Every wave in it, whatever its length or intensity, proceeds onwards in it according to well 

known laws, all with the same speed, unaltered in direction, from its source in electrified matter to the 

confines of the Universe, unimpaired in energy unless it is disturbed by the presence of matter. 

However the waves may cross each other, each proceeds by itself without interference with the others. 

[***] To detect something dependent on the relative motion of the ether and matter has been and is 

the great desire of physicists. But we always find that, with one possible exception, there is always 

some compensating feature which renders our efforts useless. This one experiment is the aberration of 

light, but even here Stokes has shown that it may be explained in either of two ways: first, that the 

earth moves through the ether of space without disturbing it, and second, if it carries the ether with it 

by a kind of motion called irrotational. Even here, however, the amount of action probably depends

upon relative motion of the luminous source to the recipient telescope. So the principle of Doppler 

depends also on this relative motion and is independent of the ether. The result of the experiments of 

Foucault on the passage of light through moving water can no longer be interpreted as due to the 

partial movement of the ether with the moving water, an inference due to imperfect theory alone. The 

experiment of Lodge, who attempted to set the ether in motion by a rapidly rotating disc, showed no 

such result. The experiment of Michelson to detect the ethereal wind, although carried to the extreme 

of accuracy, also failed to detect any relative motion of the matter and the ether [Emphasis Added]."[2] 

The Einsteins turned reason on its head and called these two a posteriori problems, a 

priori "postulates". The Einsteins phrased their two "postulates", as follows: 

1"1 (a). Examples of a similar kind, as well as the failed attempts to find a motion of the earth relative 

to the 'light medium', lead to the supposition, that the concept of absolute rest corresponds to no 

characteristic properties of the phenomena not just in mechanics, but also in electrodynamics, on the 

contrary, for all systems of coordinates, for which the equations of mechanics are valid, the same 

electrodynamic and optical laws are also valid, as has already been proven for the magnitudes of the 

first order. 

1 (b). The laws according to which the states of physical systems change do not depend upon to which 

of two systems of coordinates, in uniform translatory motion relative to each other, this change of state 

is referred. 

12 (a). [L]ight in empty space always propagates with a determinate velocity c irrespective of the state 

of motion of the emitting body. 

2 (b). Every ray of light moves in the 'resting' system of coordinates with the determinate velocity c, 

irrespective of whether this ray of light is emitted from a resting or moving body. Such that 

velocity = (path of light) / (interval of time) , 

where 'interval of time' is to be construed in the sense of the definition of § 1." 

Note that the first "postulate", the principle of relativity, refers only to "moving 

systems" and the second "postulate", the light "postulate", refers only to a proposed "resting 

system". Note further, that the light "postulate" refers only to a proposed source independence 

of light speed, but not to an observer independence, because this "postulate" assumes a prior 

privileged frame and medium in the 1905 paper, the "resting system". The paper later 

presumes that c' = c +/- v, relative to the "resting system". 

1Many assert that the Einsteins employed only these two "a priori postulates" in their 

theorization, as opposed to FitzGerald, Larmor, Lorentz, and Poincaré, who required the 

additional hypotheses of length contraction and time dilatation to arrive at the same 

formulation - long before the Einsteins. Ad hoc hypotheses were frowned upon at the time, 

due to Newton's admonitions against them, such that the removal of hypotheses was seen as 

an improvement. The two postulate myth is substantially and demonstrably false. The two 

postulates are not postulates, but rather are the deduced conclusions of the theory - 

summations of the supposedly observed phenomena of the day. 

After asserting the two "postulates", the Einsteins raised a straw man argument based a 

non sequitur. They asserted that the two "postulates" appeared irreconcilable with each other. 

If light speed is constant in the "resting system", then how can it also be isotropic in a 

"moving system"? This is a (manufactured) dilemma, because, in some inexplicable way, the 

Einsteins argue that the first postulate, the principle of relativity, compels that light speed 

from a given light signal be isotropic for all systems in uniform motion with each other. 

However, this is clearly a non sequitur, because the principle of relativity no more compels 

light speed isotropy for all "moving systems", then the principle of relativity requires that a 

body resting relative to one "moving system" k also rest relative to another "moving system" 

K, which is in motion relative to the first. Einstein also raised the opposing problem. How can 

light speed be isotropic in the "resting system" and also be isotropic in a "moving system"? Of 

course, these questions presume the conclusion before it has been proven, the conclusion 

being that light speed from any given signal is isotropic in the "resting system" and all 

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"moving systems", which are in uniform translatory motion with respect to the "resting 

system". To knock down these straw men, the Einsteins turned the "two postulates" into one 

"postulate", the conclusion which is sought. 1The Einsteins asserted that it is the combination 

of the two postulates, not either postulate by itself, which "deduces" c' = c between the 

moving system and the resting system, by simply asserting that c' = c, before it has in any way 

been proven: 

"It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one 

expresses by means of these equations, that light (as the principle of the constancy of the velocity of 

light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as 

measured in the moving system." 

After irrationally presuming this conclusion, the Einsteins proceeded to pretend that 

they had not presumed it: 

"Now, we have to prove that every ray of light propagates with the velocity c as measured in 

the moving system, in case this is, as we have taken for granted, the case in the resting system, 

because we still have not offered up the proof that the principle of the constancy of the velocity of 

light is reconcilable with the principle of relativity." 

However, the combination of the two postulates induces c' = c +/- v, not c' = c. One 

must take the supposed empirical phenomenon of c' = c as a point of departure for an 

inductive analysis, not a deductive synthesis, to induce a fundamental geometry, which 

fundamental geometry then deduces the identity c' = c and the covariance of the laws of 

physics, as a synthetic theory. The Einsteins averred, before any proof was offered: 

"It is easy, with the help of this result, to ascertain the magnitudes ξ, η, ζ, because one 

expresses by means of these equations, that light (as the principle of the constancy of the velocity of 

light, in conjunction with the principle of relativity, requires) also propagates with the velocity c as 

measured in the moving system. For a ray of light emitted in the direction of increasing ξ at the time τ 

= 0, the following equations are valid: ξ = cτ. . ." 

Note the non sequitur, which begs the question: That allegedly if the speed of light is 

c in the "resting system" the principle of relativity compels that it also be c in the "moving 

system"; which, without the prior hypotheses of the Lorentz Transformation, clearly is not a 

rational conclusion, for if I rest in the resting system, the principle of relativity does not 

compel that I also rest in the moving system. Rather, the Einsteins simply confused their 

conclusion as an additional premise, which renders the two "postulates" redundant, or renders 

one postulate deducible from the other, and in no sense a postulate. 

As Einstein, himself, avowed, "the real basis of the special relativity theory" is not the 

conclusion of light speed invariance and the covariance of the laws of physics in Lange's 

"inertial systems". As Albert Einstein later admitted, the real set of a priori postulates is the 

"Lorentz Transformation", replete with its dreaded ad hoc hypotheses. The Lorentz 

Transformation deduces all velocity comparisons, not just invariant light speed, which is a 

specific speed, and a derived unit, not a general geometry. 

Later formulations of the special theory of relativity change the 1905 light postulate, 

from the Einsteins constant speed of light exclusively in the "resting system", into the 

invariance of light speed in all of Lange's inertial systems. But this renders the principle of 

relativity redundant to, or deducible from, the light "postulate", and, therefore, not a 

"postulate", per se, because the light "postulate" then asserts the identity of Lange's inertial 

systems as light speed invariance, and the principle of relativity is already proven in the light 

"postulate". On the other hand, if we pretend that the principle of relativity is the covariance

of the laws of physics embracing Maxwell's theory, given the "Lorentz Transformation" as a 

premise, then the second "postulate" is already incorporated in the first "postulate". 

If we are to assume that the Einsteins, in their 1905 paper, deduced, not induced, the 

Lorentz Transformation from invariant light speed; we would further have to fallaciously 

assume that empirically observed Lorentz Transformation metrics provoked the Einsteins to 

induce an unobserved invariant light speed and the unobserved symmetry of phenomena, as 

self-evident general truths induced a posteriori from empirically observed and reciprocally 

measured: length contraction, time dilatation and relative simultaneity. Such is obviously not 

what happened, and such is not what is argued in the 1905 paper. 

On the contrary, supposedly observed invariant light speed and the supposedly 

observed symmetry of electrodynamic phenomena led Voigt [3], FitzGerald [4] and Larmor 

[5] to scientifically induce, a posteriori, the general geometry of the (misnamed) "Lorentz 

Transformation", which general set of hypotheses supposedly deduced all "known" 

phenomena in non-existent hypothetical "inertial systems". The Einsteins pseudo- 

Metaphysics, their ontology of redundancy, simply disguised the more scientific, though 

likewise irrational, work of their predecessors, in a way which attempted to make it appear 

that the Einsteins had deduced that which must be induced, and had avoided hypotheses, 

which they had not avoided, but rather induced, through fallacy of Petitio Principii. 

Most of the post-1905 statements of the special theory of relativity substitute a 

completely different proposition for the "two postulates". Einstein, himself, substituted one 

light theorem, in 1907, for the "two postulates" of 1905: 

"the 'principle of the constancy of the velocity of light' [***] for a system of coordinates in a 

definite state of motion [as opposed to solely in the 'resting system' as in 1905.]" [6] 

which presumes the Lorentz Transformation from which this "postulate" is deduced, and 

which presumes the tacit hypotheses of an isotropic and homogenous absolute space [7] and 

"a definite state of motion" relative to that absolute space. This new light "postulate" 

represents, therefore, not a postulate, but a deduction, a theorem, and a phenomenon. Einstein 

admitted, in 1907, that this "postulate" could not be a priori, but must, instead, be a 

posteriori: 

1"That the supposition made here, which we want to call the 'principle of the constancy of the 

velocity of light', is actually met in Nature, is by no means self-evident, nevertheless, it is - at least for 

a system of coordinates in a definite state of motion - rendered probable through its verification, which 

Lorentz' theory based upon an absolutely resting aether has ascertained through experiment." [8] 

1The so-called "postulates" are simply a restatement of supposed experimental facts, 

and are not postulates, but empirical facts generalized as "laws" and "theorems". As Robert 

Daniel Carmichael stated: 

"The experiments which we have described (and others related to them) are fundamental in the 

theory of relativity. The postulates in the next chapter are based on them. These postulates are in the 

nature of generalizations of the facts established by experiment. [***] In the next chapter we shall 

begin the systematic development of the theory of relativity. It will be seen that its fundamental 

postulates, or laws, are based on the experiments of which we have given a brief account and on others 

related to them. [***] The postulates, as we shall see, are simply generalizations of experimental facts; 

and, unless an experiment can be devised to show that these generalizations are not legitimate, it is 

natural and in accordance with the usual procedure in science to accept them as 'laws of nature.'" [9] 

H. A. Lorentz questioned Albert Einstein's "method" of pretending that induction is 

deduction: 

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1"Einstein simply postulates what we have deduced, with some difficulty and not altogether 

satisfactorily, from the fundamental equations of the electromagnetic field. [***] I have not availed 

myself of his substitutions, only because the formulae are rather complicated and look somewhat 

artificial". [10] 

1We soon discover in the introduction of the Einsteins' 1905 paper a clear statement of 

the fallacious objective of their entire paper: 

"These two assumptions are sufficient in order to arrive at a simple and consistent 

electrodynamics of moving bodies, taking as a basis Maxwell's theory for resting bodies." 

Is Maxwell's theory for resting bodies a third postulate? One of the "two assumptions", 

the first "postulate", is that the laws electrodynamics of moving bodies be consistent among 

systems of reference in uniform translatory motion with respect to the "resting system". Of 

course, the reasoning presented is circular, first assuming via the first "postulate" that the laws 

of electrodynamics are consistent, then arguing that this mandated consistency, as a premise, 

causes consistency as an effect. It is the first of many circular arguments found in the 

Einsteins' 1905 paper. How do we determine that which constitutes an "inertial system", other 

than circularly, as in: An inertial system is one in which there is no net force acting on the 

system; there is no net force acting on a system, when it is inertial? 

Maxwell's theory for resting bodies is Maxwell's theory of the medium, a privileged 

frame, the aether. However, the Einsteins alleged that the aether was "superfluous" to their 

theory. The Einsteins irrationally wrote with the same pen that the aether was superfluous, 

while asserting it as a basis for their theory. 

In the introduction to the 1905 paper, we are being primed to venture forth from 

Maxwell's theorems for bodies resting in the aether, so that we can return to them, Petitio 

Principii, as the covariant laws of moving bodies, while being asked to pretend that the aether 

is superfluous, so that we aren't too shocked when simultaneity is claimed to be relative, 

again, Petitio Principii, via an impossible light synchronization assumption of light speed 

invariance, or c' = c, which premise is also the conclusion of the theory. 

For example, Albert 1Einstein stated in 1949: 

"[T]he following postulate is [***] sufficient for a solution [***] L-principle holds for all 

inertial systems (application of the special principle of relativity to the L-principle) [***] With the 

help of the Lorentz transformations the special principle of relativity can be expressed thus: The laws 

of nature are invariant with respect to Lorentz-transformations". [11] 

Compare Albert Einstein's later statement to Willem de Sitter's statement of 1911: 

"The principle of relativity can be enunciated as the postulate that the transformations, with 

respect to which the laws of nature shall be invariant, are 'Lorentz-transformations.'*" [12] 

Einstein, ever the plagiarist, stated in 1952: 

"The whole content of the special theory of relativity is included in the postulate: The laws of 

Nature are invariant with respect to the Lorentz transformations."[13] 

Modus Operandi for Plagiarism 

1 Einstein disclosed his modus operandi for manipulating credit for the synthetic 

theories of others, when he stated in 1936:

"There is no inductive method which could lead to the fundamental concepts of physics. 

Failure to understand this fact constituted the basic philosophical error of so many investigators of the 

nineteenth century. [***] Logical thinking is necessarily deductive; it is based upon hypothetical 

concepts and axioms. How can we expect to choose the latter so that we might hope for a confirmation 

of the consequences derived from them? The most satisfactory situation is evidently to be found in 

cases where the new fundamental hypotheses are suggested by the world of experience itself."[14] 

This is a clear statement by Einstein that he would have science deduce a thing from 

itself, taking the world of experience as a hypothesis, only to deduce the world of experience 

as an effect, of itself. Of course, Mileva and Albert were forced to present the real hypotheses, 

which they stuck in the middle of their arguments by way of induction, or an attempt at 

induction, which analyses they attempted to disguise as deductions from a priori principles, 

but which "a priori principles" were well-known summations of phenomena. 

Einstein wanted people to believe that it is irrelevant that his predecessors induced the 

theories he later copied, because Einstein just invented them, sua sponte, irrationally, after he 

had read them, and therefore deserved credit for them: 

"Invention is not the product of logical thought, even though the final product is tied to a 

logical structure."[15] 

Conclusion 

Einstein stated, together with Infeld: 

"Physical concepts are free creations of the human mind, and are not, however it may seem, 

uniquely determined by the external world."[16] 

Certainly, the two "postulates" of the theory of relativity were not, "free creations of 

the human mind," but were, instead, summations of the empirical observations of the wellknown 

phenomena of the day framed with the familiar concepts of the day. What Infeld and 

Einstein meant by "free" is difficult to fathom, and it is simply repetitive to say that creations 

of the mind are creations of the mind. Einstein's vague notions are perhaps the result of his 

plagiarizing Newton, Mach, Pearson, and others, on the principle of logical economy and 

watering down what they had written with Einstein's simplistic and naïve talk. If "free" is to 

mean unrestricted in any sense, no human mind is "free". We are limited in our concepts, 

experience, and scope, and we are socialized, indoctrinated and inculcated into certain beliefs. 

Despite Einstein's assertions, there is no mutual exclusion between being creative and being 

logical. One can create logical hypotheses through creative induction. 

It is the Lorentz Transformation which is the product of creative inductive logic, with 

its hypotheses of length contraction, time dilatation and relative simultaneity, and which is the 

fundamental postulate of the special theory of relativity. Invariant light speed and the 

covariance of the laws of physics are deducible from the Lorentz Transformation, the laws of 

physics, and the definition of inertial motion, which are more fundamental in the special 

theory of relativity, than invariant light speed. Speed must be composed of the more 

fundamental elements of distance and duration. Speed is a derived unit. Therefore, the 

synthesis of the special theory of relativity comes in deducing invariant light speed from the 

hypotheses of an isotropic and homogenous space, Maxwell's theory of the medium, the 

theory of inertial motion, and the hypotheses of length contraction, time dilation and relative 

simultaneity. This is precisely the conclusion Einstein was obliged to admit, in 1935: 

"The special theory of relativity grew out of the Maxwell electromagnetic equations. So it 

came about that even in the derivation of the mechanical concepts and their relations the consideration 

of those of the electromagnetic field has played an essential role. The question as to the independence 

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78 

of those relations is a natural one because the Lorentz transformation, the real basis of the special 

relativity theory[. . .]"[17] 

To argue, as the Einsteins did argue in 1905, that invariant light speed and the 

mandated identity of Lange's inertial systems deduces invariant light speed and the mandated 

identity of Lange's inertial systems, is to argue in fallacies of Petitio Principii, which the 

Einsteins did do, in an attempt to hide their plagiarism of the induced hypotheses of 

Boscovich, Voigt, FitzGerald and Larmor.[18] 

Notes 

1 - M. Einstein-Marity and A. Einstein, "Zur Elektrodynamik bewegter Körper", Annalen der Physik, 

Series 4, Volume 17, (1905), pp. 891-921. 

2 - H. A. Rowland, The Physical Papers of Henry August Rowland, The Johns Hopkins Press, 

Baltimore, Maryland, (1902), pp. 673-674. 

3 - W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der 

Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished 

Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English 

translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is 

credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in 

1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39, 

Number 3, (June, 2001), pp. 211-230; URL Lorentz 

acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the 

"Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig, 

(1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica, 

Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars, 

(1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity, 

Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1, 

1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of 

Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford 

University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122. 

4 - G. F. FitzGerald, "The Ether and Earth's Atmosphere (Letter to the Editor)", Science, Volume 13, 

Number 328, (1889), p. 390. 

5 - J. Larmor, "A Dynamical Theory of the Electric and Luminiferous Medium", Philosophical 

Transactions of the Royal Society of London A, Volume 185, (1894), pp. 719-822; Volume 186, 

(1895), pp. 695-743; Volume 188, (1897), pp. 205-300; and Aether and Matter, CUP, (1900). 

6 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch 

der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416. 

7 - See: A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, Toronto, Melbourne, 

(1982), p. 142; where Pais refers to Einstein's so-called "Morgan manuscript" of 1921. Einstein 

plagiarized this from: N. R. Campbell, "The Common Sense of Relativity", Philosophical Magazine, 

Series 6, Volume 21, Number 124, (April, 1911), pp. 502-517, at 505. See also: R. D. Carmichael, 

"On the Theory of Relativity: Analysis of the Postulates", The Physical Review, First Series, Volume 

35, (September, 1912), pp. 153-176; and "On the Theory of Relativity: Mass, Force and Energy", The 

Physical Review, Series 2, Volume 1, (February, 1913), pp. 161-197. 

8 - A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerung", Jahrbuch 

der Radioaktivität und Elektronik, Volume 4, (1907), pp. 411-462, at 416.

9 - R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley & 

Sons, Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14. 

10 - H. A. Lorentz, The Theory of Electrons, Dover, New York, (1952), p. 230. 

11 - A. Einstein, The Theory of Relativity and other Essays, Carol Publishing Group, (1996), pp. 6-8. 

12 - W. de Sitter, "On the Bearing of the Principle of Relativity on Gravitational Astronomy", Monthly 

Notices of the Royal Astronomical Society, Volume 71, (March, 1911), pp. 388-415, at 388-389. 

13 - A. Einstein, Relativity, the Special and the General Theory, Crown Publishing, Inc., New York, 

(1961), p. 148. 

14 - A. Einstein, Ideas and Opinions, Crown Publishers, Inc., New York, (1954), p. 307. 

15 - A. Einstein, quoted in A. Pais, Subtle is the Lord, Oxford University Press, Oxford, New York, 

Toronto, Melbourne, (1982), p. 131. 

16 - A. Einstein and I. Infeld, The Evolution of Physics, Simon & Schuster, New York, London, 

Toronto, Sydney, Tokyo, Singapore, (1966), p. 31. Compare to the more lucid, prior statements of: W. 

K. Clifford, The Common Sense of the Exact Sciences, Dover, New York, (1955), pp. 193-194. E. 

Mach, "The Economy of Science", The Science of Mechanics, Open Court, LaSalle, Illinois, (1960), 

pp. 577-595. K. Pearson, The Grammar of Science, Second Revised and Enlarged Edition, Adam and 

Charles Black, London, (1900), pp. 30-37. H. Poincaré, Dernières Pensées, Flammarion, Paris, (1913); 

English translation Mathematics and Science: Last Essays, Dover, New York, (1963), pp. 22-23. 

Einstein often plagiarized these works. 

17 - A. Einstein, "Elementary Derivation of the equivalence of Mass and Energy", Bulletin of the 

American Mathematical Society, Series 2, Volume 41, (1935), pp. 223-230, at 223. 

18 - Cf. C. J. Bjerknes, Albert Einstein: The Incorrigible Plagiarist, XTX Inc., Downers Grove, 

Illinois, USA, (2002), ISBN 0971962987. 

Selected Bibliography 

R. D. Carmichael, The Theory of Relativity, Mathematical Monographs No. 12, John Wiley & Sons, 

Inc., New York, Chapman & Hall, Limited, London, (1920), pp. 13-14. 

H. Dingler, Die Grundlagen der Physik, synthetische Prinzipien der mathematischen Naturphilosphie, 

Verlag der Vereinigung wissenschaftlicher Verleger, Leipzig, (1919). 

S. H. Guggenheimer, The Einstein Theory Explained and Analyzed, The Macmillan Company, New 

York, (1925). 

J. Mackaye, The Dynamic Universe, Charles Scribner's Sons, New York, (1931). 

W. Kantor, Relativistic Propagation of Light, Coronado Press, Lawrence, Kansas, (1976). 

S. Goldberg, Understanding Relativity, Birkhäuser, Boston, Basel, Stuttgart, (1984). 

- - - - - 

[A presentation of the author is given at the end of his previous paper published in this 

same issue of Episteme] 


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La nuova teoria del cielo 

La cosmologia osservativa di Halton Arp 

(Alberto Bolognesi) 

Questo articolo cerca di comunicare informazioni e interpretazioni alternative dell'universo 

che sono state a lungo ostacolate e, in qualche caso, perfino soppresse. Sono tutte di natura 

osservativa e si basano essenzialmente sui risultati ottenuti al telescopio dall'astronomo 

americano Halton Arp, a cui sono legato da lunga e profonda amicizia. 

La ragione per cui questi dati stentano tanto a circolare è che la loro accettazione 

determinerebbe automaticamente uno sconvolgimento scientifico e culturale paragonabile 

almeno a quello che si produsse con la falsificazione del Sistema Tolemaico. "L'astronomia e 

l'intera fisica - è stato autorevolmente sancito - dipendono totalmente dalla fisica delle 

particelle la quale a sua volta proviene direttamente dal Big Bang. Con il Big Bang e 

l'espansione dell'universo - concordano Murray Gell Mann, David Schramm e Stephen 

Hawking - astronomia e fisica hanno cessato per sempre di esistere come discipline 

autonome". 

Amen. E se i biologi molecolari inaugurano le loro indagini sul funzionamento del cervello 

umano con riferimenti espliciti alla nucleosintesi prodottasi nella "fornace primordiale", si 

dovrebbe aggiungere che non solo fisica, astrofisica e costanti universali, ma chimica, 

biochimica, botanica, zoologia, storia e filosofia si trovavano in qualche modo già iscritte 

nella prodigiosa formula dell'Inizio, intesa come un tutto creato dal nulla. 

L'alternativa kantiana che il tutto sia inaccessibile all'esperienza è una concezione in disuso: 

oltre al sottoscritto - che è un dilettante - non conosco più di una dozzina di astrofisici che 

dichiarano apertamente che l'unico universo di cui abbia senso parlare è quello osservabile o 

potenzialmente osservabile, e che l'espressione "tutto l'universo", "condizioni iniziali" e "fine 

dell'universo" sono prive di qualsiasi contenuto scientifico. 

Poiché un protone, un neutrone o un elettrone non possono mai essere creati o distrutti 

isolatamente in un'interazione di particelle, i cosmologi deducono che il loro numero totale è 

stato fissato rigorosamente al momento del "Fireball". Non un fermione di più e non un 

fermione di meno. Dio - o chi per esso - ha parlato una volta sola. Dalla massa delle galassie 

alle singole stelle, dalla balenottera azzurra al giaguaro, alla zanzara tigre, tutto dipende 

interamente e unicamente dalle condizioni iniziali. Tutto. Ma proprio tutto. All'obiezione di 

Leibniz - perché c'è qualcosa al posto di nulla? - i teorici della Palla di Fuoco oppongono 

l'esistenza del falso vuoto, il magico tappeto delle fluttuazioni virtuali, i formicolii del nulla, 

"l'aperto del puro compossibile". Basta associare al mondo fisico un'energia positiva e alla 

gravitazione un'energia "negativa" per avere l'universo a costo zero, tutto e nulla 

contemporaneamente. Più uno meno uno uguale zero, "poiché nulla era - come già scriveva 

Edgar Poe nel 1848 - tutto è". Eureka!

Una testimonianza a tarallucci e vino di questo trionfo moderno ci è fornita dal bellissimo 

libro di Dennis Overbye ("Cuori solitari del cosmo"), che descrive i canti e i lazzi di famosi 

astronomi che ridiscendono in pulmann dall'osservatorio Keck, sulla cima del Mauna Kea: 

"Sai qual fu la conclusion, dopo molte ore di osservazion? - cantavano festanti - L'universo è 

in espansion, sempre in espansion, sempre in espansion …". 

Ma qualcosa è andato storto, e nei dispositivi ad accoppiamento di carica applicati ai telescopi 

sono apparsi sempre più numerosi enigmatici ponti, filamenti luminosi di materia e sinistre 

connessioni che collegano oggetti che dovrebbero essere invece lontanissimi fra loro. Allora? 

"La festa appena cominciata … è già finita?. 

DILETTANTI DENIGRATORI E RIVOLUZIONI SENZA PROVE 

Il preambolo mi consente di fissare drasticamente i termini della questione. Che cosa succede 

alla cosmologia, alla fisica delle particelle, ma anche alla fisica ordinaria e all'epistemologia, 

se le connessioni fra oggetti di diverso spostamento spettrale sono reali? 

L'assunzione fondamentale su cui è costruita tutta la conoscenza attuale dell'universo è che lo 

spostamento verso il rosso deve rappresentare una velocità. Non basterebbe infatti che 

rappresentasse una mera misura delle distanze come nell'originario "effetto Hubble": per 

avere un universo in espansione, velocità e distanza devono in qualche modo coincidere. Uno 

spostamento verso il rosso in relazione lineare con la sola distanza eliminerebbe il Big Bang, 

darebbe di nuovo un universo statico, togliendo di mano ai cosmologi la sospirata "età 

dell'universo" e ai fisici delle particelle la mitica "era di Planck". E perfino ovvio che il 

sistema del mondo contemporaneo deve fare quadrato attorno alla recessione delle galassie. 

Non ci sono alternative: questo effetto deve essere "universale" e aumentare in proporzione 

diretta alla distanza che ci separa da esse. Più elevato è il redshift più lontane sono le galassie, 

più lontane sono le galassie più velocemente devono allontanarsi. Anche il profano capisce 

facilmente che è una questione di vita o di morte: le velocità devono essere reali. 

Ma rispetto a cosa? Se prendiamo tre galassie A, B e C fra loro molto lontane e le disponiamo 

su una retta immaginaria, quella che sta in mezzo deve allontanarsi radialmente rispetto alle 

altre due che recedono più rapidamente. Come è possibile? Se A e C si allontanano 

reciprocamente e proporzionalmente alla loro distanza, come fa B a recedere verso C se C 

vede B recedere verso A? 

A B C 

∗←⎯→ ∗ ←⎯→ ∗ 

←⎯⎯⎯⎯⎯⎯→ 

Il solo modo di intendere la recessione universale non è evidentemente di assegnare una 

velocità alle galassie, ma di attribuire una velocità alle distanze. Non è la fuga delle galassie, 

ma la fuga delle distanze! Per aver dichiarato e scritto questo una trentina di anni fa, sono 

stato incolpato di "infangare l'immagine pubblica del mondo scientifico" e inserito nella lista 

dei proscritti dalla divulgazione scientifica. 

In un clima più liberal, oggi i cosmologi ammettono che non sono le galassie a fuggire 

attraverso lo spazio separandosi le une dalle altre, ma che è lo spazio stesso a dilatarsi e ad 

espandersi trascinando con sé gli oggetti cosmici. Si fa ossessivamente riferimento all'uvetta 

di un panettone che cresce nel forno, e così tutto va a posto se si è disposti ad assegnare al 

vuoto e alla metrica le qualità di una pasta che lievita col tempo. (Chiedersi poi chi alimenta il 

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forno sarebbe "altamente provocatorio"). Ma questa precisazione ha un costo drammatico e i 

cosmologi ammettono adesso, con scarso entusiasmo, che lo spostamento verso il rosso delle 

galassie "non è dovuto all'effetto Doppler" (J. Gribbin, Enciclopedia di Astronomia e 

Cosmologia). Cioè, a rigore non è dovuto alle loro velocità. 

Se però vi iscrivete alla Facoltà di Astronomia il redshift cosmologico vi verrà spiegato 

sistematicamente in questo modo: "Consideriamo due fotoni che partono dalla sorgente con 

un ritardo Δ t l'uno rispetto all'altro. Poiché in quel Δt l'universo si espande, la sorgente si 

allontana di una quantità vxΔt e il secondo fotone deve percorrere una distanza più lunga 

per giungere fino a noi: il ritardo Δt' con cui lo riceviamo è perciò maggiore". Ma questo è 

l'effetto Doppler canonico, e gli educatori sanno bene che c'è qualcosa che non va, perché è 

ovvio che la dilatazione deve avvenire nel tempo attraverso lo spazio che lievita mentre i 

fotoni sono in viaggio, non quando "il primo e poi il secondo fotone si stacca dalla sorgente" 

per intraprendere il suo lungo percorso fino ai nostri strumenti! Come faccia allora una 

lunghezza d'onda a "stirarsi" nello spazio che cresce in misura uguale e contraria alla 

direzione di propagazione della radiazione elettromagnetica, è un inquietante capitolo di 

spettroscopia che attende ancora di essere scritto. 

Altri trent'anni di proscrizione? Sarebbe un bel traguardo per un cinquantasettenne. 

Prima di passare ad alcune confutazioni osservative raccolte da Halton Arp vorrei chiudere il 

greve argomento riportando la lettera di un dilettante pubblicata di recente da una rivista 

specializzata. "Che cos'è che veramente si espande? - si chiede con passione il signor Ariberto 

Papini di Siena - Perché si fa presto a far dilatare la superficie di un palloncino: è di gomma! 

Oppure un lenzuolo: è di stoffa! Ma come si fa a fare espandere, oppure ad incurvare 

qualcosa di non materiale: il vuoto, il nulla?". La profonda risposta fu che "gli aspetti della 

cosmologia non sono intuitivi, e che alla comprensione dell'espansione dell'universo si arriva 

solo per via matematica poiché l'estrema astrazione di alcuni concetti rende ardua una 

spiegazione divulgativa. Comunque tenga presente che la gravità frena la materia - rispetto a 

cosa?! - ed è la materia ad espandersi. Essa con tale espansione crea lo spazio. Ovvero, le 

galassie non si espandono in uno spazio circostante, ma lo spazio stesso è creato 

dall'espansione dell'Universo" (Nuovo Orione n. 123, agosto 2002). 

Cioè lo spazio è creato dall'espansione dello spazio. Soddisfatti o rimborsati. 

RIVOLUZIONI SENZA PROVE? 

O gli oggetti di Arp sono tutte illusioni ottiche o i cosmologi difendono un'espansione 

dell'universo smentita dall'osservazione astronomica. Non è possibile una soluzione 

"salomonica" o di compromesso e questo rende la controversia ancora più aspra e 

drammatica. Poiché galassie interagenti con redshift discorde non possono essere 

contemporaneamente vicine e lontane, connesse e disconnesse, lente e veloci, il punto di vista 

convenzionale è costretto ad invocare sistematicamente effetti di prospettiva, allineamenti e 

accavallamenti accidentali nella profondità del cielo. 

Né potrebbe accontentarsi di attribuire all'oggetto con redshift eccedente uno spostamento non 

cosmologico assegnando a quello con minore spostamento verso il rosso un redshift 

sicuramente e interamente cosmologico. 

Giudicate voi. 

La prima immagine (Fig. 1) che ho selezionato da un gran numero di casi esistenti, mostra un 

quasar che cade davanti a una galassia ellittica, la NGC 1199. L'oggetto compatto indicato 

con una freccia ha uno spostamento verso il rosso abbastanza elevato (z = 0,044) mentre 

quello della galassia è modesto (z = 0,009). Per la legge di Hubble e per la buona sorte della 

cosmologia del Big Bang l'oggetto di tipo quasar dovrebbe invece trovarsi dietro (cioè molto 

più lontano della galassia ellittica).

Fig. 1 

L'immagine successiva (Fig. 2) rappresenta la galassia NGC 4319 e il quasar Markarian 205 

connesso da un visibile ponte di materia. Ma lo spostamento verso il rosso della galassia è z = 

0,006 mentre quello del quasar è di 0,07, cioè dovrebbe trovarsi undici volte più distante 

secondo la "legge" che tutela l'espansione dell'universo. 

Fig. 2 

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La fotografia seguente (Fig. 3) rappresenta il Sestetto di Seyfert, un gruppo di galassie in 

interazioni che hanno all'incirca la stessa magnitudine apparente. Cinque di esse hanno più o 

meno lo stesso redshift (z = 0,015) ma quella indicata con la freccia presenta uno spostamento 

quasi cinque volte maggiore, il che la renderebbe cinque volte più lontana e di enormi 

dimensioni. 

Fig. 3

La quarta immagine (Fig. 4) mostra la suggestiva catena di galassie blu VV 172. Quattro di 

queste galassie hanno un valore di redshift che oscilla intorno a z = 0,05 mentre quella 

indicata con una freccia presenta uno spostamento verso il rosso estremamente elevato: z = 

0,12. Chi crede davvero che questa galassia non faccia parte della configurazione e che si 

tratti di un lontanissimo oggetto blu che si è andato ad incastrare accidentalmente fra quattro 

compagne blu lungo la nostra linea di vista, alzi la mano: e chi alza la mano sostiene 

implicitamente che si tratta della galassia blu più grande di tutto l'universo … 

Fig. 4 

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La quinta immagine (Fig. 5) presenta tre quasar nei bracci a spirale di NGC 1073. C'è una 

probabilità su cinquantamila che si tratti di un allineamento accidentale. 

Fig. 5 

E ancora, in Figura 6, una fotografia profonda di tre quasar intorno a NGC 3842. Qui c'è una 

possibilità su un milione di trovare per caso questa associazione. 

Fig. 6

La settima immagine mostra la spirale barrata a due bracci NGC 1097 con i suoi quattro getti 

luminosi. Ci sono almeno cinquanta quasar attorno a questa galassia straordinariamente attiva. 

Fig. 7 

Fig. 8 

(Grafico dei quasar individuati attorno a NGC 1097 

da Arp, Wolstencroft e He nel 1979). 

Concludo questa "rivoluzione senza prove" con la foto (Fig. 9) ottenuta da N. Sharp della 

coppia di galassie NGC 7603 A e B, foto che i lettori di Episteme già conoscono per via della 

recentissima e sensazionale scoperta effettuata dagli astronomi M.L. Corredoira e C.M. 

Gutierrez. Rappresenta il coronamento di cinquant'anni di ricerche che hanno fruttato ad Arp 

soltanto l'allontanamento dall'Osservatorio di Monte Palomar. Sebbene siano stati pubblicati 

sulla celebre rivista "Astronomy and Astrophysics", i risultati continuano a circolare nella 

comunità astronomica come l'ennesimo, imbarazzante X file. 

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Le due galassie collegate da un evidentissimo ponte di materia hanno rispettivamente uno z: 

0,029 per l'oggetto più grande e z: 0,057 per la compagna più piccola. Al momento della 

scoperta della clamorosa discordanza (1971) Arp notò subito due condensazioni di aspetto 

stellare immerse nel braccio, e auspicò che i futuri spettrografi potessero analizzarne i dettagli 

e determinarne gli spostamenti verso il rosso. Impresa riuscita a Corredoira e Gutierrez 

trent'anni dopo col N.O.T. di La Palma, e con tecnologia progredita: le due condensazioni 

hanno mostrato gli spettri tipici dei quasar con z = 0,391 per l'oggetto più vicino alla galassia 

principale e z = 0,243 per quello prossimo alla compagna! Così abbiamo due galassie 

interagenti con diverso spostamento verso il rosso e due quasar ad alto redshift nel filamento 

che le connette: il mondo avrebbe dovuto fermarsi per questo, almeno per un giorno, ma i 

grandi media non ne hanno nemmeno parlato. 

Fig. 9 

Che dire? C'è una terza condensazione che emerge dal nucleo della NGC 7603A: e basterebbe 

un'occhiata dell'Hubble Space Telescope o del Keck per affossare il Sistema del Mondo. 

Richiesta di ulteriori osservazioni con il telescopio orbitale a raggi X Chandra e con l'8 metri 

del VLT dell'ESO al Cerro Paranal sono state prontamente respinte. 

LA NUOVA TEORIA DEL CIELO 

Le discordanze di redshift constatate, richiedono che le condizioni di emissione della 

radiazione da parte di oggetti interagenti o posti alla stessa distanza mutino da un sistema 

all'altro. Si tratta dunque di comprendere un fenomeno fisico in grado di operare su interi 

insiemi estesi di stelle, gas e polveri, generando spostamenti intrinseci che non hanno a che 

vedere né con la velocità né con la distanza. Un meccanismo che opera ancora più 

vistosamente nei quasar, che lungi dall'essere gli astri favolosi più energetici e lontani di tutto 

l'universo, svelano la loro natura di oggetti piccoli e poco luminosi, connessi alle galassie. 

Questo cambio - val la pena sottolinearlo - non è invocato da una nuova stravagante teoria 

dell'universo ma, se non avete già dimenticato le precedenti immagini, dalle osservazioni 

stesse.

Dunque nuova fisica, nuova informazione che dovrebbe esaltare - e non deprimere! - chi 

tende ad approfondire la conoscenza della struttura cosmica. Anche se questo sembra 

aumentare la nostra ignoranza, allontanandoci da certezze gelosamente custodite. 

L'evidenza osservativa dello spostamento verso il rosso intrinseco chiama in causa 

direttamente la fisica quantistica e l'azione interparticellare che devono giustificare l'esistenza 

del mondo collegandolo al microcosmo. Per gli scopi divulgativi che si propone questo 

articolo dirò semplicemente che la varietà dei redshift intrinseci osservati richiede che le 

transizioni energetiche di un atomo di idrogeno, di elio, di ossigeno, di magnesio … devono 

trovarsi a frequenze e a lunghezze d'onda diverse da quelle che sperimentiamo in laboratorio. 

E questo dà già un'idea della immensa posta in gioco. A qualsiasi livello di conoscenza si 

trovi il lettore (e lo scrivente!) la falsificazione dell'universo in espansione impone che le 

righe degli elementi e le serie spettrali che compongono l'intero spettro elettromagnetico si 

trovino realmente alle frequenze osservate. 

Si può ben comprendere lo shock stemperato dall'ironia che ha fatto esclamare a un eminente 

fisico che "i dati di Arp implicano costanti personalizzate!": Ma questa è esattamente la sfida 

osservativa, questa è esattamente la vita sulla frontiera. 

"Che cosa determina l'energia di transizione tra due stati atomici dell'idrogeno? - si chiede 

Arp - Un fattore è rappresentato dalla carica relativa tra l'elettrone e il nucleo, l'altro fattore 

è la massa dell'elettrone che subisce una transizione tra i due possibili stati orbitali. Se le 

misure della costante di struttura fine eliminano la possibilità che le cariche elettriche 

possono essere diverse, resta solo la massa dell'elettrone" 1 . 

Poiché lo spostamento verso il rosso intrinseco è documentato dalle osservazioni, una delle 

poche interpretazioni in grado di spiegarlo efficacemente è di attribuire massa minore a tutte 

le particelle che costituiscono la materia dell'oggetto con più alto spostamento verso il rosso. 

Ciò darebbe immediatamente frequenze più basse e fotoni più spostati verso il rosso, orbite 

elettroniche "allargate" e, in pratica, isotopi più leggeri. Se dunque quasar e galassie 

compagne risultano associate a oggetti più massici, come nipotini a spasso coi nonni, una 

delle differenze più qualificanti sta nel loro tempo di formazione. E' pensabile - si chiede Arp 

- che oggetti connessi da ponti di materia, mobilizzati nei bracci di spirali o immersi in 

filamenti luminosi e in gas caldi ad alta e ad altissima energia (X e gamma) abbiano la 

medesima età del sistema a cui appartengono? 

La soluzione cosmogonica è immediata: gli oggetti cosmici con più alto spostamento verso il 

rosso devono essere stati "creati" (espulsi o condensati) in un tempo successivo rispetto a 

quelli con basso redshift. "Non appena la materia appare - scrive Arp - essa risulta altamente 

spostata verso il rosso. Col passare del tempo diventa più pesante, più grande e più luminosa 

e il suo altissimo spostamento decade verso valori più contenuti. Abbiamo in pratica la 

rappresentazione empirica di un piccolo quasar con altissimo redshift che evolve in una 

galassia compatta con spostamento verso il rosso inferiore e infine in una galassia compagna 

con leggera eccedenza nello spostamento verso il rosso" rispetto all'oggetto che l'ha generata. 

("Quasar, redshifts and controversies", 1987) 2 . 

E' dunque nei fatti, per Arp, un'evoluzione delle costanti. Ed è ironico - rileva - che il punto di 

vista convenzionale ne difenda ad ogni costo l'immutabilità invocando il Secondo Principio 

della Termodinamica. La materia creata tutta in una volta dal Big Bang con proprietà 

immutabili non rappresenta una violazione, ma le masse delle particelle variabili col tempo lo 

sono …. "Mi rendo conto che il mio universo si restringe paurosamente all'universo delle 

osservazioni - mi disse una volta - un universo locale dove la materia vi compare 

continuamente ricreata, o riciclata. I tuttologi non potrebbero accontentarsi ma ciò è 

esattamente quel che osserviamo!". Evidentemente a partire da uno stato particellare 

estremamente diffuso - ipotizza Arp - Da un "apeiron" sconosciuto e onnipervasivo che 

accende i nuclei delle galassie e che le moltiplica attraverso espulsioni secondarie come una 

gragnola ininterrotta di fuochi d'artificio. O come una pianta che germoglia. 

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E' un immagine locale ma grandiosa, che non può (né si vede come potrebbe) pretendere di 

fissare tutto l'universo. La sola definizione sensata del Mondo - insiste - è: "tutta la materia 

osservabile o potenzialmente osservabile che siamo in grado di sperimentare". 

I limiti kantiani vengono immediatamente ristabiliti: siamo all'interno di un perimetro o di una 

bolla i cui orizzonti si allargano per mezzo di strumenti sempre più progrediti, ma 

continuiamo a permanere confinati al centro del mistero. Più che una condizione umana 

sembra una condizione della fisica. 

CHE COS'È HO? 

Ma all'interno della "bolla delle osservazioni", come sull'isola di Kant battuta dai marosi 

dell'inconoscibile, possiamo ancora fare scienza. Se la creazione di materia prende posto 

nell'universo come un processo continuato, e se i redshift esprimono semplicemente l'età degli 

oggetti cosmici e non più la loro velocità e la loro distanza dal mitico Inizio del Mondo, può 

ancora avere un significato la determinazione della "costante Ho"? 

Sorprendentemente la risposta è sì. La costante di Hubble che nella cosmologia del Big Bang 

non è che un numero che quantifica la rapidità con cui l'universo si va espandendo, diventa 

nella relazione age-redshift di Arp la chiave di volta per misurare la variabilità della massa in 

funzione dello spostamento verso il rosso. L'integrazione che lega lo spostamento spettrale 

alla scala delle magnitudini apparenti è immediata, e con essa l'annosa questione dei "redshift 

anomali". 

La trasformazione della convenzionale legge di Hubble "velocity-distance" in "age-distance 

law" e in "age-luminosity law" è fissata nelle equazioni della massa variabile: 

sul redshift: 

t 

2 

= 

t0 

2 

(1) 

m mo 

2 

0 

2 

t 

1 + z = 

(2) 

t 

1 + 

1 + z 

z 1 

= 

0 

t 

2 

0 

2 

1 

t 

e sulla trasformazione delle scale temporali τ = tempo locale e t = tempo cosmico: 

2 

0 

(3) 

3 

t 

τ = 

(4) 

3t 

in cui la soluzione di Friedmann (Big Bang) viene ricondotta a uno spaziotempo piatto 

(euclideo) e a un universo statico. 

Il diagramma sottostante (Fig. 10) visualizza le due soluzioni, che a sinistra forniscono il Big 

Bang e a destra l'universo di Narlikar-Arp. Ma, ben conscio di perdere in tal modo i contatti 

con i lettori che non hanno specifiche esperienze di cosmologia, dirò subito che non intendo 

cavarmela con la mera esposizione del formalismo matematico.

Fig. 10 

(da Arp, 1997) 

E non è una passeggiata. Limitandomi all'essenziale, è evidente che non tutte le galassie sono 

grandi galassie: al contrario, queste ultime sono abbastanza rare. Nella cosmologia del Big 

Bang tutte le galassie hanno però all'incirca la stessa età mentre in quella di Arp devono avere 

età assai variegate, e dalla loro età deve dipendere la massa, lo splendore e soprattutto lo 

spostamento spettrale, mentre nell'ipotesi convenzionale i redshift misurano essenzialmente le 

velocità e le distanze prodotte dall'espansione dello spazio. 

E' ovvio che anche le galassie "in carriera" di Arp non sono destinate a raggiungere tutte la 

medesima massa e luminosità (le differenze morfologiche sono un fatto osservativo), ma in 

questo quadro non si presenta il rischio di mescolare sistematicamente oggetti di magnitudini 

assolute molto diverse. Che è poi un vantaggio che ha una terribile contropartita, perché in tal 

modo non possiamo più dire gran che sulle loro distanze. 

Anche una semplificazione così estrema riesce a mettere a nudo la prima cruciale questione: 

meglio una distanza sbagliata o una distanza incerta? E' l'eterno tallone d'Achille della scienza 

astronomica, che non può misurare nelle due dimensioni disponibili un mondo fisico che ne 

ha almeno tre: misure sbagliate non hanno contenuto scientifico, misure incerte non 

producono risultati scientifici. Basta questo preliminare per capire perché, a dispetto delle 

confutazioni osservative, l'espansione dell'universo è così strenuamente difesa. E' solo in base 

all'interpretazione cinematica del redshift che si è potuta sviluppare una tecnica in grado di 

scandagliare l'universo e di produrre spettacolari mappe tridimensionali della struttura 

cosmica. Che producono mostri, si potrebbe aggiungere, come le grandi muraglie, le "dita di 

Dio", le spropositate luminosità dei quasar, le velocità superluminali e le masse dei buchi neri 

che aumentano con la distanza. 

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Fig. 11 

Interpretazioni a confronto - Nella figura precedente appaiono cinque oggetti di debole luminosità 

molto vicini fra loro. I dettagli della composizione spettrale sono qualitativamente molto simili per 

tutti i componenti ma l'aspetto non puntiforme dei primi tre a sinistra li definisce come "galassie" 

mentre i due oggetti di forma sferica (puntiformi) appaiati sono riconosciuti come "quasar". Il redshift 

medio è z = 0,435 il che li collocherebbe a più di cinque miliardi di anni luce di distanza da noi, ma il 

quasar a destra ha un redshift quasi cinque volte più alto (che anche dopo le correzioni relativistiche 

dovrebbe essere spostato a una distanza almeno doppia). L'interpretazione cosmologica richiede che 

tre galassie e un quasar si trovino tutti alla stessa distanza mentre il quasar di destra viene a cadere 

solo accidentalmente vicino al gruppo per un effetto di prospettiva. Per Arp gli oggetti sono tutti alla 

stessa distanza, molto giovani, molto più vicini e molto meno luminosi, e il quasar di destra 

rappresenta l'ultimo nato della formazione. Si noti che il quasar più luminoso non mostra alcuna 

nebulosità circostante, che dovrebbe invece essere rivelata sul versante del compagno ritenuto più 

lontano. Non appare nessuna galassia "ospite" in 1548+144a e il quasar appare "nudo". 

(Cortesia di E.M. Burbidge). 

Come si fa a distinguere una galassia debole da una galassia lontana? 

E' l'eterno dilemma della "distanza secondo luminosità": quando la luminosità apparente di 

una sorgente luminosa è pari a un quarto della luminosità apparente di un'altra sorgente di 

medesima luminosità assoluta, la prima si trova a distanza doppia. Nella teoria del Big Bang 

quando il redshift di un oggetto è doppio, questi deve recedere a velocità doppia, quando il 

redshift è quadruplo l'oggetto si allontana quattro volte più velocemente e deve trovarsi 

quattro volte più lontano. La circolarità è in agguato: se i rapporti di luminosità apparenti non 

tornano, o coincidono sopra valori di redshift differenti, basta aumentare (o diminuire) le 

luminosità assolute. E se due galassie morfologicamente identiche e del medesimo splendore 

apparente, ma individuate in posizioni contrapposte del cielo presentano spostamenti verso il 

rosso discordi, si chiamano in causa "espansioni asimmetriche dell'universo". Non si può … 

sbagliare. 

L'alternativa di Arp è il crollo dell'espansione dell'universo, e questo implica che le distanze 

siano sbagliate di un fattore che può superare 100, le masse e le luminosità di un fattore 

10.000, le età assegnate in base al "look back time" di un fattore fino a 10 10 : un'alternativa da

Sant'Uffizio, si potrebbe dire, quando i detentori del potere temporale per colpa di un piccolo 

cannocchiale si trovavano a dover riconsiderare l'inviolabile architettura del Cielo. 

Ma il "look back time", cioè l'effetto di osservare gli oggetti cosmici allo stato non attuale per 

via della velocità finita delle propagazioni elettromagnetiche, ha importantissime e decisive 

conseguenze su entrambi i modelli di universo. Nello schema immaginario del Big Bang 

come in un film girato alla rovescia, l'età delle galassie si abbassa progressivamente e 

uniformemente con la distanza, svelando oggetti primordiali, in cui la "metallicità" (cioè la 

formazione degli elementi più pesanti all'interno delle prime stelle) tende a scomparire. Le 

galassie svaniscono per far posto a singole palle di gas di massa grandissima e di vita 

brevissima (l'ipotetica popolazione III). Più in là c'è solo "l'era della radiazione". Nella 

cosmologia osservativa di Arp, la scalata verso epoche più antiche dipende invece da un unico 

parametro, l'età della nostra galassia. Tecnicamente, quindi, la cosiddetta costante di Hubble 

rappresenta l'inverso dell'età delle nostre stelle più antiche! Per esprimermi nei termini più 

semplici: come ci apparirebbe la nostra galassia alla distanza di un megaparsec (3,261 milioni 

di anni luce)? Se la nostra galassia ha quindici miliardi di anni ci apparirebbe a un'età di circa 

14 miliardi novecentonovantaseimilioni di anni. Alla distanza stimata dell'ammasso della 

Vergine (circa 16-17 megaparsec), ci apparirebbe di una cinquantina di milioni di anni più 

giovane, mentre a 5 miliardi di anni luce si mostrerebbe all'età apparente di 10 miliardi di 

anni. 

Gli specialisti perdoneranno l'ovvietà della rappresentazione, ma a buon profitto dei non 

iniziati dirò che a 10 miliardi di anni luce la Via Lattea ne dimostrerebbe cinque e che a 15 

miliardi di anni luce (che è distanza spaziale), la nostra galassia - che pure sta là in tempo 

reale - sparirebbe come non fosse mai nata, perché la prima luce partita dalle nostre stelle più 

antiche non ha ancora potuto colmare quella distanza. E anche una buona risposta al problema 

del cielo buio in un universo statico (paradosso di Olbers) che qui non esamineremo. Come 

dovrebbero apparirci galassie molto vicine a noi e della medesima età della nostra? 

Ovviamente con uno spostamento verso il rosso molto basso, sul quale graverebbero i moti 

peculiari di avvicinamento o di allontanamento sulla nostra linea di vista (effetti Doppler) 

dovuti all'interazione gravitazionale. Che è poi, in pratica, ciò che constatiamo nel Gruppo 

Locale e nei sistemi a noi più prossimi. Ne parleremo fra un attimo. 

Apparentemente non resta che chiederci a quale spostamento spettrale dovrebbero trovarsi 

oggetti vicini molto giovani e - se esistono - oggetti vicini più antichi della Via Lattea. La 

risposta è molto semplice anche se sorprendente: gli oggetti giovani mostrerebbero un redshift 

molto alto che tenderebbe ad aumentare con la distanza. L'"orizzonte" degli oggetti 

intrinsecamente giovani diventa piuttosto angusto a causa del look back time. La risposta a 

come si presenterebbero sistemi vicini più vecchi nella soluzione di Arp è ancora più facile 

essendo intuitiva: galassie più antiche della Via Lattea mostrerebbero un redshift negativo, 

cioè in pratica esibirebbero un blueshift rispetto al nostro spettro elettromagnetico. 

Nelle parole dello stesso Arp: "M 31(la grande galassia in Andromeda di cui la nostra Via 

Lattea è una compagna) anche dopo la correzione per la rotazione galattica continua a 

esibire un elevato spostamento verso il blu. In questo caso la nostra galassia apparirebbe 

spostata verso il rosso se vista da M 31 così come M 31 risulta spostata verso il blu vista da 

noi. Questa è la sfida". 

PROFONDO ROSSO O ROSSO POCO PROFONDO? 

Resterebbe da chiedersi a quali frequenze e a quale spostamento spettrale dovrebbero 

presentarsi sistemi più antichi del nostro e della stessa M 31 se posti a grandi distanze. Ma è 

una risposta difficile anche per uno stregone. Nessuno è in grado di dire quanto "durino" le 

più grandi galassie: certo non possono essere eterne, e già questo determinerebbe dei grandi 

"buchi di buio", immense interruzioni temporali nella propagazione delle radiazioni; e poi si 

renderebbero necessarie conoscenze inaccessibili sull'omogeneità o la disomogeneità della 

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materia cosmica su scale tendenti all'infinito (cfr. K.V.L. Charlier, "How Infinite can be built 

up", 1922). Ricompaiono tutte le grandi e insolute questioni ottocentesche sul cielo buio o su 

come potrebbe mai raggiungerci una sorgente luminosa posta a distanza infinita. La scelta di 

Arp è ancora di natura empirica: poiché le galassie che presentano blueshift nell'universo 

osservabile sono pochissime, noi ci troviamo evidentemente a vivere in uno dei sistemi più 

antichi. Galassie un po' più vecchie della nostra alle più grandi distanze tornerebbero ad 

apparirci spostate verso il rosso a causa del look back time, e per il lettore che rischia di 

smarrirsi nelle proprietà dell'universo statico farò l'esempio grossolano di un sistema dell'età 

di 25 miliardi di anni (cioè di circa 10 miliardi di anni più antico della Via Lattea) alla 

distanza di 15 miliardi di anni luce. Se fosse ancora osservabile a quella distanza, ci 

apparirebbe più giovane delle nostre stelle più vecchie di circa 5 miliardi di anni, quindi non 

spostato verso il blu ma di nuovo verso il rosso. 

L'interpretazione cosmogonica di Arp dell'universo osservabile richiede che Andromeda (M 

31) sia il capostipite e in pratica l'oggetto più antico di tutto il Gruppo Locale; e ciò risolve 

anche un rompicapo di lunga data che resta inspiegato nella cornice convenzionale. E' un 

problema che mi ha coinvolto personalmente e riguarda l'enigmatica distribuzione dei redshift 

della nostra congregazione di galassie che sono tutte positive rispetto a M 31! Io segnalai 

questo risultato all'Astronomia professionale sin dal 1971, all'indomani della pubblicazione 

degli spostamenti spettrali allora disponibili dei componenti il Gruppo Locale: ma all'epoca 

propagandavo epatoprotettori e antinfluenzali e non venni preso sul serio. Scrissi a Paolo 

Maffei e a Livio Gratton che "o il Gruppo Locale si sta disperdendo o gli spostamenti verso il 

rosso non c'entrano con l'effetto Doppler". 

Il fenomeno tuttavia è stato confermato e ampliato con nuovi dati anche per l'altro gruppo di 

galassie a noi più vicino, in Ursa Major, dominato dalla grande spirale M 81, e poi esteso a un 

gran numero di ammassi dove la galassia più massiccia risulta possedere sistematicamente il 

redshift più basso. 

Fig. 12 e 13 

Distribuzione degli spostamenti verso il rosso-relativi di tutte le più importanti compagne rispetto alla 

loro galassia dominante nei gruppi di M 31 e M 81. (Cortesia di H. Arp)

E' aperta la caccia alle galassie "madri" e alle più antiche progenitrici? Un buon metodo 

potrebbe essere quello di utilizzare i quasar come indicatori delle distanze, ma bisognerebbe 

passare sul cadavere del Big Bang. 

Nella loro nuova "veste" di oggetti piccoli connessi alle galassie, giovani e poco luminosi, i 

quasar non potrebbero essere osservati intorno a galassie attive molto lontane, per le quali, in 

base alla sola relazione "age-redshift" è oltretutto molto difficile stimare la distanza. 

L'"estinzione" degli oggetti giovani (quasar, BL Lac, etc.) è una funzione che cresce assai 

rapidamente nel modello di universo di Narlikar e Arp cosicché i "progenitori" sono 

identificabili con sicurezza solo nel nostro vicinato e tuttalpiù alle medie distanze. 

Poiché la creazione di oggetti cosmici è osservativamente un fenomeno continuo, 

l'integrazione delle due scale temporali (t = tempo cosmico e τ = tempo locale) comporta 

notevoli complicazioni che qui risparmieremo al lettore. Mi limiterò a rilevare che si 

potrebbero anche osservare oggetti con il medesimo redshift (cioè con la medesima etàapparente) 

a distanze molto diverse e quindi con età intrinsecamente diverse sulla scala t del 

tempo cosmico. 

IL NUOVO SCENARIO 

Un quesito ricorrente tra i pochi esploratori di questa nuova formulazione del mondo è il 

seguente: se i quasar vengono processati e poi espulsi dalle galassie per dar forma a nuove 

galassie che a loro volta semineranno nuovi quasar in un processo a cascata, come è apparsa, 

come si è formata la prima galassia? Ovviamente, in un universo indefinitamente grande e 

antico la domanda è priva di senso: è un po' come cercare l'albero che avrebbe dato origine a 

una foresta di dimensioni illimitate: Arp non ha la soluzione complessiva della Natura e non 

ne fa mistero. 

"Da ciò che possiamo vedere le cose si formano continuamente, e continuamente cambiano 

scomparendo e riapparendo: eppure ogni cosa sembra essere in comunicazione con tutte le 

altre cose. Se la materia cosmica dispone di un tempo illimitato è possibile che sperimenti 

ogni possibilità" (Comunicazione privata, 1993). 

E' tuttavia estremamente interessante indagare come avrebbe potuto avere origine la parte 

visibile del mondo, l'universo locale delle osservazioni al tempo cosmico t = 0. Essa 

comincerebbe con un'esplosione di formazioni di tipo quasaroide di bassa luminosità, circa 15 

miliardi di anni fa. Forse a partire da singoli oggetti al centro del Superammasso Locale (che 

è oggi la più grande aggregazione di galassie conosciuta) vennero proiettate formazioni 

successive poi evolutesi in brillanti galassie della seconda generazione, come M 31 che 

occupa il centro del Gruppo Locale. Le analogie con l'Inizio degli Inizi della teoria del Big 

Bang sono ingannevoli, perché questa è una creazione continua, continuata e intermittente e 

quindi, temporalmente, l'esatto opposto del Big Bang che è invece per definizione un evento 

unico a partire dal nulla. 

Circa 8 milioni di anni dopo che una galassia come M 31 ha preso a formarsi, essa espelle una 

famiglia di compagne di cui la Via Lattea è uno dei componenti: è la foto di gruppo del cortile 

di casa, dove le compagne più giovani devono essere generalmente più attive ed aver espulso 

molto di recente i quasar del Gruppo Locale (come ad esempio, 3C 120 e i 7 quasar che la 

circondano, PKS 0123 + 25, 3C 48 e il BL Lac che si trova nelle vicinanze). 

Questo scenario empirico di creazione continua ha celebri eponimi in Fred Hoyle, Hermann 

Bondi e Thomas Gold con la Teoria dello Stato Stazionario, e anche nel suggerimento 

dell'illustre fisico Paul Dirac che ipotizzò la creazione di materia nell'universo come un 

processo "moltiplicativo" preferibilmente in prossimità di precedenti concentrazioni di 

materia più vecchia. 

Va detto però con chiarezza - ed è lo stesso Arp a farlo - che qui non abbiano nuovo spazio 

che sloggia le vecchie formazioni per dar forma a quelle nuove attraverso una metrica in 

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espansione, perché gli spostamenti spettrali "anomali" e la relazione age-redshift eliminano 

l'espansione dell'universo. 

Così le ipotizzate "superfici di massa nulla" di Hoyle e le equazioni della materia di Narlikar a 

partire da m = 0 diventano quasi nulle e quasi zero. "Per quanti sforzi si possano fare - 

ammette Arp - non è scientificamente possibile ridurre qualcosa al nulla". O si fa intervenire 

un falso vuoto, una radiazione di punto zero, uno stato iperdiffuso di materia-energia o si 

sfocia nel misticismo. Anche lui alla fine ha bisogno di un apeiron che accende i nuclei delle 

galassie primordiali: "Quale possa essere la connessione fra l'osservata creazione locale e 

l'universo in generale pone una questione affascinante ma smisurata. Nei termini delle forme 

di vita che stanno lottando con questi concetti, tuttavia è rilevante domandarsi se pure loro, 

oltre ad essere continuamente create e ricreate in forme leggermente diverse, possano anche 

trovarsi nei loro costituenti più microcospici in continuo contatto informativo con il resto 

dell'universo". 

IL MISTERO DELLA VERGINE 

Se è palesemente retorico chiedersi in quale pozzanghera si sviluppò la prima cellula, è però 

del tutto legittimo domandarsi chi fu la madre di M 31. La madre della nostra galassia deve 

pure avere una madre, e poiché stiamo parlando del nostro universo locale e non di tutto 

l'universo, la "nonna" - se esiste da qualche parte - non dovrebbe poi essere tanto lontana. 

Feci questa domanda ad Arp quasi per scherzo una decina di anni fa e lui ammise che gli 

sarebbe piaciuto avere una risposta a tutto: aggiunse subito che "sarebbe assai più fruttuoso 

conoscere il destino finale delle galassie e della materia che si condensa in stelle piuttosto 

che rintracciare una foto dell'antenato da incorniciare". "Hai una risposta anche per questo? 

- incalzai malizioso - Ma è molto interessante - fece ignorando la mia provocazione - che le 

uniche galassie non locali che presentano spostamenti verso il blu si trovano tutte al centro 

del vicino ammasso della Vergine. Sono sei, spirali Sa e Sb, molto simili alle galassie più 

vecchie che conosciamo. Se ti fidi della mia relazione age-redshift, è facile calcolare che si 

tratta di sistemi più vecchi di una ventina di milioni di anni delle galassie del Gruppo Locale: 

il problema è che questo corrisponde solo ad un incremento dello 0,1% rispetto alle nostre 

stelle più antiche, così se ti occorre anche la bisnonna dovresti forse trasferirti lassù per 

continuare la tua ricerca genealogica …". 

Gli spostamenti verso il blu delle galassie della Vergine non trovano spiegazioni soddisfacenti 

nella cornice dell'universo in espansione: alla distanza stimata di 16-17 Mpc le galassie più 

massicce hanno redshift equivalenti a velocità di recessione di circa un migliaio di chilometri 

al secondo, ma c'è una "dispersione" in eccesso enorme e un gran numero di altri membri che 

dovrebbero così recedere a velocità doppie, triple, quadruple e oltre. L'effetto viene di solito 

"calmierato" sommando a queste galassie "super veloci" un gran numero di nane a basso 

spostamento verso il rosso fino a farlo sparire, salvando così l'integrità temporale dei gruppi. 

Ma le sei galassie con blueshift vicine al centro dell'ammasso (che altro definisce un 

"cluster"?) dovrebbero possedere un moto retrogrado spettacolarmente alto rispetto al flusso 

"quieter" dell'espansione cosmica: viene giustificato con movimenti peculiari verso la nostra 

linea di vista che si sommano alla direzione di rotazione della nostra galassia, e/o con altre 

ipotesi "esotiche" e "oscure", inaccessibili all'osservazione, che qui non menzioneremo. "E' 

tuttavia un fenomeno davvero straordinario" ammette il Professor Giuseppe Galletta 

dell'Università di Padova. Ma che significa? A tutti gli effetti gli spostamenti verso il blu 

accertati al centro della Vergine sono anch'essi da annoverare fra i "redshift anomali" e 

costituiscono un'altra formidabile confutazione sperimentale dell'assioma che gli spostamenti 

delle righe spettrali delle galassie significano sempre e soltanto velocità.

LE DITA DI DIO 

Il Palladio, la mitica pietra della sapienza caduta dal cielo, non si trova più ad Atene o a Troia. 

E' oggi custodito nei penetrali dello Smithsonian Center for Astrophysic ad Harvard, montato 

su un rozzo piedistallo in uno dei corridoi dell'ala nuova ricoperta di una smorta moquette 

grigia. E' un cubo di plexiglass di circa un metro di lato, all'interno del quale si trovano 

migliaia e migliaia di palline colorate in apparente sospensione: sono rosse e azzurre, palline 

rosse per le galassie ellittiche e palline azzurre per le galassie a spirale. 

Al centro del "diorama" una sferetta bianca marca la posizione della Via Lattea, molto 

prossima a un nugolo di palline e più in là a un'altra concentrazione che nelle intenzione del 

costruttore dovrebbero rappresentare rispettivamente l'ammasso della Vergine e il più distante 

assembramento della Chioma di Berenice. E' la cartografia tridimensionale della struttura 

cosmica ottenuta attraverso la misurazione dello spostamento verso il rosso di 2.400 galassie 

(palline) in base all'"indubitabile" assunzione che il redshift rappresenta comunque una 

distanza e una velocità. 

Un'altra di queste mappe di profondità è mostrata nella Fig. 14 che compendia ulteriori 

surveys spettroscopiche di una gran numero di galassie. 

Fig. 14 

Appaiono stupefacenti strutture come "grandi muraglie", filamenti e immense bolle di vuoto. 

Presenti in tutti questi diagrammi sono le cosiddette "dita di Dio", smisurati e inspiegabili 

allineamenti di galassie che puntano direttamente alla Via Lattea e che vengono giustificati 

come "dispersioni di effetti Doppler conseguenti a moti peculiari all'interno degli ammassi" 

… (vedi Fig. 15). 

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Fig. 15 

(Le dita di Dio) 

Ma se i cartografi delle tre dimensioni avessero preso la precauzione di annotare la posizione 

in base alle luminosità e alle "taglie" delle galassie, avrebbero potuto constatare ad 

un'occhiata che le più luminose cadono sistematicamente vicino all'apice delle "dita di Dio": 

qualsiasi dilettante puntiglioso potrebbe facilmente dimostrarlo provando una volta per tutte 

che quei redshift non possono rappresentare velocità e distanze, e che queste "mappe" sono 

prive di significato come indicatori della distribuzione in profondità delle galassie. 

CROCI DI EINSTEIN, TOLOMEO E QUANTIZZAZIONE 

L'evidenza che i quasar cadono vicini alle galassie non è contestata dai cosmologi di credo 

convenzionale: viene attribuita per lo più a "vizi di selezione", a "stastistiche a posteriori" e a 

"effetti lente gravitazionali" previsti dalla teoria della Relatività. Anche la presenza di 

"materia oscura" - la cui presunta concentrazione al centro e ai bordi degli ammassi 

amplificherebbe la visibilità degli oggetti di fondo - è chiamata in causa; e quando si trovano 

coppie, tripletti, quartetti di quasar molti vicini e con analogo spostamento verso il rosso, 

questi diventano automaticamente "candidati lenti". 

"E' anche un buon modo di sfoltire i quasar- feci notare a un influente astrofisico nel corso di 

un dibattito - e sarebbe istruttivo per la platea comprendere perché la loro concentrazione 

intorno alle galassie attive è una statistica a posteriori, mentre le lenti gravitazionali non lo 

sono". 

"Naturalmente lei è libero di non crederci - fu la risposta - ma l'ha detto un certo Einstein! 

Vada a guardarsi la «croce» che porta il suo nome, e poi mi sappia dire …". 

L'immagine della "Croce di Einstein" è riportata qui sotto (Fig. 16), e mostra quattro quasar 

centrati nel nucleo di una galassia a spirale che si trova a una distanza stimata di circa 500 

milioni di anni luce.

Fig. 16 

(Einstein Cross) 

Poiché i quasar sono ritenuti gli astri più distanti dell'universo e poiché l'osservazione di un 

simile raggruppamento profondo (dentro un secondo d'arco) sarebbe per lo meno improbabile, 

i cosmologi ne deducono che si tratta dell'allineamento accidentale di un unico oggetto 

distante nove miliardi di anni luce "spaccato" in quattro dalla massa della galassia molto più 

vicina a noi, che gli cade di fronte sulla nostra linea di vista. 

Oppure i quasar sono quattro, e stanno emergendo ortogonalmente dal grembo della galassia 

con l'altissimo spostamento intrinseco dovuto alla loro giovane età. Ma così vien giù tutto, la 

Croce, il Big Bang e settant'anni di cosmologia. 

Improbabile. L'allineamento, tuttavia, dovrebbe essere così esatto che la chance prospettica è 

calcolabile in 2 x 10 -6 , mentre la massa richiesta per il nucleo della galassia che fa da "lente" 

dovrebbe essere almeno 1.1 x 10 10 masse solari!! 

Questo valore eccede quello dei nuclei delle più massicce galassie dell'universo, mentre 

qualsiasi astronomo d'osservazione, potrebbe confermare ad un'occhiata che "l'oggetto lente" 

in questione è in realtà una galassia nana! Il lettore che cerca affannosamente di decidere dove 

stanno i quasar nell'universo, può tornare alla Figura 9, se crede; ma questa non è ancora tutta 

la storia della Croce di Einstein, perché Arp e Philip Crane, riprocessando le immagini 

ottenute dall'Hubble Space Telescope evidenziarono una linea Lyman alpha che connetteva il 

quasar di destra e quello sottostante al materiale di bassa densità della galassia "lente". La 

rivista "Nature" si rifiutò di pubblicare il risultato, che tuttavia apparve su "Physics Letters" 

(A, 168, 6) nel 1992. 

99

100 

Fig. 16 bis 

Contorni di immagine che mostrano elongazioni e connessioni di materiale 

con il nucleo della galassia centrale (da Arp e Crane, 1992). 

La reazione finale fu che Arp e i suoi subalterni non credono nemmeno alla Relatività 

Generale, ma anche qui la sottile distinzione è che essi semplicemente non credono che la 

"Croce di Einstein" sia davvero un effetto lente gravitazionale. 

QUANTIZZAZIONE 

Ma esiste un'altra conferma (del tutto indipendente dai dati di Arp) che i redshift delle 

galassie e dei quasar non possono essere attribuiti all'espansione dell'universo. Si tratta della 

quantizzazione che emerge dall'analisi dell'intera distribuzione spettrale degli oggetti cosmici, 

veri e propri numeri magici ricorrenti, per i quali non si può evitare di darne almeno un cenno. 

Uno dei risultati più raccapriccianti dell'interpretazione ortodossa è che l'affollamento dei 

quasar attorno alle galassie attive comporterebbe immensi coni allungati i cui vertici puntano 

invariabilmente verso la Terra. Abbiamo visto che un problema analogo sorge quando si tende 

a rappresentare in sezioni profonde la distribuzione delle galassie in base alla relazione 

distanza-velocità: appaiono inspiegabili incolonnamenti in fila indiana ("le dita di Dio") 

intervallati da enormi "pareti" e zone di vuoto ("struttura a bolle") con la terra ancora al centro 

(Figure 14-15). 

Un'équipe di ricercatori esaminò i dati disponibili per galassie appartenenti a zone di cielo 

contrapposte (T. Broadhurst et alt., Nature, 343, 72, 1990) trovando fronti e muraglie di 

oggetti che ricorrevano in mezzo a zone quasi completamente vuote a intervalli regolari di 

130 megaparsec! (Fig. 17). Questi dati inattesi provocarono enorme stupore, ma quando fu 

chiaro che essi contraddicevano qualsiasi teoria di formazione delle galassie in accordo col 

Big Bang, si obbiettò che le porzioni di cielo indagate erano troppo piccole per essere 

"rappresentative", e che si imponevano quindi ulteriori investigazioni su sezioni di cielo più 

estese e profonde, con telescopi più potenti. Che è poi un'impresa titanica, perché i telescopi 

di maggiore apertura hanno un campo d'osservazione ridottissimo (il 10 metri del Keck I 

spazia ad esempio 1/250 della grandezza della luna piena) e non è mai chiaro dove si sta 

guardando.

Fig. 17 

Tuttavia le numerose surveys successive hanno "confermato" l'esistenza di muraglie e di bolle 

di vuoto o, equivalentemente, che i picchi di redshift risultano sistematicamente quantizzati a 

valori preferiti. L'ortodossia rimane "abbottonata" nei confronti della periodicità, perché la 

presenza a intervalli discreti di muraglie e gusci concentrici di galassie riporterebbe 

trionfalmente Tolomeo al centro dell'universo; le "bolle di vuoto" tuttavia sono in alcuni casi 

così grandi che nella cornice del Big Bang non ci sarebbe tempo sufficiente per formarle. 

Come ha dichiarato a più riprese l'astronoma Judith Coehn, le grandi strutture avrebbero 

potuto formarsi solo accordando un tempo di gran lunga superiore "alla presunta età 

dell'universo", cosicché non è più chiaro nemmeno all'ortodossia quale significato accordare 

alle molte reclamizzate "mappe di profondità" (vedi Figure 15-16). 

L'evidenza che i redshift delle galassie compaiono a valori discreti era tuttavia disponibile da 

molto tempo. Nel 1976 l'astronomo del Caltech William Tifft rilevò da un campione 

numeroso di galassie binarie che le differenze di redshift cadono costantemente nell'intervallo 

di 72-144-216 km/sec. e multipli: il risultato venne subito ridicolizzato in quanto nessuno 

sarebbe stato disposto ad accordare velocità di recessioni quantizzate alle galassie binarie. 

Inoltre i moti reciproci di interazione avrebbero dovuto cancellare qualsiasi periodicità anche 

nel caso che l'effetto fosse stato reale: Arp ricorda che si ironizzò a lungo sulla possibilità di 

un annullamento retroattivo del titolo accademico di Tifft. Ma tutte le rilevazioni successive 

su coppie di galassie confermarono costantemente questo risultato, che fu nuovamente 

evidenziato con misure radio dell'idrogeno neutro, che sono in grado di determinare i redshift 

nel modo più accurato. Dove siano andati a finire i moti gravitazionali relativi resta un 

mistero insoluto sul tavolo degli astrofisici (e dello stesso Arp!): nel frattempo però è 

diventata schiacciante l'evidenza che anche i redshift dei quasar sono fortemente quantizzati 

su valori preferiti. 

L'astronomo svedese Karl Karlsson trovò che i picchi ricorrenti potevano essere riprodotti da 

una formula ∆log(1-z) = costante, che nella tabella riportata qui sotto 

z = 0,30 z = 1,96 

z = 0,60 z = 2,64 

z = 0,96 z = 3,47 

z = 1,41 z = 4,49 

assume il valore cost. = 0,089. 

Il punto di vista tradizionale non è mai intervenuto a smentire la periodicità degli spostamenti 

verso il rosso dei quasar perché nella cornice cosmologica del Big Bang la loro collocazione a 

101

102 

grandi distanze ha pur sempre un significato che è in stretta relazione con l'evoluzione 

dell'universo. Ma non c'è dubbio che qualunque possa essere il meccanismo che impartisce 

valori discreti allo spostamento delle righe delle galassie e dei quasar, questa è un'altra prova 

decisiva che il redshift non può essere attribuito a velocità. 

Val la pena concludere questo blitz nella quantizzazione ricordando che nel sistema 

cosmologico a creazione continua di Arp e di Narlikar i redshift degli oggetti cosmici 

esprimono le loro età di formazione, ma non necessariamente le loro distanze. Così le loro età 

(apparenti) dovrebbero essere miscelate dal look back time in quantità intermedie e cancellare 

così ogni traccia della periodicità. La proposta di Arp e che la quantizzazione sia in relazione 

diretta a passaggi evolutivi "permessi" che eludono stati intermedi nella "progressione" della 

massa variabile, rendendo così la sua evoluzione osservabile solo a certi stati discreti. Questo 

riporta l'astrofisica nell'alveo della meccanica quantistica e costituisce una formidabile sfida 

per la ricerca e per la scienza del futuro. 

LA RIVOLUZIONE PUÒ ATTENDERE? 

L'osservazione delle fasi di Venere e di Mercurio non produsse immediatamente 

l'Illuminismo, ma una lenta agonia. E' storia nota: grandi differenze nella percezione della 

realtà provocano inevitabilmente lacerazioni e conflitti profondi prima di riconciliarsi in un 

nuovo paradigma. Ma la rivoluzione di Copernico, la genialità di Keplero o l'evidenza 

empirica di Galileo non rappresentarono la vittoria degli illuminati sugli ottusi, dei sapienti 

sugli incolti, degli "eretici" sui "collaborazionisti". Al contrario, gli oppositori che all'inizio 

erano il mondo intero, furono spesso persone di grande intelligenza. 

Il progresso scientifico si realizza però quasi sempre quando qualcuno, nella bonaccia 

dell'unanimità, esclama: "E' sbagliato!". O grida, come nella favola di Andersen, che il Re è 

nudo. Naturalmente questo non significa che la scienza abbia sempre torto, ma che l'Autorità 

istituzionalizzata della conoscenza deve essere perennemente in discussione: è vero che 

nessuna futura razionalità potrà mai riportare la terra al centro dell'universo o restituirle una 

forma piatta, ma è presumibile che tutte le teorie, compresa quella di Narlikar e Arp, siano 

destinate col tempo a essere riformulate. Ciò che non può essere cambiato, o modificato, o 

soppresso, sono i bracci, i filamenti, le connessioni osservative di materia che legano oggetti 

di diverso spostamento spettrale e che impongono la falsificazione dell'assunzione 

fondamentale della cosmologia. 

Paradossalmente, è proprio l'accettazione dell'evidenza che si rivela l'ostacolo più difficile. 

L'astronomo Massimo Capaccioli ha dichiarato (sottovoce) che "Forse Arp ha ragione, ma 

fra cento, o mille anni", e se ciò è vero questo stesso articolo è in anticipo di cento o mille 

anni, destinato ad essere fatto a pezzi dalla Contemporaneità in attesa di una eventuale 

riabilitazione postuma. 

Chi allontana i dati di Arp e ne sospende il giudizio rinviando la questione all'infinito ragiona 

più o meno così: "Nonostante queste «scomode» osservazioni non sembra che ce la caviamo 

tanto male; abbiamo una teoria della creazione cosmica che è matematicamente corretta fino 

all'istante 10 -43 , un modello della struttura della materia che funziona e un emergente teoria 

delle Supercorde che promette di unificare il tutto e il nulla nel rispetto delle leggi della 

fisica. E' vero che la predizione di Stephen Hawking di trovare una master equation che 

spieghi tutto entro il duemila («da stampare su teeshirts»)non si è avverata, ma chi può dire 

cosa troveremo tra dieci anni? Perché l'universo deve essere per forza complesso quando 

può essere invece semplicissimo? Non è colpa della scienza se gli eventi sono caotici e 

impredicibili, non è colpa della scienza se la natura è competitiva e non cooperativa, o se la 

società è sempre più cinica e violenta: mica si può incolpare le GUT (Great Unified 

Theories) per la fondamentale irrazionalità dell'esistenza!. 

E non c'è dubbio. Se si evita di considerare le confutazioni e le falsificazioni eliminandole 

dalla discussione nessuno si chiederà più se la scienza possa avere ottenuto le risposte

sbagliate da tutte le più importanti questioni cosmologiche. E se sono sbagliate, anche il Big 

Bang, le GUT, le Supercorde e forse "la fondamentale irrazionalità dell'esistenza" sono da 

riscrivere. Come sempre in tutte le grandi rivoluzioni, il fatto è più culturale che scientifico. 

Vorrei concludere questa mia esposizione della controversia con due aneddoti di natura 

sociologico-osservativa, se così si può dire. Il primo è a lieto fine, e riguarda il braccio che 

collega le due galassie con redshift altamente discorde NGC 7603 A e B e i due quasar che vi 

sono immersi, di cui ho già parlato in precedenza (vedi Fig. 9). Appena mi fu nota, comunicai 

questa decisiva scoperta anche a un insigne fisico relativista di Bologna, invitandolo senza 

mezzi termini a prendere una posizione. 

La cortese risposta fu: "Non rifiuto di guardare nel cannocchiale di Galileo, e, delle due, di 

fronte all'immagine trasmessa sono incline a dar ragione a lei. Ma non posso giurarci. Qui 

vident sciunt? Mah … nel cannocchiale si vedevano le stelle medicee, ma anche Saturno 

tricorporeo … Aspettiamo. Il tempo farà (forse) giustizia". 

Avrei dovuto accontentarmi? "Aspettiamo … che cosa? - replicai prontamente - Io guardo 

galassie da quarant'anni e a meno di dubitare delle fasi dei pianeti interni, giurerei che le 

due galassie in questione sono connesse da un visibile ponte di materia. Lei no? Può anche 

tenere i due quasar nello sfondo, se crede, confidando in una possibilità su un milione, ma 

non può allontanare le due galassie senza sopprimere l'astronomia osservativa. Il tempo 

servirà solo a mantenere lo status quo. Dobbiamo convenire che la storia che si ripete non ci 

insegna nulla?". 

Dopo qualche tempo ricevetti una comunicazione che mi preannunciava l'inserimento dei dati 

di Arp in un'importante Seminario sulla Cosmologia per il dottorato in fisica, e sarò 

eternamente grato a quel Professore per il suo atteggiamento costruttivo. 

Il secondo episodio è assai meno incoraggiante ed è un esempio tipico di come l'establishment 

cosmologico reagisce di fronte a osservazioni di segno opposto. 

La Figura 18 mostra una mappa in raggi X ottenuta da W. Pietsch nel 1994 con il telescopio 

orbitale tedesco ROSAT centrato sulla galassia attiva ed espulsiva di tipo Seyfert NGC 4258. 

Fig. 18 

103

104 

Si notano immediatamente due intense emissioni X allineate ai due lati della galassia che è a 

sua volta una forte emittente di raggi X. Due sorgenti così perfettamente speculari avrebbero 

meno di una probabilità su mille di appaiarsi accidentalmente nello sfondo e in modo così 

esatto ai due bordi della galassia su una linea che passa per il nucleo. Era dunque di 

straordinario interesse astrofisico approfondire subito la natura di queste due sorgenti: ma un 

radioastronomo dichiarò preventivamente che le due emissioni erano in realtà "echi 

elettronici dovuti al sistema di rivelazione quando si gira lo strumento, ben noti a chi conosce 

la tecnica nel dettaglio"! 

Disgraziatamente per lui le due emissioni avevano controparti ottiche che Pietsch, Vogler, 

Kahabaka, Jain e Klein ("Astronomy and Astrophysics Letters, 1995) confermarono subito 

come candidati quasar. Io non ebbi più notizie del radioastronomo e commentai la cosa su un 

giornaletto amatoriale, rammaricandomi che "dopo trent'anni di allineamenti prospettici nel 

visibile, abbiamo adesso false eco nei raggi X che possiedono controparti ottiche che poi 

risultano essere quasar …". 

Ma la storia era ancora ben lontana dalla conclusione, perché nessuno voleva prendere gli 

spostamenti verso il rosso dei candidati quasar. Arp riferisce nel suo recente ultimo libro 

"Seeing Red" che numerose Istituzioni richiesero l'analisi spettroscopica degli oggetti, senza 

alcun esito. Ci riuscì alla fine, due anni dopo, Margaret Burbidge, che con il riflettore di tre 

metri di Monte Hamilton rilevò z = 0,65 per il quasar a sinistra e z = 0,40 per quello di 

destra. Gli spettri ottenuti sono riprodotti nei grafici che mostro qui sotto, e non è senza 

emozione che il lettore può vedere ancora una volta le righe di elementi noti come l'ossigeno, 

il magnesio, l'idrogeno, etc. posizionate su lunghezze d'onda lontanissime da quelle che si 

formano in laboratorio. 

Fig. 19 e 19 bis 

E' un'altra decisiva testimonianza di differenti stati della materia cosmica e un'altra cruciale 

osservazione a favore della natura riproduttiva delle galassie.

La Rivoluzione può attendere? Con commenti indipendenti sopra quel risultato, Arp ed io 

adoperammo termini analoghi di "tumulazione della cosmologia corrente": solo che io parlai 

di "ultimo chiodo nella bara del Big Bang" e lui di "ultimo fiore". Anche questo, credo, fa la 

differenza fra un piccolo dilettante e un grande scienziato. 

Note 

1 Recenti misurazioni della struttura fine su un campione di quasar effettuato da J. Webb e J. Prohaska 

(Physical Review, Sept. 2001) sembrano riproporre la possibilità di variazioni intrinseche nella carica 

dell'elettrone. Integrando questi risultati nella cornice cosmologica che colloca i quasar ai confini 

dell'universo, Paul Davies e altri hanno suggerito la possibilità che al momento del Big Bang la 

velocità della luce tendesse all'infinito! (Nature, agosto 2002). Qui il commento potrebbe essere: che 

duro prezzo sono disposti a pagare i sostenitori della Palla di Fuoco per tenere i quasar alle loro 

distanze di redshift. 

2 L'induzione ricavata da Arp su base osservativa ha una formulazione matematica completa e rigorosa 

nella "teoria della massa variabile" sviluppata da Hoyle e Narlikar già agli inizi degli anni Settanta 

("Action at Distance in Physics and Cosmology", S. Francisco, 1974). E' chiamata anche teoria 

generale della gravità conforme e descrive la massa delle particelle come funzione della posizione e 

del tempo. Informazioni dettagliate sono reperibili anche nel nuovo libro di Arp "Seeing Red", 

Apeiron, 1998, sull'Astrophysical Journal, Narlikar e Arp, 405:51-56, 1993, in "Origini", Autori vari, 

Il Poligrafo, 1994 e nel volume dell'autore di questo articolo, "Eppur non si muove!", - La controversia 

sull'espansione dell'universo - Studio Stampa, 1996. 

- - - - - 

[Una presentazione dell'autore si trova nel numero 2 di Episteme - si veda anche 

il suo contributo nella sezione "Commenti Ricevuti" della I Parte di questo 

stesso fascicolo della rivista] 

"virgilio" 

105

106 

I. Maxwell's Equations 

Beyond Maxwell-Lorentz Electrodynamics 

(George Galeczki) 

Freeman Dyson published twelve years ago [1] "Feynman's proof of the Maxwell equations". 

He recalls that in 1948 Feynman showed him this "proof assuming only Newton's law of 

motion and the commutation relation between position and velocity for a single particle." 

Although formally obtaining the two "vacuum equations" (i.e. those without source terms), 

the claimed "proof" of the full Maxwell equations is wrong mathematically, physically and 

conceptually. On top of all this, it expresses the - nowadays common - arrogance of 

mathematical physicists giving priority to formalism against empirical facts. 

As a matter of fact, Maxwell's equations (ME) represent the mathematical expression of the 

experimentally discovered laws of Gauss, Ampère and Faraday and are widely used in 

physics and engineering. Several remarks and comments are in order, each of them being 

subsequently discussed in more detail: 

1/ The basic formulation of ME - as derived from experiments - is in integral form 

pertaining to a finite, closed area or volume. 

2/ The ME are formulated for continuous fields and are called, therefore, field equations. 

3/ ME hold for closed circuits only. 

4/ The sources of the fields are continuous charges and continuous current densities. 

The discrete, quantized charges introduced in Maxwell's theory are foreign elements. 

5/ ME are tautological in the sense that they merely represent relationships between fields 

and their sources. One has to provide the initial charge distribution in order to be able to 

calculate the field distribution, or vice versa. 

6/ ME is unable to describe the interaction between two discrete charges. 

7/ ME is unable to supply the equation of motion of one charge in the field produced by all 

others. 

8/ ME are not suited for the description of open circuits like antennas. 

9/ ME are unable to prescribe the exact conditions under which a system will radiate, or not. 

The notorious example is Bohr's planetary model of the hydrogen atom. 

10/ ME are unable to provide a stable model for the elementary charge. 

11/ ME are generally covariant and do not single out the Lorentz transformation (LT) of the 

"special" theory of relativity (STR). 

12/ ME are formulated in terms of independent, Eulerian coordinates x, y, z, t and partial 

derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t .

ME in their original, integral form and in modern notation are: 

∫ E.ds = - ∫ ∫ (∂B/∂t).da ∫ ∫ 

B.da = 0 (1) 

∫ ∫ D.da = ∫ ∫ ∫ ρ dV ∫ H.ds = ∫ ∫ (j + ∂D/∂t).da (2) 

Contained in the above is the equation of continuity: 

∫ ∫ j.da = - ∫ ∫ ∫ 

ρdV (3) 

where ρ and j denote charge and current density, respectively. 

In all cases the regions of integration are assumed to be stationary and mechanically rigid. 

ME in differential form , as derived from (1), (2) and (3) by means of Stokes' and Gauss' 

theorem, are: 

∇ × H = j + ∂D/∂t ∇ × E = -∂B/∂t (4) 

∇ . D = ρ ∇ . B = 0 (5) 

and the corresponding equation of continuity: 

∇ . j = -∂ρ/∂t (6) 

ME in differential form express the relationship that must exist between the four field vectors 

E, D, H and B at any point within a continuous medium (?). In this form, because they 

involve space derivatives, they cannot be expected to yield information at points of 

discontinuity in the medium. However, the integral form can always be used to determine 

what happpens at the boundary surface between different media. It follows then, that the 

tangential components of E and H (except perfect conductors) and the normal components 

of B and D (if no surface charges are present) have to be continuous at the interface. 

II. Maxwell's Equations and "Special" Relativity 

As already said, besides generalizing Ampère's circuital law by introducing the "displacement 

current", Maxwell's achievment was to express the experimental laws of Coulomb, Gauss, 

Ampère, Faraday in mathematical terms. The modern, vector form of ME was introduced by 

Gibbs. Einstein's "special" relativity of 1905 has built heavily upon electromagnetism and, 

assuming the validity of ME in all inertial frames of reference (IFR's) introduced the 

incomprehensible "postulate of light velocity invariance". This constancy is not that refering 

to the light source - a wellknown fact in classical wave theory - but to the independence of the 

velocity of light from the uniform velocity of the observer/detector relative to the source. 

Since in the special case of vacuum-as-continuous-medium the ME displayed covariance (not 

invariance!) under the so called Lorentz transformations (LT), ME and STR became 

indissolubly tied together, one implying so to say the other. This strategy proved itself very 

useful, since every criticism of STR was authomatically seen as criticism of ME, thus 

contributing to the survival of the contradiction ridden STR. 

The said bi-univocal correspondence between ME and STR is manifested, however, only if 

one has in mind the differential form of ME. The reason is that STR is a local, point-event 

theory, with local simultaneity and position and velocity dependent time! Due to this 

feature of STR, only local conservation laws of energy and momentum are compatible with 

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108 

STR. While valid in the hydrodynamic approximation - a continuum theory - the local, 

differential conservation laws fail in the case of discrete, extended systems. The global 

time required in this case, independent of position and velocity, is anathema to STR. Farady's 

law of induction assumes tacitely such a global time and distant simultaneity, thus allowing 

the definition of inductance and self-inductance for macroscopic, closed circuits. Since the 

stationary circuits appearing in the integral form of ME are incompatible with STR, it is quite 

understandable why the STR "philosophy" gave almost exclusive prominence to ME in 

differential form and eliminated the integral form from physics textbooks and monographies. 

As a matter of fact, this form - more rich in physical information - is actively in use in 

engineering books on electromagnetism [2]. 

III. General covariance of Maxwell's equations 

It was repeatedly and forcefully pointed out by Post [3] that Maxwell's equations are 

general covariant. Post quotes that Kottler, Cartan and van Dantzig (KCD), quite 

independently of one another concluded on the natural invariance of ME, independent of 

any metric or linear connection. Post strongly emphasized the clean functional separation 

obtainable between the constitutive equations { D(E), B(H), J(E) } and the field equations. 

In this approach the constitutive equations instead of ME carry all the metric 

information, while the field equations (4) and (5) are covariant under all possible space and 

time coordinate transformations: Galilean, Lorentzian, conform and so on. The use of (E, D, 

B, H) rather than two field vectors eliminates the cgs free-space field identification. The latter 

tied the cgs situation irrevocably to an inertial reference frame. A free-space inertial situation 

is defined by an explicit constitutive relation: 

D = ε0E , B = µ0H (7) 

Which can be proven to be invariant under the Lorentz group, as well as under scale changes 

of the conformal group. Here is the place to mention the qualitative difference between 

invariance and covariance: a physical law is said to be invariant under a coordinate 

transformation when the vectors/tensors entering the law remain unchanged, while in the case 

of covariance the components of the vectors/tensors are transformed, or in Thomas Phipps' 

words "scrambled", according to the same rules as the coordinates,. Only after performing this 

scrambling the equations in question remain form invariant. 

The superiority of the KCD approach is that the field equations retain their form when a 

transition is made from an inertial to a non-inertial frame, in particular a rotating frame. 

(N.B. Jan Evert Post was the chief theoretician of the ring laser gyro project, which produced 

the most sensible detector of rotation, i.e. of the degree of non-inertiality). Moreover, the form 

invariance of ME is independent of whether the fields exist in free space or in matter. The 

information about the reference frame and the state of motion of the matter therein is 

conveyed exclusively by the nature of the constitutive equations. The general form of these 

equations is tensorial and the applications to specific problems was intensively investigated 

by Post. 

IV. The force of Lorentz and Maxwell's equations 

It is clear from what has been said till now that the Maxwell field equations (4) and (5) 

expresses a law of nature and will retain their validity so long their limitation to closed 

circuits is assured. The tautological nature of ME follows from the absence of "detector 

charges" in the rhs, since only the source charges and their distribution is considered. It 

means that the ME are intrinsically unable to provide either a force law between discrete 

charges, or an equation of motion for individual charge within a system of charges. Here I can

mention another fundamental difficulty connected with the discrete vs. continuum dichotomy, 

reflected in the use of two different kinds of coordinates: the already mentioned four 

independent, Eulerian x, y, z, t and the three time dependent Lagrangean coordinates x(t), 

y(t), z(t). The former are suited for field theories, while the later for particle dynamics. Fields 

are functions of x, y, z, t, meaning that they have different values at the points of a 4D 

continuum. They don't "propagate" in the 4D continuum. The solutions x(t), y(t), z(t) of the 

dynamical equations of motion, on the other hand, are 3D vectors and the coordinates "move - 

so to say - with the particle". This already shows that STR is at least formally compatible with 

pure field theories, but incompatible with (discrete) particle dynamics [4]. Anyway, quite 

independently of STR, in order to brake the tautology, ME have to be completed by a force 

law and an equation of motion for discrete charges, the very program of Lorentz who 

introduced the quantized electrical charges into Maxwell's field theory. The ME supplemented 

by the Lorentz force-law (LF) is called Maxwell-Lorentz electrodynamics (MLE). Lorentz 

himself remained unsatisfied with his force-law: 

FL = q (E + v × B) (8) 

In his own words [5]: "It is got by generalizing the results of electromagnetic experiments. 

The first term represents the force acting on an electron in an electrostatic field [F1=qE] . On 

the other hand, the part of the force expressed by the second term may be derived from the 

law according to which an element of a wire carrying a currect is acted on by a magnetic 

field [dF2 = (qv x B , assuming Jds = qv ] . After having been led in one particular case to the 

existence of the force [F1 = qE] and in another to that of the force [F2 = qv x B ] , we now 

combine the two in the way shown in the equation, going beyond the direct result of 

experiments by the assumption that in general the two forces exist at the same time." 

(a) The two 'particular cases' here 'combined' are, however, quite incompatible. In one case we 

have a charge at rest, in the other the charges are moving. 

(b) Experiments with 'a wire carrying current' have to do with neutral currents, yet the 

derivation contradicts this neutrality. The discovery of the Hall effect, formally described as a 

"modified Ohm's law": 

j = σE + k(E × B) (9) 

where σ is the conductivity and k a constant, seemingly supports (8), but everybody familiar 

with the experimental set-up used in the Hall effect studies will agree that E and B above 

belong to different systems: a dc - or ac - source for E and a completely separated permanent 

or electro-magnet for B . Maxwell's theory requires, however that E and B belong to the same 

system of charges and currents. As shown elsewhere [6], the Lorentz force should have 

been written as: 

FL = q (E (1) + v × B (2) ) (10) 

i.e. a phenomenological external force, rather than fundamental force acting on a charge 

belonging to the same system, as implied by ME. The upper indexes (1) and (2) indicate that 

the electric, respective magnetic field belong to different systems, therefore ME and LF do 

not form a coherent Maxwell-Lorentz theory as claimed in present day textbooks and 

monographies! The reason for this persisting mess is the seeming compliance with SRT's 

LT. This belief is, however, totally wrong, since: (a) The LT apply only to E and B belonging 

to the same system and (b) The velocity v in most applications is a non-uniform velocity 

between magnets an current carrying wires, while the velocity entering the LT is the 

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uniform relative velocity between two inertial frames of reference. This confusion goes 

back to Einstein's failure to distinguish between his theory involving schesic velocities 

referred to abstract "reference frames" and relative velocities between moving masses, as 

implied by Mach's program. For this reason STR is not a true relativity theory! Using a 

somewhat different terminology - 'principle of relativity vs. 'principle of relative motion' - 

this point was discussed in a paper by Bartocci and Capria [7], too. This explains also why the 

aged Ernst Mach unmistakable declined the rôle of spiritual father of the "special" (very 

special, indeed!) theory of the young Einstein. 

V. Magnetic field, vector potential and induction 

In the spirit of the ME in their integral form, B (2) in (10) has always to be produced by a 

closed current loop: 

B (2) (r) = I' ∫ (ds' × R)/R 3 (11) 

where R = r - r' and the integral is performed around the closed current loop. Attempts to 

generalize the Biot-Savart law for time-variable magnetic fields have been made by 

Jefimenco [8] in the form: 

B = (µ0/4π) ∫ ∫ ∫ {[j]/r² + (1/rc)∂[j]/∂t} × (r/r) dV' (12) 

where [..] denotes the retardation symbol indicating that the quantities between the square 

brackets are to be evaluated for t' = t - r/c , where t is the moment for which B is calculated. It 

is interesting to note that that Eq. (12) does not contain displacement currents, thus indicating 

that although time-dependent magnetic fields and displacement currents are coupled together, 

displacement currents are not sources of magnetic fields in the conventional sense. 

Definition (11) of the magnetic field B - rightly called magnetic flux density in older books - 

is incompatible with the "Lorentz transformed E field" definition of B in "special" 

relativistic electromagnetism: 

B = V × E (13) 

valid for uniform velocity V only! This incompatibility brings us to the most important issue 

of (electromagnetic) induction and the status of Faraday's "flux rule". According to textbook 

(and also monography) knowledge, electromagnetic induction were always due to a time 

variable magnetic flux crossing a closed conducting loop. Although Faraday discovered both 

this so called transformer induction as well as the motional induction, only the first is 

embedded in the integral form of ME formulated for stationary integration regions. This 

deficiency of the integral ME is, of course, transferred to the differential form of the 

Maxwellian law of induction: 

∇ × E = -∂B/∂t (4) 

The correct expression for the induced electromotive force (emf), in terms of the vector 

potential A, follows from the integral form: 

emf = ∫ E.ds - (d/dt) ∫ ∫ B.da = -(d/dt) ∫ ∫ (∇ × A).da = -(d/dt) ∫ 

which provides the formula: 

A.ds (14)

Eind = -dA/dt (15) 

for the induced electric field Eind. Keeping the integration region stationary, one gets the 

'transformer field': 

Eind = -∂A/∂t (16) 

The difference between Eq. (15) containing the total time derivative d/dt and Eq. (16) 

containing the partial time derivative ∂/∂t is huge and has fatal consequences for "special" 

relativity! This is obvious, since in ME the four partial derivatives ∂/∂x , ∂/∂y , ∂/∂z , ∂/∂t are 

on equal footing (see, for example, Eq.(6)) and obey the LT. The presence of the total time 

derivative, by giving to the time derivative a distinct status, destroys the Lorentz 

covariance of ME! 

Here is the place to mention the incompleteness of the traditional formula for the total 

derivative of a vector field: 

dA/dt = ∂A/∂t + (v.∇)A (17) 

and the time rate of change "seen" by a point moving with velocity v in a vector field A [9]: 

Although the vector identity: 

dA/dt = ∂A/∂t + (v.∇)A + (A.∇)v (18) 

(v.∇)A + (A.∇)v + A × (∇ × v) - ∇(v.A) = -v × (∇× A) = -v × B (19) 

for v.A = const. and ∇ × v = 0 leads to the 150 years old formula of Neumann: 

Eind = -∂A/∂t + v × B (20) 

equation (18) covers all known situation of electromagnetic induction, including those where 

Eq. (19) fails. Eq. (20) is still in exclusive use, although it has never been rigorously justified. 

Neumann - just like later Lorentz with his force law (8) - just juxtaposed Faraday's and 

Maxwell's transformer field and the empirical field found in the unipolar induction 

experiments of Faraday and in the (then) recently discovered Hall effect, called motional 

induction field. Wesley derived for the first time (!) the most general law of induction which 

includes (20) as a particular case. The surprising result is that the law based upon (18) is able 

to describe phenomena governed by the term (v.∇)A like the Aharonov-Bohm (AB) effect 

and the Marinov motor [10]. The demystification of the "strange quantum-mechanical (AB) 

effect" [10] and its explanation in the framework of electrodynamics has been a real tour de 

force. The term (A.∇)v is presently insufficiently investigated, but preliminary results seem to 

support its explaining the interaction between two toroidal magnets (closed magnetic field 

configurations) [11], which, according to Maxwell's electromagnetism should not interact. 

The local form of the correct law of induction, involving the total derivative (18), puts an end 

to the perennial disputes between the supporters of fields and potentials, respectively. It has 

to be clear that the description by means of A is more general than the usual by means of B, 

since it provides an induced electric field even if ∇Φ = 0 (Φ denotes here the scalar 

potential), ∂A/∂t = 0 and B = ∇ × A = 0 . 

One is tempted to say that Maxwellian electrodynamics overcame all difficulties and retained 

its original form since, after all, the use of the truncated form (17) for the total derivative was 

not Maxwell's fault. The painful fact for STR-supporters is, however, that Eqs. (4) and (5) do 

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not cover all experimental situation and - acutely painful - that they do not remain 

Lorentz covariant if one replaces the partial time derivative with the total one!! 

VI. Beyond the Lorentz force law 

The force law of Lorentz (8) applies only in situations where the fields E and B are static, or 

quasistatic, when radiation could safely be neglected. In such situations, however, Eqs. (4) 

and (5) decouple in two pairs of electrostatic and magnetostatic equations, respectively: 

and 

∇ × E = 0 ; ∇D = ρ (21) 

∇ × B = j ; ∇B = 0 (22) 

This explains the upper indexes appearing in Eq. (10), indicating that the sources of E (1) and 

B (2) are different. Moreover, as already pointed out, the field B has to be produced by a closed 

current loop. It follows then, that the force of Lorentz can by no means be applied to a 

system of two charges, so that charge (1) moves in the field B (2) and vice-versa: 

d(m1v1)/dt = q1(E (2) + v1 × B (2) ) ; d(m2v2)/dt = q2(E (1) + v2 × B (1) ) (23) 

No wonder that this two-body problem would violate the linear momentum conservation 

law, since the sum of internal forces would be different from zero! The replacement of 

particle linear momentum p by (p - q.A) - as suggested by the "operator formalism" of 

quantum mechanics - doesn't save the conservation law. 

The inability of Lorentz force to describe the simplest system of two interacting charges is 

presented in textbooks and monographies as due to the fact that "at least one charge path has 

to be closed", which is obviously false! In a dense plasma, for example, even in external 

magnetic fields, where charges are permanently colliding with each other, there may well be 

no closed paths at all. The fact that the external magnetic field is produced by the closed 

circuits of the electromagnets is irrelevant for the plasma system! 

There exists a rich experimental evidence for the failure of Maxwell-Lorentz electrodynamics 

at low velocities (v/c

vhere V = v - v' and dV/dt denote the relative velocity and the relative acceleration 

between the moving charges. This truly relativistic (Machian) and instantaneous force law 

explains all known experiments at low velocities with metallic currents, including Ampère's 

moving bridge one and the 'electromagnetic rail gun' used in frame of the SDI program 

[12] which both imply longitudinal forces between parallel metallic current elements. It is 

notorious that the Lorentz force - acting perpendicular on current elements - is unable to 

account for these experiments. In spite of this, the belief in uniqueness of the Grassmann- 

Biot-Savart-Lorentz (GBSL) force law is so strong, that Ampère's law (25) - called by 

Maxwell "the cardinal formula of electrodynamics" - is not even mentioned in the vast 

literature on electrodynamics. Once again, this belief is motivated by the seeming compliance 

of the Lorentz force (8) with the LT, i.e. with STR. Wesley put his finger on the sorepoint of 

the interminable controversy about Lorentz vs. Ampère force. The supporters of the LF cramp 

to the equivalence of the two forces when two closed current loops are involved. This is 

totally irrelevant as it is only a question of the analysis of the mechanical forces between the 

two objects, the metallic bridge and the remainder of the circuit as a mechanical object. 

However, Grassmann's derivation of his law (equivalent with that of Lorentz) is only valid 

for mechanically rigid electrical circuits. This means that the GBSL law cannot be 

applied to the electrical circuit involved in the non-rigid Ampère bridge! 

Weber's law correctly describes the motion of electric charges in vacuum - for example in the 

electron microscope - since in this case E and B are external and B is produced by closed 

current loops. The useful phenomenon of "self-focussing", or "pinch effect" wellknown to 

electron microscopist, is also explainable within the traditional frame of Maxwellian 

electrodynamics, as attraction between parallel currents. 

Remarkably, Ampère's and Weber's laws comply with Newton's third law (actio = reaction), 

since the forces act instantaneously along the line joining the current elements, or the 

moving charges. This condition for law velocities is one of the requirements for a system 

being non-radiating even for charges moving with high (v >> c) velocities. As a matter of 

fact, both the hydrogen atom and the 'rotating ring electron model' are conservative, i.e. 

non-radiating, provided the forces are of Weber type! 

VII. Some comments on rapidly varying fields and radiation 

1/ The characteristic feature of Maxwell's equations is the presence of the terms ∂D/∂t and 

∂B/∂t which couple the electric and magnetic fields and lead to the existence of 

electromagnetic waves, or radiation. The field equations completed with the Lorentz force 

law (the MEL equations) are therefore incoherent, since the fields in the LF expression are 

static, or quasistatic, which means that radiation is neglected. No wonder that the attempts of 

Dirac and others to add "radiation terms" to the equation of motion of the electron leads to 

strange "runaway solutions" and other unsolved difficulties. 

2/ The 104 years old Liénard-Wichert formula [9] for the retarded potentials corresponding to 

a point-charge moving with acceleration a along the positive direction of the x-axis has been 

seriously questioned by Chubykalo and Smirnov-Rueda [13] and independently by Wesley 

[9]. This indicates that the "special" relativistic Maxwell-Lorentz electromagnetism is an 

unsatisfactory theory by itself, although the reason is hidden in the mathematics of 

d'Alembert's wave equation, rather than in the ME themselves. 

It is textbook knowledge [13] that the solutions of the wave equation (d'Alembertian) are: 

Φ = ∫ ∫ ∫ [ρ]/R.dV + Φ0 ; A = ∫ ∫ ∫ [j]/R.dV + A0 (27) 

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which are the retarded potentials. Φ0 and A0 denote the solutions of the homogeneous wave 

equation. This is OK. From here one usually derives: 

and the fields: 

Φ = q/(R - v.R/c) ; A = qv/(cR - v.R) (28) 

E = - q(1 v²/c²)(R - vR/c)/(R - R.v) 3 + qR × {(R - vR/c) × a}/(R - R.v/c) 3 c² (29) 

B = (R × E)/R 

Chubykalo and Smirnov-Rueda show that formula (29) does not satisfy the d'Alembert 

equation along the x-axis at any time. This follows from the fact that the wave equation for 

Exdescribes only transverse modes and - on the other hand - the x-component according to 

(29) is different from zero. Thus, the Liénard-Wichert potentials, as solutions of the complete 

set of Maxwell equations, are inadequate for describing the properties of electromagnetic field 

along the direction of an arbitrarily moving charge. Whitney [14] found another inadequacy 

of the Liénard-Wichert potentials for describing the properties of relativistic fields. Further, it 

is easy to verify that the Poynting vector calculated with Eq. (29) equals zero, i.e. no energy 

transport takes place along the x-axis, while the energy conservation law requires both energy 

density and divergence of the Poynting vector to be different from zero! 

The criticism of Wesley [9] is even more fundamental and relies upon the fact that in the 

wave equation of a field theory, the four variables x, y, z, t have to be independent 

(Eulerian) as explained also in [4]. Despite this clear mathematical requirement that r' and t' 

be independent variables, in the integral representation (28) of the retarded potentials Liénard 

and Wiechert argued incorrectly that the independent space variable r' is a dependent 

function of the time variable t'.The change in the 'delta function' - which accounts for the 

point-like nature of the charge - leads to the correct expressions for the retarded Coulomb 

potential: 

Φr = q'/Rr (30) 

where Rr = R(t)/(1 - v/c) for an observer moving directly away with v < c from the point 

charge. 

3/ The ubiquitous presence of radiation, i.e. of electromagnetic fields detached from their 

fields requires the existence of a unique, fundamental frame of reference, relative to which the 

energy transmission velocity is "c". This is a consequence of the fact that the velocity of light 

doesn't obey either the hypotheses of Ritz ("ballistic propagation", or dependence on the state 

of motion of the source), or the untenable second postulate of "special" relativity which is 

discused in [15]. The existence of a fundamental frame of reference which could be 

experimentally approached by successive approximations, is in line with Maxwell theory, but 

disagrees with "special relativistic electrodynamics" which states the validity of ME in any 

inertial frame of reference. 

VIII. Conclusions 

- Maxwell's equations (ME) retain their validity for closed current loops. 

- ME have to be completed with a force-law and a corresponding equation of motion. 

- In all applications the force of Lorentz is a phenomenological external force, with different

sources for E and B, the latter being produced by closed circuits. 

- MLE fails to explain low-velocity experiments with non-rigid loops. 

- Ampère and Weber's force law accounts for all electrodynamic phenomena in which 

radiation can be neglected. 

- MLE in its accepted form is unable to account for all induction phenomena. 

- The correct law of induction is given by the total derivative of the vector potential. This is 

compatible with ME, but destroys the Lorentz covariance of the theory. 

- The vector potential is of primary importance and is uniquely defined for specific systems. 

- There is no "gauge invariance". 

- Low-velocity Weber electrodynamics is truly relativistic in the sense of Mach. 

- The presence of radiation requires an absolute, fundamental frame of reference. 

References 

[1] Dyson F. J. "Feynman's proof of Maxwell equations", Am. J. Phys. 58 (1990) 209-211 

[2] Jordan E. C. and Balmain K. G., "Electromagnetic Waves and Radiating Systems" 

(Prentice-Hall, Inc., New Jersey, 1968) p. 103 

[3] Post E. J. "Formal Structure of Electrodynamics" (North Holland Publ. Co.,Amsterdam, 

1962); "Kottler-Cartan-van Dantzig (KCD) and Noninertial Systems", Found. of Physics, 

9 (1976) 619-640 

[4] Galeczki G., "Minkowski Scalar Invariant Incompatible with any Equation of Motion" 

(Proc. 2-nd Intrnational Workshop: "Physics as a Science", Koeln, 1997) 

[5] O'Rahilly A., "Electromagnetic Theory: A Critical Examination of Fundamentals",Dover 

Publ. Inc., New York, 1965) Vol. 2, p. 561 

[6] Galeczki G., "What does the Lorentz force have to do with Maxwell's equations?", 

Galilean Electrodynamics, 9 (1998) 95-98; Galeczki G., "What does the Lorentz force 

have to do with special relativity?", Galilean Electrodynamics 8 (1997) 1-4 

[7] Bartocci U. and Mamone Capria M., "Symmetries and Asymmetries in Classical and Relativistic 

Electrodynamics", Found. of Physics 7, (1991) 787-801 

[8] Jefimenko O. D., "Comment on "On the equivalence of the laws of Biot-Savart and 

Ampère", by T. A. Weber and D. J. Macomb [Am. J. Phys. 57, (1989) 57-59]", Am. J. 

Phys. 58, May 1990, 505 

[9] Wesley J. P.,"Induction Produces Aharonov-Bohm Effect", Apeiron, 5 (1998) 89-95; 

[10] Selected Topics in SCIENTIFIC PHYSICS" (Benjamin Wesley, Blumberg, 2002) 

[11] "Force between two identical coaxial toroidal solenoids" (in print) 

[12] Graneau P. and Graneau N, "Newton versus Einstein: How Matter Interacts with Matter" 

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(Carlton Press, Inc., New York, 1993); "Wesley J. P., Selected Topics in Advanced 

Fundamental Physics" (Benjamin Wesley, Blumberg, 1991 

[13] Chubykalo A. E., "Action at a distance as a full-value solution of Maxwell equations: 

The basis and application of the separated-potentials method", Phys. Rev. E, 53, (1996) 

5373-5381 

[14] Landau L. and Lifchitz E. M., "Théorie du Champ" (Éditions de la Paix, Moscou, 1965) 

[15] Whitney C. K. "A quantum of light shed on classical potentials and fields", Apeiron (?) 

[16] Galeczki G. and Marquardt P., "Requiem fuer die Spezielle Relativitaet" (Haag und 

Herchen, Frankfurt a. M., 1997) 

Acknowledgement 

I am indebted to Paul Wesley, Thomas Phipps Jr., Jan Post and Patrick Cornille 

for stimulating exchange of ideas during the years. 

- - - - - 

George Galeczki received a Licence in Physics from Bucharest University in 

1968, M.Sc. (1975) and D.Sc. (1979) degrees from The Technion - Israel 

Institute of Technology - in Haifa (Israel), for works in the field of ordered 

magnetism. In 1979 he received the Michael Landau for his research beyond his 

work toward a degree. After lecturing three semesters at the Technion, he 

moved to the governmental research center RAFAEL, where he did (mostly 

classified) work on HgCdTe-infrared detectors. After cumulating two sabbatical 

years, he left Israel, responding to an invitation from the University of Cologne 

(Germany). There he did research on heterodyne HgCdTe-infrared detectors for 

astrophysical applications and continued, in parallel, his critical work on 

fundamental physics started in 1978 under the influence of Nathan Rosen ("the 

EPR one") and Marinov's successful experiment to measure the absolute 

velocity of the Earth. He published about 50 papers on magnetism, narrowbandgap 

semiconductor physics, nanoscopy, and about an equal number of 

papers criticizing "special" and general relativities, Copenhagen quantum 

mechanics, and Big Bang theory. He is the co-author (with Peter Marquardt) of 

REQUIEM TO SPECIAL RELATIVITY (in German, published by Haag + 

Herchen, Frankfurt/Main, 1997) and organizer (with P. Marquardt and J. P. 

Wesley) of three (1997, 2000, 2002)International Workshops: PHYSICS AS A 

SCIENCE. 

He is presently an independent science consultant, science writer, 

president of the Society for the Advancement of Physics, R.S. and member of the 

Natural Philosophy Alliance. 

Society for the Advancement of Physics, R.S. 

nc-galeczge@netcologne.de

The State of Experimental Evidence for Length Contraction, 2002 

Dedication. 

(Delbert J. Larson) 

I wish to dedicate this work to the memory of John E. Chappell, Jr. In all my travels I have 

never met anyone so singly and heroically devoted to debunking the special theory of 

relativity. John led a difficult life, made difficult largely because of his questioning of the 

correctness of the scientific status quo coupled with his stubborn refusal to simply go away 

quietly and do something else. It is unfortunate that John lived his life when he did. In most of 

the recent past centuries, John's view that logic should prevail over absurdity was accepted as 

an axiom. It is my hope that most future centuries will return to that common sense notion as 

well, sparing future logic-based scholars the torment and ridicule that John had to endure 

during his time in this world. The earthly community of space time research has suffered a 

severe loss with his passing. We shall miss him. 

* * * * * 

Abstract. The idea that physical objects become shorter as they move is now well established 

in physical theory. Both the classical theories of Lorentz, Larmor, Fitzgerald and Poincare and 

the more radical special theory of relativity of Einstein incorporate a physical length 

contraction into their worldview. However, no direct measurement of length contraction has 

ever been done. One experiment that tried to observe the effect of a length contraction was 

done by Sherwin, who found no evidence of a length contraction. This paper will analyze the 

assumptions underlying Sherwin's experiment to show that Sherwin's experiment is in fact 

equivocal concerning the existence of a length contraction. This paper will also make mention 

of another important recent observation that has relevance to the issue of the existence of 

physical length contraction. 

Introduction. 

* * * * * 

In an earlier work (see reference 1) I tried to completely analyze the state of evidence for and 

against the existence of a length contraction in nature. My conclusion at that time was that one 

could not with scientific certainty state that a length contraction really exists. While there was 

and is strong evidence for a time dilation (see reference 2), there has never been any direct 

measurement of length contraction. In fact, one very important experiment, by Sherwin (see 

reference 3), seemed to provide compelling evidence that there was indeed no length 

contraction. The intervening years between my earlier work and the present have not changed 

the fact that no direct measurement of length contraction has been made. However, I now 

understand that Sherwin's experiment may not be as strong a refutation of length contraction 

as Sherwin and I had at first believed. In addition, a second set of experiments has come into 

existence in the last several years concerning earth tide measurements that has a bearing on 

the experimental evidence for length contraction. This paper will look in some depth into the 

possible physics behind Sherwin's experiment, and briefly discuss the issues involving 

measurements of earth tides at CERN. 

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Sherwin's Experiment. 

My earlier work (reference 1) showed that despite the vast majority of experiments done to 

that time no firm conclusion could be made as to whether or not a length contraction really 

exists. Indeed, the earlier paper showed that if 1) moving observers incorrectly assume that 

the speed of light is isotropic and equal to c in their reference frame; and 2) a Larmorian (or 

Lorentzian) time dilation exists in nature; then 3) the observers will arrive at the conclusion 

that the Lorentz transformations are valid for electrodynamic phenomena, even if a length 

contraction does not actually exist in nature. But beyond the issue of electrodynamics (such as 

that used in the design of particle accelerators) reference 1 also shows that no other 

experiment done can definitely prove that there is a length contraction. Especially important is 

the Michelson Morley experiment. Reference 1 goes into detail about the possibility that the 

null result of the Michelson Morley experiment might be caused by node entrapment. The 

node entrapment theory is that the electromagnetic oscillation is forced to be null at a pair of 

boundaries (the mirrors), and it is this enforced boundary condition that also forces zero 

fringe shifts to result from the Michelson Morley experiment. Once you remove that famous 

experiment (and others directly related to it) from the evidence in support of length 

contraction, you quickly find that there are no experiments that show the reality of the length 

contraction. 

However, while there are no experiments that unequivocally prove the existence of a length 

contraction, I emphasized one experiment that strongly suggested the absence of a length 

contraction. That crucial experiment was the one done by Sherwin (reference 3). 

In Sherwin's experiment, a spring was made to revolve at a high rate. Sherwin realized that if 

the Lorentz worldview was correct, that the spring would undergo a length contraction when 

it was aligned with its motion through the ether, while it would not experience the length 

contraction when it was aligned perpendicular to its motion through the ether. By arranging 

for the rotational motion of the spring to be in resonance with the spring's natural harmonic 

motion, Sherwin expected to see oscillations excited in the spring. He saw no such 

oscillations. Sherwin interpreted the lack of oscillations as experimental support for Einstein's 

special relativity (reference 4), and experimental evidence in contradiction to the Lorentz 

theory (reference 5). In my earlier work (reference 1) I interpreted Sherwin's null result as 

indicating the lack of a length contraction. Further thought indicates to me that the actual 

situation is less than clear, and that both Sherwin and I were basing our conclusions on an 

unstated assumption. 

The relevant issue is what happens to the spring as it makes its rotation, and the essence of 

this question gets down to a matter of what fundamentally determines an object's length. As 

far as present science is advanced, I would summarize my belief that length is determined by 

the spacings between the nuclei of the atoms making up the object. Those spacings can be 

analytically determined by quantum mechanics. Within a single atom, the distribution of the 

electron cloud is determined by two competing effects. More energy is required for increased 

curvature of the wave function - the favored lower energy states would have larger physical 

size from this effect. However, the Coulomb potential energy favors smaller physical size. 

The equilibrium physical size of an individual electron cloud is determined by minimizing the 

total energy found by combining these two effects as approximated by the Shroedinger 

equation, and more accurately by QED. For lattices, such as those found in metals and 

springs, the calculation is more complicated, but the same basic interplay between wave 

function curvature and Coulomb forces is what determines an object's length.

The issue of length contraction in Sherwin's experiment can be simplified by looking at 

several atoms (or ions) within the spring. Four such atoms are depicted in Figure 1. In the 

figure, a circle (or ellipse) indicates that region within which an ion's electron densities are to 

be associated with the nucleus at the center of the circle (or ellipse). (In scanning tunneling 

microscope pictures of the atoms on a solid surface, one sees bumps and valleys 

corresponding to high and low densities of the electron clouds. The circles and ellipses of 

Figure 1 would correspond to the valleys of such scans.) Figure 1 depicts the four 

representative atoms aligned in the x direction. The figure shows two cases. The first case is a 

depiction of the atoms at rest with respect to a Lorentzian ether, while the second case shows 

the atoms when they are moving in the y direction through a Lorentzian ether and hence 

length contracted. 

Figure 1. A cartoon of four atoms within a spring. Top half of the figure corresponds to 

a spring at rest with respect to a Lorentzian ether. Bottom half of the figure corresponds 

to a spring moving at velocity v with respect to a Lorentzian ether. The velocity v is 

assumed to be in the y direction. The spring extends in the x direction. 

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In Sherwin's experiment the spring is constantly rotated. Figure 2 shows the four 

representative atoms when they are aligned in the y direction. Figure 2 again shows two cases. 

The first case is a depiction of the atoms at rest with respect to a Lorentzian ether, while the 

second case shows the atoms when they are moving in the y direction through a Lorentzian 

ether. The second case shows the atoms after they are length contracted. 

Figure 2. A cartoon of four atoms within a spring. Left half of the figure corresponds to 

a spring at rest with respect to a Lorentzian ether. Right half of the figure corresponds 

to a spring moving at velocity v with respect to such an ether. The velocity v is assumed 

to be in the y direction. The spring extends in the y direction. 

Sherwin realized that the length contraction proposed by Lorentz was different than that 

proposed by Einstein. The Lorentz contraction was real, whereas the Einstein contraction was 

relative. Hence, since any frame is equivalent to any other in relativity, and the spring's 

motion in the earth-based inertial frame is symmetric about the center of motion, there is no 

orientation dependent length contraction predicted by special relativity as determined by an 

earth based observer. Since any inertial frame is as good as any other in special relativity, the 

prediction made by special relativity is that no resonant oscillations of the spring should be 

observed. However, for the real length contractions of the Lorentz theory, the spring should 

truly contract along its long dimension when it is aligned with it's velocity through the ether. 

The Lorentzian situation is shown in Figure 3.

Figure 3. A cartoon of four atoms within a spring moving through a Lorentzian ether in 

the y direction at velocity v. Top half of the figure corresponds to a spring oriented 

along its direction of motion. Bottom half of the figure corresponds to an orientation 

perpendicular to the direction of motion. 

By synchronizing the rotational motion of the spring with the spring's natural harmonic 

motion, Sherwin hoped to excite resonantly driven harmonic oscillations of the spring. His 

argument was that length disturbances should propagate no faster than the speed of sound 

throughout the spring, since that is what they do in any other type of length disturbance. 

Therefore, when the longer spring (extended along x) rotates 90 degrees (so that it extends 

along y) there isn't enough time for it to come to its new equilibrium, and the natural F=kΔx 

forces (from Hooke's Law) will excite oscillations. 

Sherwin found no such oscillations. He took this to indicate a lack of a Lorentz contraction. In 

my original work (reference 1) I found nothing wrong with Sherwin's original arguments, so I 

pointed to his experiment as providing evidence that a length contraction did not exist in 

nature. However I now realize that both Sherwin and I were relying on an unmentioned 

assumption. We both assumed that the spring was a rigid body - rigid all the way down to its 

atomic connections. Looking again at Figure 3, I am assuming that the connection between 

atoms is always such that point A connects to point C. That is, I assume that there is a rigid 

connection point between each atom, and that as the spring revolves, the centers of the atoms 

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revolve around the spring's rotation point, and the atoms themselves rotate once as they 

revolve, ever keeping points A and C connected between each atom in the spring. 

But there is another possibility. Rather than being rigidly connected at points A and C, it is 

possible that the individual atoms slide along their common boundary as the spring is rotated. 

This situation is shown in Figure 4. 

Figure 4. A cartoon of four atoms within a spring moving through a Lorentzian ether in 

the y direction at velocity v. Top half of the figure corresponds to a spring oriented 

along its direction of motion. Bottom half of the figure corresponds to an orientation 

perpendicular to the direction of motion. 

The situation is further clarified in Figure 5. Figure 5 shows five atoms within the spring in 

three possible orientations. If the spring is rotating counterclockwise in the figure, the atoms 

start out with their points A and C in contact. After less than a 90 degree rotation, the atoms 

are still in contact, but now they are not in contact at points A and C. After a 90 degree 

rotation, the atoms have their points B and D in contact.

Figure 5. A cartoon of five atoms within a spring moving through a Lorentzian ether in 

the y direction at velocity v in three rotated positions. 

If the atoms slide along their common boundary, Figure 5 shows how a null result of 

Sherwin's experiment can be obtained within a Lorentzian ether. Rather than the speed of the 

length contraction be required to propagate along the spring at the speed of sound, the length 

contraction is already there! It is just that the contact point moves along the atomic boundaries 

as the spring is rotated. 

The simple diagrams above show the relevance of slippage versus rigid contact in one 

dimension. But of course the springs are three dimensional. Still, the same principle can be 

shown to apply for three dimensional objects. Figure 6 shows the case of two rows of atoms 

within a spring. Again, if the atoms slide along their common point of contact they are able to 

smoothly transition from the case of a longitudinal length contraction of the spring to that of a 

transversely contracted spring. For the case of three dimensions one would only need to add 

atoms centered above and below the gaps between the two dimensional image shown in 

Figure 6. 

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Figure 6. A cartoon of ten atoms within a spring moving through a Lorentzian ether in 

the y direction at velocity v in three rotated positions. 

From the above analysis it can be seen that if solids behave such that the individual atoms 

within them slide along their common boundary as they rotate, then the null result of 

Sherwin's experiment can be understood even in the presence of a Lorentzian ether. If 

however, individual atoms within a solid maintain rigid contact at the atomic level, Sherwin's 

original arguments remain valid. Once again, an underlying assumption about nature must be 

made in order to interpret the results of an experiment. Therefore no conclusive statement can

e made concerning whether or not Sherwin's experiment can be used to rule out (or in) any 

particular space time theory. 

Earth Tides. 

An additional experiment has also been conducted since the time that I wrote reference 1 that 

has bearing on the question of length contraction. CERN researchers have detected changes in 

the time it takes particles to orbit their particle storage rings and have correlated those orbital 

period changes to lunar position. From these experiments they have inferred a change in path 

length that the particles must have traversed, assuming that the speed of the particles was 

constant. (At LEP, under standard relativity or the Lorentzian theory, the electron velocity is 

constant and extremely close to the speed of light.) 

These experiments could, in principle, be used as evidence for or against a length contraction. 

If there were no Lorentzian length contraction, and if Lorentzian time dilation alone is 

responsible for our inference of a length contraction (as shown in detail in reference 1), and if 

the speed of the particles is indeed constant, then the daily rotation of the earth could lead to 

different orbit times for the orbiting particles as a function of time of day. 

A full analysis of the LEP observations is very worthy of future study. 

Conclusion. 

At the time I wrote my earlier work (reference 1) I concluded that the experimental situation 

was not entirely clear as to whether or not nature contained a length contraction. By looking 

at all of the experimental evidence, it is clear that Einstein's relativity is the most in doubt, 

because of the experimental tests (reference 6) of Bell's Theorem (reference 7). At that earlier 

time I stated that the experiment of Sherwin appeared to support the case that there was no 

length contraction, but that Lorentz's theory should not be ruled out solely due to Sherwin's 

result. However, given my understanding of the experimental situation at the time, I made the 

point that there was some suggestion in the experimental data that a length contraction does 

not, in fact, exist. 

With the further analysis done herein it is now clear that Sherwin's test does not clearly 

indicate whether or not a Lorentzian length contraction exists. In addition, further analysis of 

the situation with regard to earth tide measurements at CERN may provide some suggestion 

that a length contraction does exist. 

But even with the additional insight and experimental data, I remain firm in my conviction 

that it will remain questionable whether or not there is a length contraction until a definitive 

experiment can be done. A definitive experiment could involve accelerating spheres of 

sufficient size so that ultrashort laser pulses could be fired across the spheres as they move. 

Then, the shadows thereby produced could be measured. The spheres would then have to be 

slowed down and brought to rest again. By measuring their size, as determined by the 

shadows of the light, both before, during, and after their motion, a unique measurement could 

be done concerning length contraction. (The before and after measurements are required in 

order to ensure that the spheres are not somehow mechanically altered during the acceleration 

and deceleration processes.) While even that experiment might be questioned (as can any 

experiment) it would be a far more direct measurement of length contraction than anything 

done to date. 

As of July, 2002, it is still not proven that a length contraction exists. 

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References. 

1. D. J. Larson, Physics Essays 7, 476, 1994. 

2. J. Bailey, K. Borer, F. Combley, H. Drumm, F. Krienen, F. Lange, E. Picasso, W. von 

Ruden, F.J.M. Farley, J.H. Field, W. Flegel and P.M. Hattersley, Nature 268, 301 (1977). 

3. C.W. Sherwin, Phys. Rev. A. 35, 3650 (1987). 

4. A. Einstein, Ann. Phys. 17, 891 (1905). 

5. H.A. Lorentz, Proc. R. Acad. Amsterdam 6, 809 (1904). 

6. A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49, 1804 (1982). 

7. J.S. Bell, Physics (NY) 1, 195 (1965). 

July 15, 2002 

- - - - - 

Delbert Larson, Ph. D. in Physics in 1986, in the field of particle accelerators, 

has published over 50 papers on a variety of physics topics. He has designed 

and built several complete particle accelerator systems over the years, 

including a 2.5 MeV, ampere intensity electron beam system and a 10 MeV He- 

3 ion beam system for PET isotope production. He served as a leading designer 

of the cancelled Superconducting Super Collider, doing longitudinal dynamics 

designs for that lab. Dr. Larson has written computer applications for space 

charge inclusive transverse ion optics and a separate code for longitudinal 

particle optics. Dr. Larson's computer codes have been used at laboratories 

around the world. Dr. Larson is presently leading the design of particle 

accelerators for use in medical therapy. 

Delbert7@aol.com

The Most General Fundamental Failures of Modern Physics 

(Delbert J. Larson) 

I have some thoughts on the most general and fundamental failures of modern Physics I 

would like to share. As I see it, there are three general and fundamental failures of modern 

physics: 

Failure 1 - Abandonment of Objective Reality. 

I believe that the first fundamental failure of modern physics is the forfeiture of the concept of 

an objective reality. This failure has it's roots in relativity and quantum mechanics. In their 

famous paper, Einstein, Podolski and Rosen (EPR) showed how, assuming an objective 

realty, quantum mechanics must be incomplete. Their argument was refined by Bohm, but it 

fell to Bell (name forever to be praised) to develop inequalities capable of testing whether or 

not quantum mechanics does indeed violate relativitistic causality. The tests have been done, 

(Aspect, et al, were the first, but there have been many more experiments since) and quantum 

mechanics does indeed predict the correct results of the Bell's inequality experiments. But 

underlying the EPR argument was an assumption. The assumption was that relativity was 

correct, and it is a readily obtained result of relativity that no cause can create an effect if the 

cause is separated from the effect by a relativistic spacelike interval. Faced with the 

conundrum of Bell's inequalities being an experimental reality, modern physics therefore 

faced a choice. One could either set relativity aside, or set objective reality aside. Modern 

Physics chose the latter. I believe that the wrong choice was taken. Einstein was very clear in 

his reverence for an objective reality, and so am I. It is clear to me that relativity should have 

been set aside as a result of the tests of Bell's inequalities, and that the concept of an objective 

reality should have remained paramount. (Note that the Lorentzian theory has no problem 

with cause and effect being separated by a relativistic spacelike interval - what is important 

there, since simultaneity is absolute, is simply that the cause precede the effect. With absolute 

time, the concept of "precede" is well established in the Lorentz theory in all frames, and one 

does not need to specify event separations as "space like", "time like" or "light-like".) Also 

note that the Lorentzian theory leads to almost all of the same experimental predictions as 

relativity. I have discussed this, and other issues, more fully in [1]. 

Failure 2 - The Trend toward Complexity. 

I believe the second fundamental failure of modern physics is it's continued growth into 

complexity. Renormalization theory, quark generations, mixing angles, and on and on, have 

been considered to be "revolutionary advances" in understanding. And, as each one 

individually has come about, each one, individually, does indeed advance understanding. But, 

physics has now reached the point where one really needs to study for decades to 

"understand" the present state of the art, as many, many single steps keep being added to the 

"standard model". I view this situation as being very similar to that which existed just prior to 

Copernicus. The "music of the spheres" was a celebrated theory to explain the motion of the 

stars and planets in the skies. Now, this theory is much maligned by present day physics, as it 

is clear now that the Copernican way (with Kepler, and later, Newton) was far, far simpler. 

But rather than ridicule the "music of the spheres" it would be far better if modern physics 

stopped to think about what the science was at that time. It took a great deal of careful 

observations to map the stellar and planetary motions. It further took a great deal of detailed 

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mathematics to understand the "music of the spheres" theory, as there were many such 

spheres that, as a system, came together to accurately - and correctly - predict the motion of 

all heavenly bodies. The theory was very complex, and took many years, and a high intellect, 

and mathematical study, to understand. But once understood, it passed all experimental tests! 

That is why it was so fevently held on to. It wasn't that the scientists of the time were stupid 

(as is often smugly inferred). Rather, the opposite was true. They were very intelligent to 

understand such a complicated theory. And after devoting decades to understanding things, 

building upon the theory year after year, the practitioners were quite understandably reluctant 

to consider any simple alternative. Afterall, a simple alternative was - simplistic! And far less 

intellect was needed to understand it. Clearly Kepler was just naive! 

I have had an amusing incident that is relevant here. I have come up with a "preon" model.[2] 

It dovetails into the quark-lepton model, but it only postulates 6 fundamental particles, and it 

identifies the weak force as a radioactive decay, reducing the forces of nature from four to 

three. Hence, it is FAR SIMPLER that the standard model. (The standard model now employs 

6 quarks, plus 6 antiquarks, and they each come in three colors. That's 36 quarks! Then there 

are 12 leptons. And gluons, photons, weak intermediate vector bosons and gravitons. Mixing 

angles are employed to further explain events. How many spheres do they need?) But in 

reviewing my paper for Physical Review Letters, the reviewer quoted Occoms Razor, saying 

that the Standard Model employed far fewer "spheres" than did my new proposal. Recalling 

Galileo (name forever to be praised) "Shall we Laugh, or Shall we Cry?" 

Failure 3 - An Insistance on the Illusion of the Simplicity of Point-like Entities. 

I believe that the third fundamental failure of modern physics is it's insistance on point-like 

particles. In some sense this harkens back to the ancient particle versus wave argument. But it 

is more than that, because a particle would not necessarily have to be of zero size. While the 

concept of a point is mathematically simple, it also leads directly to physical infinities, and 

the need for "renormalization". It is my view (again see [1]) that while the math might be 

more inconvenient with finite distributed bodies, nature might not be mathematically 

convenient. But I believe that nature will prefer finite solutions to her problems. 

References. 

[1] "An Absolute Theory for the Electrodynamics of Moving Bodies", Physics Essays, volume 7, 

number 4 1994 page 476. 

[2] "The A-B-C Preon Model", Physics Essays, volume 10, number 1, 1997, page 27. 

Also, if anyone is interested in a rigorous ether model, please see: 

[3] "A Derivation of Maxwell's Equations from a Simple Two-Component Solid-Mechanical Aether", 

Physics Essays, volume 11, number 4, 1998. 

- - - - - 

[A presentation of the author can be found at the end of his previously published 

paper]

Le basi sperimentali della propulsione non newtoniana 

(Emidio Laureti) 

Il concetto di propulsione denominato dall'ASPS (Associazione Sviluppo Propulsione 

Spaziale) PNN (Propulsione Non Newtoniana) nel dettaglio propulsione senza espulsione di 

massa di reazione (o di fotoni) nasce con la fondazione dell'ASPS nel 1979. Nel 1992 viene 

concepito un sistema di propulsione elettromagnetico (SC23) che sfruttando opportunamente 

le fasi delle correnti e dei campi magnetici nei circuiti in alta frequenza rendeva possibile in 

linea teorica l'apparente violazione del principio di conservazione della quantità di moto nella 

accezione newtoniana. Tale apparenza è in realtà dettata dal semplice fatto che in 

elettrodinamica proprio per l'inesistenza di una interazione istantanea del campo e.m. (tutte le 

interazioni si propagano al massimo con la velocità della luce c) il principio di azione e 

reazione nella accezione newtoniana non vale in quanto informulabile [1]. Mentre continua a 

valere la conservazione dell'impulso totale, se si include nel sistema dei corpi che esercitano 

fra di loro forze di azione e reazione anche il campo e.m.. 

Attraverso la procedura illustrata nel prototipo denominato SC23 [2] (a cui è stato concesso il 

brevetto nell'Aprile del 2000 ) si realizza una sequenza di interazioni e.m. in cui il principio di 

azione e reazione non vale mai essendo le forze elettrodinamiche di azione e reazione dirette 

nella stessa direzione e verso. Identicamente si ha una sequenza di istanti in cui è appunto 

L'INCLUSIONE del campo e.m. nel principio di conservazione della qdm a conservare il 

principio stesso [3] in quanto l'impulso totale acquistato dal sistema in una direzione è uguale 

e opposto a quello del campo e.m. (va sottolineato [3] che tale impulso non deve essere 

confuso con quello del sistema di propulsione funzionante a rinculi fotonici). Tutta questa 

procedura passa necessariamente attraverso una condizione sperimentale che non è stata 

debitmente controllata per oltre 200 anni. 

Sui testi classici di elettrodinamica infatti si nega che possano esistere forze elettrodinamiche 

tra circuiti aperti in cui scorre corrente oscillante, ovvero che tali forze abbiano significato per 

circuiti aperti solo matematico e non fisico [4], [5]. Tale impostazione era necessaria poichè 

l'esistenza stessa di forze elettrodinamiche tra tratti di circuito aperto, in cui scorre corrente 

variabile, implicitamente avrebbe dato la possibilità di violare il Principio di Azione e 

Reazione come classicamente si definisce, permettendo la propulsione senza espulsione di 

massa di reazione. Che tale violazione sia possibile e necessariamente conseguente lo dicono 

gli autori stessi che parlano delle formule di Laplace riferite a circuiti aperti [4], [5]. Solo se la 

generazione di forze tra circuiti aperti è impossibile, il Principio di Azione e Reazione può 

evitare la "particolarizzazione" e il superamento. 

Ad esempio il testo di E. Amaldi (uno dei "ragazzi" di via Panisperna) dice che le formule di 

Laplace sono "espressioni matematiche vuote di significato fisico" [4]; mentre il testo del 

Perrucca dice " ... in casi meno simmetrici, a voler dedurre le azioni elettrodinamiche dalla 

successiva applicazione delle due leggi di Laplace non risulta di regola soddisfatto il principio 

di azione e reazione … " [5]. L'unica forza elettrodinamica tra circuiti aperti che può esistere 

in alta frequenza sarebbe il solo striminzito impulso fotonico p = E/c , dove p è l'impulso 

requisivo scambiato, E è l'energia, e c è la velocità della luce. 

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Per dimostrare che queste erano solo assunzioni dovute all'assenza di sperimentazione 

sull'elettrodinamica in alta frequenza occorreva verificare soprattutto che la forza 

ettrodinamica in alta frequenza poteva essere anche ATTRATTIVA e non solo repulsiva. 

In primis va ricordato che ricercatori esterni all'Asps, pur con obbiettivi diversi dalla PNN, 

realizzarono alcune configurazioni sperimentali sui circuiti aperti [6]. Questi autori [7] nel 

perseguire l'obbiettivo di dimostrare l'inapplicabilità della forza relativistica di Lorentz nel 

caso di circuiti aperti, incidentalmente dimostrarono che l'Equazione Cardinale di Ampere 

(non relativistica) era valida per i circuiti aperti. Essi scrivono esplicitamente "No where in 

the literature before appears such investigation of the forces between physically non closed 

circuits … " che è quello che dice pure da tempo l'Asps, con l'aggiunta di una spiegazione 

elementare alla mancanza di tale investigation: ovvero che l'accettazione acritica e/o 

limitativa delle Maxwell equazioni (nello specifico l'uso che l'autore fa della cosiddetta 

"corrente di spostamento") ha in pratica bloccato ogni iniziativa di sperimentazione fisica 

sulla dinamica dell'elettromagnetismo ad alte frequenze [8], [9],[10], [11], [12]. 

Negli anni immediatamente seguenti il 1992 l'Asps iniziò faticosamente a acquisire apparati 

sperimentali idonei alla PNN o più correttamente e ad adattare alla PNN l'esistente. 

Soprattutto si definirono e si migliorarono progressivamente le tecniche di rilevamento dei 

dati sperimentali. Dal 1999 iniziarono sistematicamente i primi esperimenti circa la possibilità 

di esistenza di forze elettrodinamiche tra circuiti aperti. 

Uno step delle nostre attività sperimentali è stato appunto quello di dimostrare in primo luogo 

che tali forze esistono se si approntano gli apparati sperimentali in grado di dimostrarne 

l'esistenza. 

In un esperimento condotto dall'Asps un conduttore aperto appeso a un pendolo balistico 

viene attratto da un dipolo emittente onde e.m. se il conduttore è opportunamente 

condizionato e progettato per essere un circuito in cui la corrente di autoinduzione è in fase 

con quella della sorgente emettente il campo e.m.. 

Negli ultimi mesi del 2001 dopo innumerevoli tentativi e modifiche venne realizzata prima 

una configurazione sperimentale in cui alcuni dei bracci dei dipoli del sistema di propulsione 

non newtoniano SC23 si spostavano in un unico verso della stessa direzione [13] con un 

impulso maggiore di E/c ,sotto alimentazione del generatore di potenza SXP2000. 

Alcuni bracci di SC23 "nuotano" in pratica nel campo elettromagnetico da loro emesso, 

perché ogni campo e.m.,una volta emesso,è indipendente dalla sorgente. 

Nello stesso periodo (Dicembre 2001) una sintesi e una reinterpretazione di tutte le 

esperienze condotte permetteva di concepire un prototipo finalmente operativo: SC2.12. 

Successivamente nel Febbraio 2002 si ottimizzarono alcuni parametri di tale prototipo 

portandolo addirittura a competere con le spinte dei motori a ioni. 

Si ricapitolano brevemente gli eventi di tale esperienza: 

Secondo la procedura già illustrata in Nova 91 Gennaio-Febbraio-Marzo 2002 [14], il 

prototipo SC2.12 (vedi foto qui di seguito) è attaccato a un pendolo balistico lungo circa 1 

metro, mentre i sistemi che ne rilevano lo spostamento sono un laser che illumina di taglio la 

superficie del prototipo e un fascio di luce prodotta da quello che è chiamato "il nostro 

occhiale", ovvero un sistema laser + lente che proietta un'iride sulla parete.

La scatola contenente la variante di SC2.12 è nascosta da una copertina di Nova Astronautica, 

issn: 0393-1005, Organo Ufficiale dell'ASPS. L'occhiale illumina una "appendice-indice" 

attaccata in basso sulla copertina che copre il prototipo SC2.12 e proietta una iride circolare 

su una parete. 

SINTESI: 

Un laser illumina la coopertina quasi orizzontalmente, mentre l'occhiale illumina più in basso 

l'indice attaccato alla copertina (indice non presente nella foto di SC2.12 con copertina). 

Il prototipo sotto alimentazione elettrica irraggia un campo e.m. rilevato dal "Field Strength 

Meter" (non presente nella foto di SC2.12 con copertina). 

Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico 

rilevato dal "Field Strength Meter" SC2.12 avanza nella direzione dell'osservatore di circa 

3,136 millimetri e conseguentemente l'illuminazione del laser si allunga da destra verso 

sinistra, per poi tornare indietro quando l'alimentazione elettrica al prototipo viene disattivata. 

L'illuminazione dell'indice da parte dell'occhiale è proiettata su una parete del Lab del Dip. 

Ra-1 dell'ASPS in forma di iride. L'occhiale è a circa 13 cm dall'indice e a circa 373 cm dalla 

parete. L'iride proiettata sulla parete ha un diametro di circa 11 cm. 

Evento Sperimentale: simultaneamente all'aumento del campo elettromagnetico 

rilevato dal "Field Strength Meter" SC2.12 avanza da sinistra a destra nella direzione 

orizzontale con uno spostamento amplificato di circa 9 cm. La proiezione dell'indice torna 

indietro quando l'alimentazione elettrica e quindi il campo e.m. viene disattivato. 

Il rapporto Fpnn/p tra la spinta pnn Fpnn e il rinculo fotonico p (pag.8 di Nova Astronautica n. 

91) [14] era pari a 1363 , se alcuni parametri PNN non erano ottimizzati. 

Lo spostamento S in millimetri sul pendolo balistico era pari a: 

S=1,045 millimetri 

A 50 watt il rinculo fotonico dava una spinta di 0,017 milligrammi (pag.7 di Nova 91). 

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Moltiplicando 1363*0,017milligrammi si ottiene una spinta Fpnn = 23,171 milligrammi per 

quanto descritto in Nova 91 [14]. 

Viene illustrata una spinta ottimizzata con modifica di alcuni parametri di SC2.12 

L'Iride in media ha un diametro di circa 11 cm. 

Come da riferimento sulla scala graduata sul muro lo spostamento dell'indice è di circa 

9 cm in modo che si evince uno spostamento Sm in millimetri del prototipo sul pendolo 

pari a: 

Sm = 90 millimetri * (13/373) = 3,136 millimetri 

cioè è triplo rispetto al precedente (e sempre a 50 watt). 

Ricordando i parametri precedenti la spinta Fpnn diventa pari a: 

Fpnn=(3,136/1,045)* 23,171 milligrammi = 69,535 milligrammi 

Il guadagno rispetto al rinculo fotonico è di circa 4090 volte. 

Conclusioni e ulteriori analisi 

Le esperienze condotte dall'Asps su pendolo balistico hanno dimostrato che nella definizione 

dell'intensità della forza in alta frequenza intervengono anche dei parametri inaspettati ma 

sempre legati strettamente alla corrente e al campo magnetico con cui si determina 

l'interazione. 

L'intensità di spinta Fpnn che la PNN può determinare attualmente è compresa tra circa: 

23 milligrammi < Fpnn < 70 milligrammi 

Essa è confrontabile con la propulsione ionica ma con il vantaggio di un elevatissimo impulso 

specifico dato che il sistema PNN non espelle massa di reazione ma utilizza solo energia e.m. 

per generare la spinta. 

Come da esperienza riportata in Nova Astronautica n.91 2002 (pag.3-8) [14], anche la 

spinta amplificata di SC2.12 nel Febbraio 2002 presentava ROS, ovvero SWR elevati. 

Un calcolo successivo portava a quantificare l'utilizzazione di almeno il solo 40% dei 50 watt 

erogati dall'alimentatore. 

La spinta pnn Fpnn a 70 milligrammi utilizzava pertanto circa 20 watt. 

Ora la spinta di un FEEP thruster è di circa 1 millinewton per 60 watt, ovvero 102 

milligrammi. 

La spinta di SC2.12 a 60 watt utilizzati per la spinta va pertanto triplicata e risulta essere 

dell'ordine dei 210 milligrammi ovvero doppia a parità di consumo energetico rispetto a 

quella del FEEP Thruster, ovvero dell'ordine dei 2 millinewton. 

Da notare che l'Impulso Specifico dei motori dello Space-Shuttle è di 460 secondi. 

L'Impulso Specifico dei motori ionici tipo FEEP thrusters è compreso tra 6000 e 10000 

secondi. 

L'Impulso Specifico Ipnn di SC2.12 è invece: 

Ipnn =(23*10 -6 Kg x (9 x 10 16 metri 2 /sec 2 )/50 watt) = 4.14 x 10 10 secondi .

Ovvero più di un milione di volte più elevato di quello del motore a ioni. 

Bibliografia 

[1] E. Laureti, "Non validità del Principio di Azione e Reazione in elettrodinamica", Nova 

Astronautica, Vol. 20 n.86, 2000. 

[2] E. Laureti, "Il Prototipo SC23", Nova Astronautica, Vol.18 n. 77, 1998. 

[3] E. Laureti, "La PNN e il Principio di Azione e Reazione", Nova Astronautica, Vol. 19 n. 82, 1999. 

[4] E. Amaldi, Fisica Generale II, Università di Roma, 1965, pag. 290-291. 

[5] E. Perrucca, Fisica Generale e Sperimentale II, Un. Tip. Ed. Torinese 1949, pag. 627-628. 

[6] P.T. Pappas & T. Vaughan, "Stigma Antenna Force Experiments", in The Thorny Way of Truth, 

IV, East-West, Graz, 1989, pag. 158-168. 

[7] P.T. Pappas,"Forces on a Stigma Antenna", Physics Essays, 3, 3, 211, 1990. 

[8] E. Laureti, "Brevetto di SC23 e Attività Sperimentali", Nova Astronautica Vol.20 n. 96, 2000. 

[9] A.P.French, J.R.Tessman, Am. J. Phys., 31, 201, 1963. 

[10] F.W. Warburton, "Displacement Current, a Useless Concept", Am. J. Phys., 22, 229,1954. 

[11l J.C. Maxwell, "A Treatise on Electricity and Magnetism", V2, Dover, New York, 1954. 

[12] E. Laureti, "Riflessioni sulla Conservazione della quantità di Moto e Basi sperimentali della 

PNN", Nova Astronautica, Vol.21 n. 87, 2001. 

[13] E. Laureti, "Per Santa Rita e San Gabriele santi Protettori dell'ASPS Hurra!", Nova Astronautica 

Vol. 21 n. 90, 2001. 

[14] E. Laureti, "Setup sperimentale di SC2.12", Nova Astronautica Vol. 22 n. 91, 2002. 

- - - - - 

Emidio Laureti è nato a Roma nel 1947. Si è laureato in Fisica nel 1974 

presso l'Università di Roma, con una Tesi dal titolo "Correzioni Relativistiche al 

Fattore di Forma Elettrico del Deuterio". Attualmente è docente di Matematica e 

Fisica nelle scuole medie superiori. Fondatore e Presidente dell'Associazione 

Sviluppo Propulsione Spaziale (ASPS) nel 1979, si occupa insieme ad altri 

collaboratori di attività sperimentali su concetti di propulsione di tipo 

"propellantless", all'ASPS definiti Propulsione Non Newtoniana (PNN). Dal 

1982 è Direttore Responsabile di Nova Astronautica (issn: 0393-1005), Organo 

Ufficiale dell'ASPS. 

Associazione Sviluppo Propulsione Spaziale 

Via Nino Martoglio 22 , 00137 Roma - Italia 

Tel: 06-87131068 

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134 

http://www.asps.it - as.ps@flashnet.it

Neopitagorismo e Relatività 

(Rocco Vittorio Macrì) 

«Da quando i matematici hanno invaso la teoria della 

relatività, io stesso non la capisco più» (Albert Einstein) 

Ci troviamo in un'epoca che - per la prima volta nell'intero arco del pensiero scientificofilosofico 

- vede la fisica padroneggiare, porre confini e dettare legge all'interno della sfera 

filosofica. Siamo a quasi un secolo di distanza dalla seconda rivoluzione scientifica, la quale 

ha scosso i pilastri della stessa gnoseologia: i concetti di spazio, tempo, simultaneità, cosmo, 

esistenza… vengono fatalmente rielaborati e trasformati, tallonando la cosiddetta crisi dei 

fondamenti della matematica. Gli stessi principi primi aristotelici subiscono "scacco matto": 

«Mediante la meccanica quantistica viene stabilita definitivamente la non validità del 

principio di causalità» sentenzia Heisenberg 1 . Nasce la logica quantistica. È la fisica che, per 

la prima volta, "ridisegna" la filosofia… 

Sulle macerie del pensiero classico aleggia la figura, diventata oramai leggenda, che incarna e 

personifica la rottura col passato, l'autorità che ha cambiato per sempre la nostra immagine 

del mondo, la scintilla divina con la quale il Fato innescò "la rivoluzione", come egli stesso 

ebbe a dire: «Per punirmi del mio disprezzo nei confronti dell'autorità, il Fato fece un'autorità 

di me stesso» 2 . Albert Einstein fu l'artefice della metamorfosi moderna, che avendo posto «la 

matematica al centro dell'esperienza», come documenta Gaston Bachelard, e introducendo 

una visione elastica dello spazio e del tempo, sarebbe diventato pietra angolare del più grande 

cataclisma intellettuale della storia del pensiero scientifico. Nel suo continuo "detonare e 

detronizzare", la rivoluzione einsteiniana avrebbe attivato una serie di «choc epistemologici» 

nel cuore stesso della comunità scientifica, che - scrive Bachelard nel 1934 - obbligano lo 

scienziato a rimettere tutto in discussione: «Il fisico è stato costretto tre o quattro volte da 

vent'anni a questa parte a ricostruire la propria ragione, e, intellettualmente parlando, a rifarsi 

una vita» 3 , fino al punto di mettere all'indice le stesse categorie di pensiero che avevano 

resistito e brillato per più di due millenni. L'unica possibilità di accesso alle nuove conquiste 

relativistico-quantistiche - ammette Abraham Pais - è «quella data da Einstein, è che la stessa 

logica classica deve essere modificata» 4 . 

Si tratta ora di analizzare l'influenza, il rapporto e perfino il legame parentale che la 

"gaussiana" concezione del pensiero matematico che spazia da Gauss a Cantor fino a Hilbert 

ha avuto nei riguardi della sconvolgente ideazione, progettazione ed elaborazione della fisica 

e metafisica contemporanee, e se Einstein può essere visto (suo malgrado) come l'anello di 

collegamento tra la cosiddetta Scuola di Göttingen e la Scuola di Copenhagen, tanto più che è 

ormai ben assodato che la seconda ha completato il lavoro di "svuotamento categoriale" 

iniziato dalla prima 5 . Allora il fisico moderno potrebbe essere considerato un «pitagorico» 

non solo perché - come abbozza quel «genio rivoluzionario tra i fisici» 6 - «considera il criterio 

della semplicità logica come strumento indispensabile ed efficace per la sua ricerca» 7 , ma 

soprattutto perché «sostiene che il principio veramente creativo, nella fisica teorica, è quello 

della costruzione matematica» 8 . Anzi, si dovrà ammettere altresì, che si è andati oltre Pitagora 

- parliamo appunto di "neopitagorismo" - dal momento che «Einstein accetta il punto di 

partenza dell'assiomatica, secondo cui il contenuto logico-formale della matematica è 

nettamente separato dal suo contenuto effettivo o intuitivo» 9 . 

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136 

1. Il "ritorno" a Pitagora 

Fa parte ormai della mentalità scientifica comune che, «le grandi teorie raramente sono 

semplici» 10 e per comprenderle «c'è bisogno di un livello davvero elevato nella conoscenza 

della matematica» 11 . «La scienza moderna si fonda quasi per intero sulla matematica» 12 . 

Raffinati modelli matematici hanno oggi assunto la guida non solo durante la creazione dei 

modelli fisici, ma addirittura durante il relativo processo ermeneutico, ridando splendore a 

Pitagora e all'affermazione del suo discepolo Filolao: «Senza il numero non sarebbe possibile 

pensare né conoscere alcunché». Sotto questa luce le parole di Dirac (1931) appaiono 

paradigmatiche: «Il più potente metodo di avanzamento che può essere suggerito oggi è 

quello di impiegare tutte le risorse della matematica pura, nel tentativo di perfezionare e 

generalizzare il formalismo matematico che costituisce la base esistente della fisica teorica, e, 

dopo ogni successo in questa direzione, di tentare di interpretare le nuove forme matematiche 

in termini di entità fisiche» 13 . 

«La cultura occidentale è caratterizzata da una sorta di mito della matematica, dalla fede, 

forse dovuta a Pitagora, in una sua virtù esplicativa e quasi trascendente. A molte persone, 

descrivere in termini matematici una struttura sintattica o delle relazioni di parentela sembra 

già una "spiegazione" sufficiente» 14 . Nel passare dal «Nihil certi habemus in nostra scientia 

nisi nostram mathematicam» del Cusano al programma di Dirac («Scoprire prima le 

equazioni e poi, dopo averle esaminate, gradualmente imparare ad applicarle […] È più 

importante avere bellezza nelle equazioni che trovare accordo tra equazioni ed esperimenti» 15 ) 

transitano 5 secoli, ma visti da una prospettiva epistemologica hanno l'aspetto di un viaggio a 

ritroso di due millenni: è, in un certo senso, un ritorno a Pitagora. Contrariamente alle 

aspettative di Bertrand Russell che avrebbe desiderato per il Novecento «una ritirata da 

Pitagora» 16 il sentiero intrapreso dalla fisica contemporanea porta ad una rivalutazione della 

Scuola di Kroton, il ritorno cioè «a una tradizione molto antica» 17 . «Sembra che i pitagorici 

siano stati i primi ad intendere la forza creativa inerente alle formulazioni matematiche», 

bisbiglia Heisenberg 18 . «Frammisti ai loro discorsi sui numeri amici e nemici, i pentagrammi 

mistici, i numeri perfetti, l'armonia delle sfere e così via, troviamo quelle proprietà dei numeri 

e delle figure spaziali, chiare da un punto di vista logico, che successivamente troveranno 

posto nel limpido giardino degli Elementi di Euclide» 19 . 

È vero che Aristotele denuncia nella sua Metafisica che i Pitagorici abbiano attribuito al 

numero quella funzione di causa materiale che gli Ionici attribuivano all'elemento sostanziale 

della realtà corporea: «Costoro sembrano ritenere che il numero sia principio non solo come 

costitutivo materiale degli esseri, ma anche come costitutivo delle proprietà e degli stati dei 

medesimi» 20 , e che la fisica contemporanea incarna tale credo quasi come "mistero orfico" 

seguito dai nuovi adepti con nomi altisonanti quali quelli di Hilbert, Minkowski, Einstein, 

Heisenberg, Pauli, Dirac, ecc. Pur tuttavia, la "metrica pitagorica" originaria era ben lontana 

dal moderno nichilismo hilbertiano che svuota il pensiero matematico in una asettica e fredda 

intelaiatura logica priva di semantica e contenuti intuitivi. Al contrario, era fondata 

sull'evidenza e l'intuizione che l'"umano" si ritrovava già nella sua intima costituzione 

psichica: l'elevazione mistica e la poetica visione del kosmos come armonia ne danno diretta 

testimonianza. In fondo Copernico, Keplero, Galileo, Newton… depositano a favore di questa 

prospettiva 21 . Ma come direbbe ai nostri giorni un Russell: «La logica e la matematica… sono 

l'alfabeto del libro della natura, ma non il libro stesso» 22 . 

Esisteva inoltre la visione iperuranica di un sapere matematico che intelaia la struttura del 

mondo in modo monolitico, irremovibile, unitario, anelastico, intrasferibile, non 

assoggettabile o soggiogabile: professione di fede che da Pitagora, rimbalzando su Platone, 

attraversa i secoli come un raggio luminoso riflesso ora da Cartesio, ora da Leibniz fino ad 

arrivare a Husserl: «Nessun Dio può minimamente modificare ciò, come non può modificare 

il fatto che 1 + 2 = 3 o che sussistano altre verità essenziali» 23 . Perfino Hume, dopo aver

"dissacrato" e "soggettivizzato" ogni supremo principio sotto la guida dell'empirismo, si 

inginocchia reverente dinanzi all'«apoditticità» della matematica, a «quelle realtà che sono 

sicurissime e certissime» 24 , come testimonia lo stesso Kant nella sua Critica della ragion 

pratica: «Eppure lo stesso Hume non estese l'empirismo al punto da comprendervi anche la 

matematica. Egli pensava che le proposizioni matematiche siano analitiche, e, se questo fosse 

esatto, esse sarebbero effettivamente apodittiche» 25 . 

Vedremo come questa certezza inizierà a incrinarsi all'inizio dell'Ottocento e come Gauss 

segnerà un'era nuova di stampo strumentalista e trans-intuizionista, che porterà prima alla 

nascita ed accettazione delle geometrie non-euclidee e successivamente alla matematica 

formalista e pragmatista del nostro secolo, attraversando i transfiniti di Cantor. «Dopo quel 

radicale mutamento del pensiero matematico - rileva Renato Nobili - anche nella fisica fu 

aperta la via alla determinazione di nuove costituzioni di significato e alla costruzione di 

modelli matematici astratti, totalmente irriducibili al genere delle rappresentazioni 

fenomenologiche del mondo visibile. Parallelamente a ciò, anche le istanze epistemiche 

generali del pensiero fisico subirono trasformazioni profonde; cosicché, ad esempio, quelle 

nozioni oggettivistiche e metafisiche forti che furono le Verità, le Leggi e i Principi della 

Natura nel volgere di pochi decenni furono abbandonate e rimpiazzate da nozioni deboli, 

soggettivistiche e pragmatistiche, quali sono le rappresentazioni, le leggi e i modelli 

matematici copiosamente fioriti sul diramato albero della fisica teorica contemporanea» 26 . 

2. "Gaussbuster" ovvero all'origine della metafisica moderna 

Esiste un curioso parallelismo tra Gauss e Einstein: entrambi hanno messo in moto un 

processo epistemologico rivoluzionario - che sbocciò sulle masse come inedite e sbalorditive 

immagini del mondo incrinanti l'"autorità", il "senso comune", le "evidenze", le "certezze" del 

pensiero classico - più grande di quanto potessero sospettare, un passo più grande di loro 

stessi il cui controllo fatalmente sfuggirà di mano e a nulla varranno i tentativi di recupero. 

Similmente alla "canonizzazione" avuta da Einstein nel novembre del 1919 per la conferma 

delle previsione della sua Relatività generale in seguito alle misure sulla deflessione della luce 

durante l'eclissi del 29 maggio 1919 fatte dalla spedizione guidata da Eddington 27 , Johann 

Carl Friedrich Gauss (1777-1855) ebbe la sua nel dicembre 1802, quando l'astronomo 

Wilhelm Olbers, ad un anno di distanza dalla scoperta di Cerere e dalla successiva 

scomparsa 28 , posizionò il telescopio seguendo i dati forniti da Gauss, "riscoprendo" così 

l'asteroide dileguato. Il risultato fece di Gauss «una celebrità europea» 29 . La riscoperta di 

Cerere fu per «il principe dei matematici» un successo clamoroso, a commento del quale 

Laplace veniva a definire Gauss «uno spirito ultraterreno in un corpo umano» 30 . 

Con l'avvento dell'era gaussiana la definitiva accettazione e sistemazione dei numeri 

complessi 31 e la scoperta delle geometrie non euclidee fecero vacillare l'intera struttura 

epistemologica, che dovette rinunciare a ogni pretesa di assolutezza: potevano esistere altri 

numeri, altre algebre e altre geometrie di pari dignità epistemica. Come ebbe a osservare il 

matematico tedesco Felix Klein, «Gauss si erge alla testa del XIX secolo non solo 

cronologicamente» 32 . La nuova visione gaussiana che veniva a imporre i caratteri empiriostrumentaliste 

sul terreno della teoresi greca doveva però pagare un prezzo altissimo: la 

rinuncia all'autoevidenza 33 . Un tradimento al pitagorismo antico indicato dai Frammenti 

rimasti del discepolo più illustre, Filolao: «La natura del numero e dell'armonia non 

ammettono alcun inganno perché l'inganno non è loro proprio. La natura dell'indeterminato e 

dell'impensabile e dell'irrazionale porta l'inganno e l'invidia». Ciò veniva a manifestarsi sulle 

due colonne del fondamento del pensiero classico: l'aritmetica e la geometria, pietre angolari 

del pensiero umano dal tempo degli antichi Greci, «fortezze inespugnabili» fondate su verità 

autoevidenti che avrebbero trovato un inesauribile campo di applicazione nello studio della 

natura. «Coloro i quali credevano - spiega Russell - (come in generale si credeva sul 

continente) che fosse possibile una conoscenza del mondo reale certa e indipendente 

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138 

dall'esperienza non avevano che da additar[le]… : soltanto un pazzo avrebbe messo in dubbio 

la [loro] validità, e soltanto uno sciocco ne avrebbe negato il riferimento oggettivo» 34 . 

Il carattere certo e unitario che rivestiva la nostra conoscenza del mondo veniva intaccato alla 

radice: l'incontrovertibilità delle verità autoevidenti era stata messa in questione da 

convenienze empirio-pragmatiste, e «insieme con essa vacillavano secoli di fiducia 

nell'esistenza e nella conoscibilità di verità inattaccabili relative all'universo» 35 . «Anche se 

non abbiamo elementi per stabilire se Gauss sia stato influenzato direttamente dagli scritti di 

Hume», appare evidente come Gauss all'inizio dell'Ottocento «pensasse che l'intera 

matematica è priva di verità» 36 . In una lettera a Bessel del 21 dicembre 1811 scrive: «Non 

dobbiamo mai dimenticare che le funzioni [di variabili complesse], come tutte le costruzioni 

matematiche, sono solamente nostre creazioni; quando la definizione da cui siamo partiti 

cessa di avere senso, non dovremo domandarci "che cos'è", ma piuttosto "che cosa conviene 

assumere per mantenerla significativa"» 37 . 

Uno sguardo indietro di qualche secolo ci consente di avere un quadro complessivo più 

esauriente riguardo le novità concettuali apportate dalla "gaussite" durante la crescita del 

pensiero scientifico. Furono la Germania e l'Italia a fornire il maggior numero di matematici 

all'inizio del rinascimento, ma l'opera più importante venne composta in Francia nel 1484 da 

Nicolas Chuquet: Triparty en la science des nombres. Qui veniva espresso per la prima volta 

un numero negativo isolato in un'equazione algebrica. Ciò nonostante, per le radici di 

equazioni che comportavano soluzioni immaginarie l'autore così si esprimeva: «Tel nombre 

est ineperible» 38 . Nella prima metà del XVI secolo i numeri negativi cominciavano ad essere 

più facilmente "manipolati" grazie all'introduzione della notazione tedesca con i nuovi simboli 

"+ e -" al posto della "più sana" notazione italiana "p e m". Pur tuttavia, nonostante si avesse 

completa familiarità con le proprietà dei numeri negativi, questi venivano ancora chiamati 

"numeri absurdi" 39 , a testimonianza del forte grado di diffidenza e perplessità diffuso nei 

matematici dell'epoca 40 (ancora ben lontani da quel morbus mathematicorum recens col quale 

Frege accuserà la struttura assiomatica moderna). Soltanto l'uso e l'abuso nella pratica delle 

tecniche e procedimenti operativi porterà all'"accettazione perché funziona" tramite la - 

oramai paradigmatica - logica del successo. Si arriva così alla oggettualizzazione delle 

procedure, ossia alla cristallizzazione di veri e propri oggetti matematici che acquisteranno 

una realtà indipendente dalle circostanze nelle quali sono stati introdotti. Per questa stessa 

ragione verranno accettati e accolti i numeri immaginari 41 . 

Scrive Kline: «Senza aver completamente superato le difficoltà connesse con i numeri 

irrazionali e con i numeri negativi, i matematici europei accrebbero i loro problemi andando a 

inciampare in quelli che noi oggi chiamiamo numeri complessi» 42 . Dalla scoperta di Scipione 

del Ferro dell'esistenza di una soluzione algebrica dell'equazione di terzo grado, allo stimolo 

che questa dette a Nicolò Tartaglia nel sistematizzarla fino all'Ars magna di Gerolamo 

Cardano del 1545 che rese di dominio pubblico le procedure risolutrici delle equazioni di 

terzo e di quarto grado (grazie all'aiuto di Ferrari), si incominciava a intravedere un residuo 

protagoreo sull'opportunità di un utilizzo infido delle radici quadrate di numeri negativi, radici 

che tuttavia Cardano chiamava «sofistiche» 43 . Il passo successivo fu fatto dall'algebrista 

Raffaele Bombelli nella sua Algebra del 1560 (ma stampata nel 1572) che tramite 

«considerazioni sofistiche» 44 - come egli stesso ebbe a dire - arrivò all'«idea assurda» del 

seme germinale del concetto di "numero complesso". Fin qui i concetti di numero 

immaginario, numero complesso (o, come venivano chiamati allora, numeri "falsi" o 

"silvestri"), e quello stesso di numero negativo vengono "supposti" ma non "proposti", ossia 

procedono sul filo metafisico della "plausibilità empirica" di stampo protagoreo: «Siccome 

funziona, usiamolo». Nel 1629 il matematico francese Albert Girard riconobbe 

definitivamente la natura delle soluzioni negative e complesse, e fu così in grado di 

perfezionare il lavoro sulla relazione che intercorre tra le radici e i coefficienti di un'equazione 

algebrica, già iniziato da François Viète 45 . Per una copertura epistemico-razionale dovremo 

però aspettare fino a Gauss che, grazie ancora una volta all'abuso del "miracolo cartesiano" di

collegamento tra il mondo algebrico e quello geometrico riuscirà a proclamare il "diritto di 

cittadinanza" a ciò che Eulero nel 1770 definiva entità «immaginarie o impossibili» 46 . Come è 

stato giustamente inneggiato allo stesso Gauss in occasione del suo cinquantesimo di 

dottorato: «Lei ha reso possibile l'impossibile» 47 . 

Grazie al parallelismo geometrico Gauss veniva a dare inizio a una nuova era dove delle 

entità metafisicamente contraddittorie 48 venivano "addomesticate" perché sovrapponibili 

empiricamente a costruzioni geometriche recuperanti l'evidenza perduta dall'altro versante. 

Così, d'altra parte, era già stato fatto secoli prima per l'uso dei numeri negativi che, a 

quell'epoca, «sollevavano maggiori difficoltà, poiché non potevano facilmente venire 

approssimati da numeri positivi, ma la nozione di senso (o di direzione su una linea) li 

rendeva plausibili» 49 . Il sodalizio algebra-geometria ha salvato "in corner" e reso ammissibili 

spesso operazioni definiti impossibili dalla prima (come il caso della «lussuria» dei numeri 

immaginari, con le parole di Thomas Jefferson del 1799 50 ), come questa d'altra parte ha reso 

omaggio alla seconda rendendo possibile operazionisticamente quel "salto" che l'intuizione 

molte volte non dava licenza di fare, come nel caso della geometria non-euclidea. Gauss 

estenderà tale sodalizio anche alla fisica, quando metterà in dubbio - scrutando tra le tre 

vette 51 - il carattere euclideo dello spazio fisico… e Einstein completerà l'opera. 

3. L'eredità di Gauss: dalla "perdita dell'intuizione" alla "libertà cantoriana" 

Il sigillo di Gauss recava il motto «pauca sed matura», ma in realtà quello che avvenne fu lo 

sviluppo di una serie continua di nuovi oggetti matematici privi di una adeguata fondazione 

filosoficamente ineccepibile e accettati in base alla suprema legge del più spregiudicato e 

"antieuclideo" pragmatismo: l'applicabilità. Nuove algebre e nuove geometrie venivano ad 

accumularsi nell'atanor sempre più "spazioso" dell'esistente matematico. Scrive mirabilmente 

Kline: «Dopo tutto, i consueti numeri reali e complessi venivano impiegati con scopi 

totalmente differenti e la loro applicabilità sembrava fuori discussione. Nonostante ciò, 

l'apparire di nuove algebre bastò per insinuare nella mente dei matematici il dubbio sulla 

verità dell'aritmetica e dell'algebra ordinaria proprio come accade a chi, entrato in contatto 

con le abitudini di una civiltà sconosciuta, comincia a mettere in discussione il proprio modo 

di vivere» 52 . La "creazione" continua di nuovi continenti matematici sui tracciati metodologici 

empiristi, fuori dalla sfera intuitiva, portò una specie di cataclisma concettuale preeinsteiniano 

nei teorici dell'epoca: «E così la triste conclusione che i matematici furono 

costretti a trarre è che nella matematica non esiste verità […] Il tentativo greco di garantire la 

verità della matematica partendo da verità autoevidenti e impiegando solo la dimostrazione 

deduttiva è stato inutile. Per molti attenti matematici era troppo duro accettare il fatto che la 

matematica non fosse un corpo di verità; sembrava quasi che Dio avesse creato una 

molteplicità di algebre e di geometrie con il proposito di confonderli, proprio come aveva 

confuso le genti di Babele facendo loro parlare lingue differenti» 53 . 

I grandi matematici che avevano affinità o intuito filosofico diedero voce alle obiezioni dei 

nuovi universi razionali. Basterebbe pensare a William R. Hamilton («Nessuna persona 

sincera e intelligente può dubitare delle proprietà principali delle rette parallele, così come le 

espose duemila anni fa Euclide negli Elementi» 54 ), a Francis Masères («Le radici negative… 

non dovrebbero mai dovuto essere ammesse in algebra, e bisogna sperare che ne vengano 

escluse» 55 ), a Eulero («È chiaro che non si può neppure includere la radice quadrata di un 

numero negativo fra i numeri possibili, e bisogna dunque dire che è una quantità 

impossibile» 56 ), a William Frend («Gli algebristi […] possono trovare dei numeri impossibili i 

quali, una volta moltiplicati fra loro, generano l'unità. Questo è un linguaggio incomprensibile 

e ripugna al senso comune; tuttavia, una volta adottato, come tante altre finzioni esso trova i 

più strenui difensori fra coloro che amano accettare le cose senza un attento esame e 

disprezzano la voce del retto pensare» 57 ), ad Augustus De Morgan («L'espressione 

immaginaria… e l'espressione negativa… hanno una caratteristica comune: quando si trova 

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una di esse come soluzione di un problema, ciò indica la presenza di qualche incoerenza o 

assurdità» 58 ), per non parlare di Cartesio, Newton, Leibniz, Carnot, ecc. Sembrava quasi 

materializzarsi l'anatema scagliato da George Berkeley nel 1734 quando provocava i 

matematici con: «È vero che [i matematici] non si sottomettono ad alcuna autorità, non 

accettano nulla per vero senza prove, e non credono ad argomentazioni inconcepibili? È vero 

che essi non hanno i propri misteri, e quel che è più importante, le loro avversioni e le loro 

contraddizioni?» 59 . Come scrisse Poincaré nel 1899: «La logica talvolta genera mostri» 60 . 

Einstein aveva visto giusto quando osservò che «il sogno della conoscenza assoluta aveva 

agonizzato a lungo, ma era stato David Hume… a dare il colpo finale ai sogni di Platone» 61 . 

Fu Gauss che recuperò gli "algoritmi metafisici" di Hume all'interno del pensiero matematico 

tramite l'empirismo dell'applicabilità e la logica del successo: «Qui [nella rappresentazione 

geometrica] si mostra come il significato intuitivo di − 1 sia del tutto fondato, e per 

ammettere queste quantità nel dominio degli oggetti dell'aritmetica non è necessario 

nient'altro» 62 . La "spinta gaussiana" avrebbe portato successivamente al nuovo paradigma 

euristico accettato in matematica. Il motto di De Morgan - «Ricordatevi di − 1 » 63 - ne 

rappresenta l'archetipo. «Ma fu ancora Gauss - scrive Kline - ad accorgersi della conseguenza 

più rivoluzionaria [della geometria non euclidea]. […] Gauss… essendosi reso conto che la 

geometria euclidea non è necessariamente la geometria dello spazio fisico, cioè non è 

necessariamente vera, mise la geometria nella stessa classe della meccanica e affermò che il 

carattere di verità deve essere attribuito soltanto all'aritmetica (e all'analisi che ne costituisce 

uno sviluppo). Questa fiducia nell'aritmetica è di per sé curiosa. L'aritmetica, infatti, non 

possedeva in quel periodo nessuna fondazione logica e la sicurezza che l'aritmetica, l'algebra e 

l'analisi fornissero delle verità sul mondo fisico derivava unicamente dall'esperienza. La storia 

della geometria non euclidea dimostra in maniera lampante quanto i matematici siano 

influenzati non dai ragionamenti che effettuano, ma dallo spirito dei tempi. Saccheri aveva 

respinto gli strani teoremi della geometria non euclidea e ne aveva concluso che Euclide era 

stato emendato da ogni neo. Un centinaio di anni dopo, invece, Gauss, Lobačevskij e Bolyai 

accettarono fiduciosamente la nuova geometria. Essi pensavano che la loro geometria fosse 

logicamente coerente e che perciò fosse altrettanto valida di quella di Euclide. Non avevano 

però nessuna dimostrazione di questa coerenza. Anche se dimostrarono molti teoremi senza 

imbattersi in evidenti contraddizioni, rimaneva aperta la possibilità che si potesse dedurre una 

qualche contraddizione» 64 . 

La scoperta che la geometria euclidea non era una verità unica, necessaria e assoluta riguardo 

al mondo fu perciò sbalorditiva, ed ebbe effetti di vasta portata e irreversibili. Essa minò alla 

base le concezioni assolutistiche della conoscenza umana in ampie regioni del pensiero: «I 

matematici vi si opposero a lungo - scrive Barrow - ma coloro che cercavano di sovvertire le 

tradizionali certezze euclidee videro in essa un segnale dell'avvento del relativismo. Il termine 

"non euclideo" venne a indicare qualche cosa di più generale di quanto valeva per le linee 

nello spazio» 65 . Una volta spalancata la porta della "trans-intuizione" e della "trans-evidenza" 

allora si aprì alla «regina delle scienze» un intero mondo di potenzialità latenti, pronte alla 

cristallizzazione per coerenza. La matematica poteva finalmente essere libera e volare 

poeticamente attraverso la creatività dello scienziato. «La geometria greca classica - chiarisce 

Kline - non aveva soltanto imposto delle restrizioni sul dominio della matematica, ma le 

aveva anche impresso un livello di rigore che ostacolava la creatività. Gli studiosi del XVII 

secolo avevano spezzato entrambi questi vincoli. Il progresso in matematica richiede un 

disprezzo quasi completo per gli scrupoli logici» 66 . 

"Disprezzo" che Cantor coltivò più di ogni altro. «La matematica - scriveva nel 1883 - nel suo 

sviluppo è completamente libera e vincolata soltanto all'evidente condizione che i suoi 

concetti siano in sé non contraddittori» 67 . Cantor era sopraffatto dal timore che i vincoli posti 

alla ricerca avrebbero potuto tagliare le ali alla creatività matematica, «giacché - egli 

affermava - l'essenza della matematica risiede proprio nella sua libertà» 68 . Senza di questa, 

sosteneva Cantor, non ci sarebbero stati i grandi sviluppi registrati nel corso del secolo; non

avremmo avuto la moderna teoria delle funzioni se Gauss o Cauchy o Jacobi o Weierstrass e 

Riemann avessero dovuto «sottoporre le loro idee nuove a un controllo metafisico» 69 . D'altra 

parte è proprio la completa assenza del «controllo metafisico» che favorirà l'empirismo logico 

prima e la «novità relativistica» poi, nel campo della fisica, fomentando - in seno a 

quest'ultima - un recupero avventato della "libertà cantoriana" e realizzando così quella che 

poi Gaston Bachelard rileverà come «impronta di una induzione così audacemente estensiva 

da poter sviare una mente poco abituata alle libertà matematiche» 70 . La linea filosoficoprogettuale 

di Cantor, largamente diffusa tra i matematici, la quale - con le parole e il 

disappunto di Gottlob Frege - considera sufficientemente giustificata una definizione che «si 

presta spontaneamente a costituire la base dei nostri ragionamenti, senza condurre mai ad 

alcuna contraddizione» 71 , si trasmetterà in seguito nel campo della fisica, tramite Einstein 

prima e Heisenberg poi, dove il contagio porterà a una vera e propria epidemia di FLOP 72 , 

sintomatica peste delle strutture portanti della scienza contemporanea. Già per il campo della 

matematica era necessario ricordare che il criterio di non contraddittorietà consente solo di 

raggiungere «una certezza empirica» - come aveva fin da allora avvisato Frege - giacché 

bisogna «in ogni caso essere pronti a incontrare da un momento all'altro qualche 

contraddizione che mandi in rovina l'intero edificio» 73 . Come esponeva H. Weyl nel 1917: 

«Una parte essenziale di quest'edificio è costruita sulla sabbia», ed una delle cause essenziali 

di questa circostanza «va ricercata unicamente nell'arbitrio (commesso sin dall'inizio in 

matematica) di considerare un campo di possibilità costruttive come un aggregato chiuso di 

oggetti esistente in sé» 74 . Ma oramai si era infiltrato anche nella fisica il nuovo credo dei 

matematici, quello che con enfasi scriveva Dedekind all'amico Weber in una lettera del 1888: 

«Noi siamo di razza divina e possediamo […] il potere di creare» 75 . 

4. Dagli assiomi ai postulati: il programma di Hilbert tradotto in fisica 

«La teoria generale della relatività contrastava con la mirabile struttura euclidea del "sacro 

volumetto di geometria" che aveva incantato Einstein in gioventù; ed essenziale, ai fini della 

teoria stessa, era la negazione dell'assoluta validità del teorema di Pitagora, per il quale, da 

ragazzo, aveva trovato una dimostrazione per proprio conto. […] A quasi tutti gli studiosi 

della geometria elementare, un'alternativa valida del sistema euclideo sembrerebbe 

impossibile. Invero, il filosofo Kant aveva dichiarato che il sistema euclideo era inevitabile, 

una necessità del pensiero umano. Ma, a cominciare dagli inizi del diciannovesimo secolo, 

dopo un periodo di incubazione che risaliva fino a Euclide, matematici audaci proposero 

effettivamente alternative non euclidee e, come si rese conto Gauss, una volta che Euclide 

avesse avuto dei concorrenti, la geometria sarebbe divenuta, per necessità di cose, una scienza 

sperimentale» 76 . Viene così tracciata da Hoffmann e Dukas la linea di collegamento tra Gauss 

e Einstein. Le "certezze euclidee" impostate dall'antichità e indicate come rocce inabissabili 

«in mezzo ai mari agitati della speculazione umana» 77 venivano poste prima in uno stato 

ipotetico e incerto dall'empirismo gaussiano, poi rese costruzioni immaginarie della creatività 

umana dal libertinismo cantoriano, e infine ricapitolate nel popperiano mondo 3 delle 

congetture perché inadeguate per la neopitagorica struttura del mondo: eccessivamente 

semplicistiche e obsolete per l'universo einsteiniano. «E in virtù di queste… rivoluzioni - 

scrive William Clifford - l'idea dell'universo, il Macrocosmo, il Tutto, come soggetto della 

conoscenza umana, e perciò di interesse umano, è andato in frantumi» 78 . Scrive Russell: «La 

rivoluzione di Einstein ha spazzato via tutto...» 79 . «Dal punto di vista della dialettica hegeliana 

la teoria della relatività era una comoda fonte di antinomie: non era necessario… trovare una 

soluzione all'interno della fisica, ma bisognava riconoscere che la materia fosse un'astrazione 

irreale e che nessuna scienza della materia poteva essere logicamente soddisfacente» 80 . Così 

l'universo di Einstein - grazie alla gaussiana mentalità che si era venuta a creare - avrebbe 

travalicato i confini pitagorici dell'evidenza e dell'intuizione: «Il mondo di Einstein è un 

mondo di numeri; questi non suppongono prima di essi né una verità a priori come la 

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condizione della loro espressione formale, né una immagine intuitiva come una condizione 

del loro significato fisico» 81 . La successiva meccanica quantistica ipostatizzerà questa sorta di 

metafisica e tramite l'«irrazionale» - per usare i termini di Meyerson -, quell'essenza aberrante 

di «aritmetizzazione del possibile», concederà quel "passo" contemplato da Bachelard: «Un 

passo ancora e il reale non è più che la causa occasionale del pensiero» 82 . Tanto che ai nostri 

giorni un Feynman può asserire: «Mi auguro quindi che riuscirete ad accettare la Natura per 

quello che è: assurda» 83 . 

Innegabile è dunque il tallonamento della nuova fisica nei confronti dello "svuotamento 

semantico-categoriale" della nuova matematica. Lo strano mondo della fisica del Novecento è 

intimamente collegato a quello astratto e immaginifico della matematica post-gaussiana 84 . 

Dopo Einstein le geometrie non euclidee non esistevano più soltanto come sistemi logici su 

fogli di carta: l'architettura dell'universo era non-euclidea e ciò si poteva toccare con mano. 

Così come, dopo Heisenberg, le nuove e strane algebre "non commutative" sviluppate a 

partire dai quaternioni di Hamilton 85 - riflesso diretto della rivoluzione gaussiana - potevano 

finalmente innalzarsi dai "mondi di carta" ed esigere altrettanta dignità "interfenomenologica" 

del mondo fisico così come lo era stato per le geometrie non euclidee 86 . Era 

la vittoria del freddo costrutto matematico - esterno e alieno alla sfera dell'evidenza, 

dell'intuizione, del senso comune - che trionfava sui detriti delle categorie kantiane, 

«completamente annichilite - postillerà Heisenberg - dalle scoperte del nostro secolo» 87 . 

Hermann von Helmholtz poteva finalmente cantare vittoria - «Essa [l'intuizione] è una 

conoscenza empirica ottenuta con l'accumulazione e il rafforzamento di impressioni simili 

ricorrenti nella nostra memoria, e non una forma di intuizione trascendentale data prima di 

ogni esperienza» 88 - così come David Hilbert poteva finalmente vedere realizzato il suo sogno 

«di dare una formulazione puramente matematica agli assiomi della fisica» 89 , liberando «gli 

assiomi che stanno a fondamento delle discipline matematiche dall'obbligo di corrispondere ai 

loro significati intuitivi originari e naturali» 90 . Siccome per Hilbert «la matematica… possiede 

coerenza ma nessun significato» 91 , era arrivato il momento di trasformare gli assiomi in 

postulati 92 (portando così a compimento l'ideale del tracciato epistemologico che da Gauss 

arriva a Cantor). D'altra parte, sottolinea il matematico Meschkowski, «se sul pensiero di 

Hilbert non riluce più, come su quello di Platone, "lo splendore dell'essere"», ciò è 

direttamente collegato alla rivoluzione gaussiana: «l'"esistenza" della geometria non euclidea 

rende impossibile all'uomo moderno di restare fermo alla concezione spaziale di Platone e di 

Kant» 93 . 

Il programma hilbertiano, pur lacerato dal celeberrimo teorema di Gödel, continuò a 

sopravvivere sotto le "vesti metafisiche" della fisica del Novecento, da Einstein in poi 94 . Lo 

sviluppo di un'algebra astratta manipolante enti matematici con procedimenti puramente 

formali, evitando ogni interpretazione sulla natura di essi, preparerà il terreno epistemico delle 

teorie scientifiche contemporanee, tanto da rendere possibile affermare che «per esempio, 

l'integrale di Feynman non corrisponde, per il momento, ad alcun oggetto matematico preciso. 

È tuttavia è il pane quotidiano dei fisici teorici» 95 . L'approccio astratto-assiomatico-formalista 

hilbertiano della fisica moderna è nettamente strumentalista, si nutre dell'efficacia empirica 

all'interno di un humus positivistico ancorato all'idea machiana di "scienza-formulario" 96 . È la 

filosofia dello 0! = 1 , del (-1) 0 = 1 0 = 1 1 = 1! = 0! . Eppure il matematico contemporaneo 

giudizioso avverte: «Malgrado lo stato insoddisfacente della matematica, la molteplicità delle 

scuole, il disaccordo sugli assiomi da accertare, e il pericolo che nuove contraddizioni, 

qualora scoperte, possano invalidare gran parte della matematica, alcuni matematici applicano 

tutt'ora questa scienza ai fenomeni fisici» 97 . Ma lo scienziato della nuova era, accecato dal 

potere predittivo della nuova scienza, ha barattato la verità con il successo: «Tutto quello che 

si può richiedere da una teoria fisica è che le sue predizioni siano in accordo con le 

osservazioni» 98 . Come osserva Russell: «Il male è intellettuale… Per conto mio, non ho 

soluzioni da prospettare; la nostra è un'epoca che sostituisce sempre più il potere agli ideali 

primitivi, e ciò accade nelle scienze come in altre cose. Mentre la scienza come

conseguimento di potere diviene sempre più trionfante, la scienza quale conseguimento di 

verità è uccisa da uno scetticismo generato dall'abilità degli scienziati». 

5. Conclusioni: le basi metafisiche della teoria della relatività 

L'avvento della Relatività, facendo saltare i quadri abituali di riferimento spazio-temporali 

insieme all'edificio concettuale della fisica newtoniana - che a Kant appariva come «quella 

conoscenza del sistema del mondo chiara e immutabile per tutto l'avvenire» - e rendendo 

inintuitivo lo spazio così come il tempo «una creazione del nostro pensiero» 99 , veniva a 

materializzare sullo sfondo della realtà fisica l'ideale "gaussiano-cantoriano-hilbertiano" 

concepito e architettato precedentemente nell'universo del costrutto matematico. La 

«rivoluzione copernicana della Relatività» avrebbe apportato un vero e proprio «terremoto dei 

concetti» - per usare dei termini che Bachelard dichiaratamente mutua da Nietzsche - sulle 

stesse fondamenta gnoseologiche, dove «tutto l'edificio della ragione è "scosso"»: «Con la 

scienza einsteiniana incomincia una rivoluzione sistematica dei concetti fondamentali» 100 . 

Dunque il frutto epistemologicamente più profondo dell'impatto einsteiniano sulla fisica è il 

suo stesso sconfinamento dal mondo dei numeri e della materia a quello del pensiero, della 

logica e dei pilastri della conoscenza, come sottolinea Hans Reinchenbach: «La teoria della 

relatività di Einstein ha dato una forte scossa ai fondamenti filosofici della conoscenza» 101 . La 

stessa Meccanica Quantistica può essere vista come una conseguenza estrema, una ipostasi 

del tracciato epistemico della teoria di Einstein: non abbiamo fatto altro - avrebbe rilevato lo 

stesso Born, uno degli artefici della meccanica matriciale - che «avere fedelmente proseguito 

sulla via che egli [Einstein] ci aveva indicato nei suoi giorni migliori» 102 . Confesserà 

Heisenberg: «Avevo soltanto… applicato il tipo di filosofia che egli stesso aveva posto alla 

base della sua teoria della relatività ristretta» 103 . È stato «Einstein - confermerà Gamow - ad 

abbandonare le vecchie idee di "senso comune" sul computo del tempo, la misura della 

distanza e la meccanica, … [arrivando] alla riformulazione della "insensata" Teoria della 

Relatività. […] Heisenberg ne dedusse che la stessa situazione esistesse nel campo della 

Teoria dei Quanti» 104 . Ecco in sintesi la storia di come si sia arrivato a relativizzare la stessa 

logica. Oramai si parla di una «pluralità» di logiche… Scrive B.L. Whorf in Le lingue e la 

logica: «Nuovi tipi di logica possono forse aiutarci a capire com'è che gli elettroni […] 

sembrano comportarsi illogicamente» 105 . 

Rileva Bachelard che intere schiere di scienziati e filosofi che durante i secoli avevano cercato 

un continuo accumulo e perfezionamento nella decodifica del reale sotto l'ombra di un'unica e 

primordiale razionalità vengono adesso travolti e devastati dalla «novità relativistica»: una 

«scienza senza antenati», la Relatività, in quanto non sarebbe «potuta sbocciare che 

nell'atmosfera di una matematica perfezionata; ecco perché la dottrina manca veramente di 

antecedenti» 106 . La matematica assurge così a «vero e proprio metodo di invenzione» 107 ; da 

"descrittore" a "creatore", la sua "carica deduttiva" diventa "induttiva": «L'espressione 

matematica da sola consente di pensare il fenomeno» 108 . Il calcolo tensoriale è per Bachelard 

esempio perfetto di «strumento matematico che crea la scienza fisica contemporanea come il 

microscopio crea la microbiologia», «Langevin diceva che: "Il calcolo tensoriale conosce la 

fisica meglio dello stesso fisico"» 109 . 

Il «pensiero relativistico» è, dunque, animato da un'«audacia induttiva», una proprietà 

"rivelata" dello strumento matematico che nella Teoria gioca un ruolo privilegiato. Ciò, però, 

non esime ma, anzi, estremizza «lo scandalo della ragione», per usare ancora una volta dei 

termini bachelardiani. Come mette bene in evidenza Bouasse nella sua critica risoluta al 

potere esplicativo della teoria di Einstein, decisamente minore rispetto a quella classica: «Si 

sopprime l'etere e ci si esime dall'insegnarci con che cosa dobbiamo sostituirlo!» 110 . Non 

possiamo dunque accettare l'invito di Hume («Allora buttatelo nel fuoco») di bruciare, tramite 

Einstein, l'unità del pensiero logico-intuitivo plurimillenario che soggiace nell'"incoscio 

collettivo" dell'umanità tutta intera. Noi non facciamo - osserva Bouasse - «i sillogismi 

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diversamente da Aristotele: anzi, Aristotele ne conosceva la teoria molto meglio della 

maggior parte dei nostri filosofi moderni. Bacon, Descartes… si sbagliavano spesso nelle 

applicazioni; ciò non toglie che i loro attrezzi, dei quali talvolta essi si servivano male, erano 

esattamente i nostri. Se Bacon, Descartes… risuscitassero, si farebbe loro facilmente 

comprendere in che cosa essi si sbagliavano, perché i loro cervelli e i nostri sono costruiti allo 

stesso modo», né sono «suscettibili di perfezionamento». E dunque - si chiede Bouasse - 

come è possibile «simultaneamente rigettare i dati intuitivi del nostro cervello sullo spazio e 

sul tempo, e serbargli […] fiducia quando si tratta di ragionare? […] Voi dite che il nostro 

cervello è un falso testimone, poi conservate la metà della sua testimonianza! […] È assurdo. 

[…] Io dico che i dati intuitivi del nostro cervello formano un blocco che non avete il diritto 

di dividere. Se ne rigettate una parte, siete fatalmente condotti a rigettare il tutto: cosa che 

sopprime ogni possibilità di conoscenza» 111 . 

Bachelard ammette il "cartesicidio" caratteristico della fisica post-relativistica, simbolo di 

agonia e sprezzo per la "dea intuizione" e parenti stretti "evidenza", "chiaro" e "distinto": 

«Siamo di fronte - egli dice - a una vera dialettica. Si procede sistematicamente negando il 

postulato di analisi cartesiana, esattamente nello stesso modo in cui si sviluppa la geometria 

non-euclidea negando il postulato di Euclide» 112 . E se un Cassirer parla di «crisi 

dell'intuizione» avvenuta «dopo le geometrie non-euclidee e dopo la relatività speciale e 

generale» 113 , non può essere nascosto al proprio intelletto - "scolasticamente" inteso - che 

«come ipotesi metafisica, la teoria di Einstein risulta contraddittoria» 114 . Inefficace la 

certificazione data da Heisenberg che «"non contraddittorio" si riferisce… alla consistenza e 

completezza matematica del formalismo che viene costruito a partire dagli assiomi» 115 , 

quando è ormai ben noto invece che la formalizzazione matematica di una teoria è ben lungi 

dallo schermare la stessa dall'incoerenza latente che sfocia a livello di quello che Bridgman 

definisce come «sfondo descrittivo enorme». Dietro alle equazioni c'è una enorme struttura 

qualitativa fatta di risultati empirici, ipotesi, generalizzazioni, scelte filosofiche, gusti 

personali, convenienze: «Quando si prenda atto, finalmente, di questa ricca realtà 

confrontandola con il ritratto della teoria scientifica tramandato dall'empirismo logico, che 

vale meno di una caricatura, si comprenderà facilmente che la teoria, accanto ai suoi 

innegabili successi, non solo può presentare punti deboli, ma può anche sopravvivere ai suoi 

stessi fallimenti» 116 . Come conferma lo stesso Bridgman: «Ogni sistema di equazioni può 

comprendere solo una piccolissima parte della situazione fisica effettiva: dietro le equazioni 

vi è uno sfondo descrittivo enorme, tramite il quale esse stabiliscono legami con la natura» 117 . 

È solo grazie all'«oscurità matematica» 118 che regna sovrana sulle nuove teorie che il novello 

"apprendista stregone" può ritenersi degno di possedere l'arcana chiave meta-ermeneutica e il 

potere ad essa congiunto. Sentendosi appartenente alla pitagorica classe dei neo-mathematicoi 

non si abbassa ad una «umana, troppo umana» rappresentazione, figlia dell'intuizione. 

L'"ammassato" gruppo degli acousmaticoi - cioè coloro che, come denunciava Cartesio già ai 

suoi tempi, «si astengono dall'esaminar molte cose... poiché stimano che possano esser 

comprese da altri forniti di maggior intelligenza, abbraccian[d]o il parere di coloro sulla cui 

autorità maggiormente confidano» 119 - si accascia ai bordi delle corsie preferenziali del 

pensiero scientifico, affidandosi ciecamente ai cosiddetti "esperti" («cieca schiavitù al 

dogma», direbbe Herbert Dingle120 ), nella convinzione che quanto non si sia riuscito a 

intendere sia dovuto ad un inadeguato e insufficiente numero di neuroni a loro disposizione; 

una sorta di "filosofia del rimando" «di cui sono preda non solo tanti studenti, ma anche tanti 

docenti» 121 . Ed ecco così il «mastery, instead of the servitude, of mathematics in relation to 

physics» denunciato da Dingle122 . Non deve sorprende allora che il matematismo entri a far 

parte della nuova ermeneutica contemporanea e a sostituire interi blocchi kantiani della psiche 

in altrettanti moduli "gaussiani". Confessa senza malizia un docente universitario di 

ingegneria elettrica del calibro di Paul Nahin: «Later, in college, I would learn that the 

operation of radio is impossible to understand, at deep theoretical level, without an 

understanding of − 1 » 123 . È la matematica che prende il posto del sillogismo aristotelico.

Come manifesta apertamente Dirac: «Le nuove teorie, considerate al di là della struttura 

matematica, sono costruite con concetti fisici che non possono essere spiegati in termini di 

cose precedentemente note allo studente, che neppure possono essere spiegati adeguatamente 

con le parole» 124 . Riesce facile concepire, a questo punto, come si stia approdando con sempre 

più facilità a riconoscere con Bridgman che «tutta la nostra conoscenza è relativa» e che in 

questo senso «la relatività in senso generale diventa un puro truismo» 125 . Si arriva così alla 

signoria della sintassi sulla semantica, all'indebolimento, detronizzazione e perdita del 

fondamento 126 , come anche di una umana comprensione 127 . 

Il pericolo di un matematismo sofisticato e "trans-categoriale" alla guida delle teorie 

scientifiche è estremamente elevato, e, se lasciato a se stesso, rischia di diventare un alieno 

alla ragione stessa: dovremo allora abituarci a vedere sorpresi e sconcertati gli stessi creatori 

delle teorie scientifiche quando i razzi di questo "Math-Alieno" travalicano e sconfinano gli 

universi dell'intuizione, come accadde allo stesso Einstein quando si scontrò con la 

precessione di Thomas 128 . Bisogna recuperare lo status baconiano di una matematica al 

servizio della ragione e non viceversa: quella che l'Einstein non ancora condizionato dalla 

spinta minkowskiana 129 era solito sottostare, come dimostra una frase dello stesso riportata da 

un suo amico nel 1920: «I'm afraid I'm wrong again. I can't put my theory into words. I can 

only formulate it mathematically, and that's suspicious» 130 . E nel 1927, in occasione del 

secondo centenario della morte di Newton, in una lettera al segretario della Royal Society e 

poi riportata su Nature (119) e su Science (65) scrive: «È solo nella teoria dei quanti che il 

metodo differenziale di Newton diviene inadeguato, e infatti viene meno la causalità in senso 

stretto. Ma non è detta l'ultima parola. Possa lo spirito del metodo di Newton consentirci di 

riportare l'armonia tra la realtà fisica e ciò che è alla base di tutto il suo insegnamento: la 

causalità in senso stretto». Auspichiamoci la stessa cosa, anzi recuperiamo con Newton 

l'essenza stessa della matematica, quando nel 1728 scrisse: «Ma è giusto che le radici delle 

equazioni debbano essere spesso impossibili [complesse], per timore che esse debbano esibire 

i casi di problemi che sono impossibili come se fossero possibili» 131 . 

Note 

1 W. Heisenberg, Il contenuto intuitivo della cinematica e della meccanica nella teoria quantistica, in 

S. Boffi (ed.), De Broglie - Schrödinger - Heisenberg, Onde e particelle in armonia. Alle sorgenti 

della meccanica quantistica, Milano 1991, p 181. 

2 Cit. in B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, Milano 2002, p. 30. 

3 G. Bachelard, Il nuovo spirito scientifico, Roma-Bari 1978, p. 156. 

4 A. Pais, Il danese tranquillo. Niels Bohr, un fisico e il suo tempo, 1885-1962, Torino 1993, p.75. 

5 Per un approfondimento si veda U. Bartocci - R.V. Macrì, Il linguaggio della matematica, 

«Episteme», 5, 2002. 

6 W. Heisenberg, Fisica e filosofia, Milano 1994, p. 44. 

7 A. Einstein, Replica alle osservazioni dei vari autori, in P.A. Schilpp (ed.), Albert Einstein, 

scienziato e filosofo. Autobiografia di Einstein e saggi di vari autori, Torino 1958, p. 629. 

8 V.F. Lenzen, La teoria della conoscenza di Einstein, in P.A. Schilpp (ed.), op. cit., p. 307. 

9 Ibidem, p. 326. Dal rischio reale di una accecante reverenza da parte della fisica nei confronti della 

matematica contemporanea, tale da ammaliare e sottomettere l'eredità di Galileo nelle mani della 

Scuola di "prestigio matematico" del momento ci mette in guardia Morris Kline nel suo capolavoro 

145

146 

Matematica: la perdita della certezza, Milano 1985, p. 15: «Le teorie fisiche più sviluppate, nella 

maggior parte dei casi, sono interamente matematiche (pur ammettendo che i risultati di tali teorie 

sono interpretati in termini di dati sensibili e di oggetti fisici: si possono sentire i suoni emessi da una 

radio pur senza avere la più pallida idea di cosa sia un'onda radio da un punto di vista fisico). Perciò 

anche gli scienziati che non si occupano in prima persona del problema dei fondamenti devono 

nondimeno porsi il problema di quale matematica possono utilizzare con sicurezza se non vogliono 

sprecare anni di lavoro servendosi di una matematica priva di salde basi». 

10 M. Polanyi, La conoscenza personale. Verso una filosofia post-critica, Milano 1990, p. 92. 

11 P.A.M. Dirac, in D. Monti, Equazione di Dirac, Torino 1996, p. 120. Racconta Sommerfeld che a 

seguito del successo che ebbe la teoria di Einstein dopo la spedizione dell'«apostolo ispirato della 

dottrina di Einstein, […] Il grande astronomo inglese Sir Arthur Eddington, […] nel 1920, un inviato 

della "Kölnische Zeitung" mi chiese qualche particolare su di essa, gli dissi che non era argomento per 

il grosso pubblico, sfornito com'è delle conoscenze matematiche necessarie per la comprensione di 

questa teoria» (A. Sommerfeld, "Per il compleanno di Albert Einstein", in P.A. Schilpp (ed.), op. cit., 

Torino 1958, p. 53). 

12 J.D. Barrow, Teorie del tutto. La ricerca della spiegazione ultima, Milano 1992, p. 316. 

13 P.A.M. Dirac, op. cit., p. 116. 

14 J.P. Changeux - A. Connes, Pensiero e materia, Torino 1991, p. 12. 

15 P.A.M. Dirac, op. cit., p. 122. Esattamente di parere opposto la tradizione dei fisici italiani di inizio 

secolo che, intendendo le rappresentazioni fisico-matematiche come parametrizzazioni descrittive di 

ciò che non può avere altro fondamento che nel territorio dell'evidenza fenomenica, con le parole di 

Antonio Garbasso nel 1910 così si pronunciava: «A voler considerare le cose con pieno rigore, si 

direbbe anzi che di necessità il modello analitico [matematico] sia più lontano dalla natura che il 

modello, in apparenza più rozzo, della fisica sperimentale. Perché se la percezione fornisce una 

immagine della realtà, e l'analogia fisica è già una rappresentazione mediata, il calcolo che traduce 

quest'analogia nel linguaggio dell'algebra, costituisce in qualche modo un'icona dell'icona dell'icona» 

(A. Garbasso, Fisica d'oggi, filosofia di domani, Milano 1910, p. 118). 

16 B. Russell, La mia filosofia, Roma 1995, p. 177. 

17 W. Heisenberg, La tradizione nella scienza, Milano 1982, p. 32. 

18 W. Heisenberg, Fisica e filosofia, op. cit., p. 84. 

19 P.P. Wiener - A. Noland (edd.), Le radici del pensiero scientifico, Milano 1971, p. 1. 

20 Aristotele, Metaph., I, 5, 985 b 23 - 986 a 16. 

21 Cfr. T.M. Tonietti, Verso la matematica nelle scienze: armonia e matematica nei modelli del cosmo 

tra Seicento e Settecento, in M. Mamone Capria (ed.), La costruzione dell'immagine scientifica del 

mondo, Napoli 1999. Il mondo antico è completamente intessuto da tale concezione. Cfr., solo per fare 

qualche esempio, Proclo, In Platonis theologiam, IV, 34; Boezio, De institutione arithmetica, I, 1 e 2; 

Agostino, Ad Orosius contra Priscianum et Origenem, PL 42, 674, e De quantitate animae, 8-12, PL 

32, 1042-1047; Alberto Magno, Metaphys., I, tr. 4, c. 2; Bonaventura, Itinerarium mentis in deum, 2, 

n. 10; Alano di Lilla, Sermo de trinitate, 255. 

22 B. Russell, op. cit., p. 238. 

23 E. Husserl, Idee per una fenomenologia, Torino 1981, I, p. 95. 

24 Nicola Cusano, La dotta ignoranza, Roma 1991, p. 76.

25 E. Kant, Critica della ragion pratica, a cura di V. Mathieu, Milano 1996, p. 53. 

26 R. Nobili, La cognizione dello spazio e il principio di dualità, Pavia, preprint 1990, p. 5. 

27 Cfr. il paragrafo 16c di A. Pais, «Sottile è il Signore…»: la scienza e la vita di Albert Einstein, 

Torino 1991, per una rassegna dei titoli del "Times" e di altre riviste scientifiche e non durante il 

momento della "beatificazione" di quel memorabile novembre: «Rivoluzione nella scienza. Nuova 

teoria dell'universo. La concezione newtoniana demolita», «Euclide al tappeto», «Notizia 

sconvolgente, che farà sorgere i dubbi perfino sull'affidabilità della tavola pitagorica», «Tempi duri 

per persone colte», «All'assalto dell'assoluto», ecc. 

28 Il 1° gennaio del 1801 l'Osservatorio di Palermo poté vantare una sensazionale scoperta fatta 

dall'astronomo Giuseppe Piazzi: il primo asteroide mai osservato, Cerere. Piazzi, tuttavia, aveva 

potuto osservare solo 9° dell'intera orbita del pianeta; una porzione fino allora considerata insufficiente 

per consentire il calcolo dell'orbita completa. Gauss accettò la sfida e arrivò a calcolare un'orbita 

ellittica innovativa rispetto ai tentativi utilizzati fino allora, che in seguito si rivelò esatta. 

29 R. Tazzioli, Gauss, principe dei matematici e scienziato poliedrico, Milano 2002, p. 36. 

30 Ibidem, p. 39. 

31 Gauss completerà l'interpretazione geometrica dei numeri complessi solo a partire dal 1831, 

perfezionando il cammino intrapreso nella sua dissertazione discussa a Helmstedt nel 1799, dove è 

contenuta la dimostrazione del famoso teorema fondamentale dell'algebra, che afferma che ogni 

polinomio a coefficienti complessi ammette almeno una radice complessa. Lo studio delle funzioni 

complesse venne poi proseguito da Cauchy che nel 1825 propose una generalizzazione dell'integrale 

definito che includesse anche le variabili complesse. 

32 Ibidem, p. 6. 

33 È vero quanto asserisce Russell: «L'autoevidenza è uno degli argomenti più problematici di tutta 

l'epistemologia» (B. Russell, Teoria della conoscenza, Roma 1996, p. 248). D'altra parte la soluzione 

tentata da questi sembrerebbe ben lontana da una compiutezza filosofica soddisfacente. Si veda, per 

completezza, oltre che Autoevidenza, in B. Russell, op. cit., pp. 248 e sgg., anche La matematica e i 

metafisici, in B. Russel, Misticismo e logica, pp. 71 e sgg., dove viene sottolineato che «l'evidenza è 

spesso un fuoco fatuo» (p. 74). 

34 Cit. in J.D. Barrow, La luna nel pozzo cosmico, Milano 1994, p. 31. 

35 J.D. Barrow, op. cit., p. 40. 

36 M. Kline, Matematica: la perdita della certezza, op. cit., p. 98. 

37 Ibidem. La similitudine con Einstein arriva addirittura nella conversione in età matura e nel rigetto 

del proprio credo epistemologico avuto prima della pienezza. Come il "secondo" Einstein nella 

maturità rinnegherà il "primo" per aver accettato la metafisica operazionista, anche Gauss, nella fase 

matura della sua vita, rimediterà e rimetterà in discussione la matrice empirista e strumentalista che 

l'aveva guidato per tutto l'arco degli anni fruttuosi e memorabili. Così come anche tutte e due le 

"riconversioni" avverranno troppo tardi in rapporto all'avvio degli sviluppi successivi, che 

cristallizzeranno invece il cammino empirio-operazionista della scienza posteriore. 

38 C.B. Boyer, Storia della matematica, Milano 1990, p. 322. 

39 Ibidem, p. 326. 

147

148 

40 «Quanto ai numeri negativi, sebbene essi fossero diventati noti in Europa attraverso i testi arabi, la 

maggior parte dei matematici del XVI e del XVII secolo non li accettava come numeri o, se lo faceva, 

non li accettava tuttavia come radici delle equazioni» (M. Kline, Storia del pensiero matematico, vol. 

I, Torino 1996, p. 294). Racconta Kline che «Pascal considerava la sottrazione di 4 da 0 come una 

totale assurdità» e che Cartesio «chiamava false le radici negative delle equazioni sulla base del fatto 

che esse pretendono di rappresentare numeri minori di nulla» e soltanto per il fatto da lui dimostrato 

che «le radici false possono essere mutate in radici reali, Descartes era disposto ad accettare i numeri 

negativi» (Ibidem, pp. 294-295). 

41 Termine coniato da Cartesio allorché approfondì l'impossibilità di "trasmutare" le radici complesse 

in radici reali, come invece era riuscito a fare per quelle negative: «Esse non sono perciò reali ma 

immaginarie, cioè non sono numeri. Descartes tracciò una distinzione più chiara dei suoi predecessori 

fra le radici reali e immaginarie delle equazioni» (Ibidem, p. 296). 

42 Ibidem, p. 295. 

43 C.B. Boyer, op. cit., p. 330. 

44 Ibidem, pp.332-333. 

45 Sottolinea però Kline che «le opinioni avanzate di Girard non ebbero tuttavia alcuna influenza» (M. 

Kline, Storia del pensiero matematico, op. cit., p. 296). 

46 Paul J. Nahin, An Imaginary Tale. The Story of − 1 , Princeton 1998, p. 31. 

47 Ibidem, p. 82. 

48 Scriveva De Morgan nel 1831: «Abbiamo dimostrato che il simbolo − 1 è privo di significato, 

anzi addirittura auto-contraddittorio e assurdo.» (P.J. Nahin, op. cit., p. 82). Aggiunge ai nostri giorni 

M. vos Savant: «Yet it is accepted, and imaginary numbers are used routinely. But how can we justify 

using them to prove a contradiction?» (Ibidem, p. 224). 

49 C.B. Boyer, op. cit., p. 332. Il "sospetto di contraddizione" che nasce dalla manipolazione con i 

numeri negativi viene così candidamente spiegata da Paul J. Nahin: «This suspicion of negative 

numbers seems so odd to scientists and engineers today, however, simply because they are used to 

them and have forgotten the turmoil they went through in their grade-school years. In fact, intelligent, 

nontechnical adults continue to experience this turmoil, as illustrated in the following wonderful 

couplet, often attributed to the poet W. H. Auden: "Minus times minus is plus. The reason for this we 

need not discuss."» (P.J. Nahin, op. cit., pp. 13-14). 

50 P.J. Nahin, op. cit., pp. 224-6. 

51 «Per verificare l'applicabilità della geometria euclidea e della sua geometria non euclidea Gauss 

misurò effettivamente la somma degli angoli del triangolo formato dalle cime delle tre montagne 

Brocken, Hohehagen e Inselberg» (M. Kline, Storia del pensiero matematico, vol. II, Torino 1996, p. 

1017). 


53 Ibidem, pp. 106-7. 

54 Ibidem, p. 107. 

55 Ibidem, p. 132. 

56 Ibidem, p. 134.

57 Ibidem, pp. 168-9. 

58 Ibidem, p. 170. 

59 Cit. in B. Russell, La mia filosofia, op. cit., p. 217. 

60 M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1136. 

61 D. Overbye, Einstein innamorato. La vita di un genio tra scoperte scientifiche e passione romantica, 

Milano 2002, pp. 126-7. 

62 M. Kline, Matematica: la perdita della certezza, op. cit., pp. 172-3. 

63 M. Kline, Storia del pensiero matematico, vol. II, op. cit., p. 1139. 

64 Ibidem, p. 1026. 

65 J.D. Barrow, La luna nel pozzo cosmico, op. cit., p. 35. «All'origine della svolta c'era stata l'opera di 

Gauss sulla geometria delle superfici, che iniziava lo studio delle proprietà intrinseche delle superfici, 

indipendenti cioè dallo spazio in cui erano immerse» (E. Giusti, Ipotesi sulla natura degli oggetti 

matematici, Torino 1999, p. 84). Nell'opera di Gauss del 1828, Disquisitiones generales circa 

superficies curvas, l'idea chiave è quella di considerare «la superficie non come la frontiera di un 

solido» ma di per sé stessa, con le parole di Eugenio Beltrami «come un velo infinitamente sottile». 

L'approccio di Gauss sarà ripreso anni dopo da Riemann, il quale - nella sua lezione di abilitazione 

tenuta proprio di fronte a Gauss nel giugno del 1854 - esporrà la sua celebre teoria delle varietà 

pluriestese. I perfezionamenti successivi di Beltrami e Ricci Cubastro riveleranno la grande fecondità 

dell'idea gaussiana nella formulazione matematica della Relatività generale, come ebbe a sottolineare 

lo stesso Einstein: «L'importanza di Gauss per lo sviluppo della fisica moderna e specialmente per i 

fondamenti matematici della teoria della relatività è enorme» (Cit. in R. Tazzioli, op. cit., p. 64). 

66 M. Kline, Storia del pensiero matematico, vol. I, op. cit., p. 465. 

67 Cit. in U. Bottazzini, Insiemi di punti e numeri transfiniti, in Paolo Rossi (ed.), Storia della scienza 

moderna e contemporanea, vol. III, tomo I, Milano 2000, p. 62. 

68 Ibidem, p. 63. 

69 Ibidem. Per questo motivo Kant era odiato da Cantor: «Kant era la sua bestia nera» (B. Russell, Una 

filosofia per il nostro tempo, Milano 1995, p. 24). Per un motivo opposto a quello di Cantor, Kant 

stava sullo stomaco anche a Russell. Sulla copertina di un libro di Cantor spedito dall'autore medesimo 

a Russell c'era scritto: «Vedo che il vostro motto è Kant o Cantor» (Ibidem). Ricorda Alan Wood in 

una conversazione avuta con Bertrand Russell la teatrale manifestazione di contrarietà che questi 

aveva «circa l'affermazione di Kant riguardo all'esistenza di un elemento soggettivo nella matematica: 

il tono della voce può essere descritto solo come di disgusto, simile a quello di un fondamentalista 

posto di fronte all'ipotesi che Mosè abbia inventato di sana pianta i Dieci Comandamenti: "Kant mi ha 

stufato."» (A. Wood, La filosofia di Russell. Uno studio sulla sua evoluzione, in B. Russell, La mia 

filosofia, op. cit., p. 223)". Einstein invece parteggiava per la tesi cantoriana, la quale - oltre a «fare 

rivoltare Kant nella tomba» (D. Overbye, op. cit., p. 131) - propendeva per una vittoria della libera 

creatività sulla rigidità delle kantiane forme a priori: «Gli assiomi della matematica sono altrettanti 

esempi dell'opinione di Einstein per cui i concetti sono libere creazioni della mente umana. […] In 

Kant… l'attività creativa della mente era limitata dalle forme a priori dell'intuizione. Ma il pensiero 

matematico se ne liberò con la scoperta di geometrie non euclidee, e si capisce quindi come Einstein 

abbia dotato il pensiero di una maggiore libertà di creazione che con Kant» (V.F. Lenzen, La teoria 

della conoscenza di Einstein, op. cit., p. 327). 

70 G. Bachelard, La valeur inductive de la Relativité, Paris 1929, p. 61. 

149

150 

71 Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p. 

257. 

72 FLOP = Falsificatore Logico Potenziale, neologismo del presente autore. Si veda, per un 

approfondimento, I FLOP nella trattazione relativistica del tempo, in F. Selleri (ed.), La natura del 

tempo, Bari 2002. 

73 Cit. in U. Bottazzini, Fondamenti dell'aritmetica e della geometria, in Paolo Rossi (ed.), op. cit., p. 

257. 

74 Cit. in U. Bartocci, Riflessioni sui fondamenti della matematica ed oltre, «Synthesis», n. 3, anno III, 

1994, p. 26. 

75 Inevitabile la ricaduta di tale mentalità sulla fisica contemporanea. Scrive Weizsäcker, ad esempio, 

che gli elettroni rimangono stabili sulle loro orbite perché le «leggi della meccanica quantistica… 

glielo impongono» (Cit. in P. Plichta, La formula segreta dell'universo, Casale Monferrato 1998, p. 

177). 

76 B. Hoffmann - H. Dukas, Albert Einstein, creatore e ribelle, op. cit., p. 144. Einstein sigillerà 

irreversibilmente, in seguito, tale visione gaussiana. Con le parole di Max Jammer: «Fu Einstein che 

chiarì come la geometria, allorché viene applicata in questo modo all'indagine dello spazio fisico, 

cessa di essere una scienza assiomatico-deduttiva e diviene una fra le scienze naturali» (M. Jammer, 

Storia del concetto di spazio, Milano 1981, p. 148). 


78 W.K. Clifford, Philosophy of the Pure Sciences, in Lectures and Essays, London 1879, vol. I, p. 

300, cit. in D. Overbye, op. cit., p. 131. 

79 B. Russell, La mia filosofia, op. cit., p. 39. 

80 Ibidem, p. 41. 

81 L. Brunschvicg, L'expérience humaine et la causalité physique, Paris 1949, p. 410. 

82 G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 197. 

83 R.P. Feynman, QED. La strana teoria della materia e della luce, Milano 1996, p. 25. 

84 Scrive Heisenberg in Fisica e filosofia: «È vero che ci apparirà anche subito chiaro che questi 

concetti non sono ben definiti nel senso scientifico e che la loro applicazione può condurre a varie 

contraddizioni; ma noi sappiamo tuttavia che essi toccano la realtà. Può essere utile a questo proposito 

ricordare che perfino nella parte più precisa della scienza, nella matematica, noi non possiamo fare a 

meno di servirci di concetti che implicano delle contraddizioni. È ben noto, ad esempio, che il 

concetto d'infinito conduce a contraddizioni che sono state analizzate; eppure sarebbe praticamente 

impossibile costruire senza questo concetto le più importanti parti della matematica» (op. cit., p. 233). 

85 «L'abbandono dell'antica ipotesi di Euclide ebbe un parallelo nella elaborazione di nuove algebre 

che rinunciavano a un altro assunto profondamente radicato, secondo il quale, quando l'operazione A 

era seguita dall'operazione B, il risultato doveva essere identico a quello prodotto compiendo prima B 

e poi A. […] La costruzione di Hamilton segnò l'inizio di un periodo in cui i matematici presero a 

creare liberamente sistemi di simboli servendosi di regole prestabilite e compatibili che ne 

governassero le combinazioni reciproche senza curarsi che tali sistemi descrivessero alcunché nel 

mondo reale» (J.D. Barrow, op. cit., pp. 38-9).

86 Così come «la teoria della relatività - scrive Heisenberg - sembra da principio una cosa astratta ed 

estranea», bisogna abituarsi («il nostro pensiero si può adattare solo lentamente all'ampliato dominio 

sperimentale e al nuovo mondo concettuale») con la teoria dei quanti «a una rinuncia ancor più 

profonda ai concetti finora abituali» (W. Heisenberg, I princìpi fisici della teoria dei quanti, Torino 

1987, p. 74). Bisogna solo aspettare, cioè, pazientemente che i nuovi concetti rivoluzionari e astrusi 

sedimentino sufficientemente nella nostra mente, come il «Maestro della Scuola Copenhagen» 

suggerisce ad Alice, sconcertata dal mondo dei quanti: «Ci farai l'abitudine presto, non temere» (R. 

Gilmore, Alice nel paese dei quanti, Milano 1996, p. 78). Rileva a questo riguardo Jenner Barretto 

Bastos Filho: «Il paradigma di Copenhagen-Göttingen ha dominato lo scenario della fisica […] Il 

positivismo, la sopravvalutazione della misura, la fuga verso il formalismo matematico, e addirittura le 

"onde di coscienza", hanno abitato stabilmente nei corsi di meccanica quantistica, operando un vero 

lavaggio del cervello» (J.B. Bastos Filho, La dissoluzione della realtà: irrealismo e indeterminismo 

nella fisica del microcosmo, in M. Mamone Capria (ed.), op. cit., pp. 448-9). 

87 W. Heisenberg, Fisica e filosofia, op. cit., p. 107. 

88 Hermann von Helmholtz, Sull'origine e il significato degli assiomi geometrici, in A. Einstein, 

Relatività: esposizione divulgativa, Torino 1967, p. 249. 


90 R. Nobili, op. cit., p. 3. «Il programma di Hilbert era più innovativo di quanto a prima vista potesse 

apparire. Fino ad allora, per accertare la coerenza di una struttura matematica era stato necessario 

fornire un'interpretazione particolare (ossia un "modello", come veniva chiamato) degli assiomi in 

questione. Se questo modello nel mondo reale esisteva, il sistema matematico veniva considerato 

coerente, nella convinzione che la realtà fisica fosse esente da contraddizioni. […] Hilbert abbandonò 

questo infruttuoso procedimento per cercare prove di coerenza che non facessero uso di modelli (né 

fisici né matematici) del significato degli assiomi» (J.D. Barrow, op. cit., p. 198). 

91 J.D. Barrow, op. cit., pp. 194-5. Scrive Bertrand Russell: «La matematica pura è interamente 

costituita da asserzioni per effetto delle quali, se un tale enunciato è vero per qualcosa, allora il tale 

altro enunciato è vero per quella cosa. È essenziale non discutere se il primo enunciato è realmente 

vero, e non indicare quale sia la cosa per la quale si suppone che sia vero. […] Così la matematica può 

essere definita come la materia nella quale non sappiamo mai di che cosa stiamo parlando, né se ciò 

che stiamo dicendo è vero» (B. Russell, Misticismo e logica, op. cit., pp. 71-2). 

92 La differenza sta nell'autoevidenza: i primi sono di per sé «chiari e distinti» direbbe Cartesio, mentre 

i secondi dovranno sottostare alla "spada di Damocle" di una possibile ventura contraddizione, 

cantorianamente potenziale. Mentre gli assiomi sono, nelle parole di Benjamin Fedorovich Kagan 

(1869-1953), «verità ammesse da ogni uomo, alle quali l'uomo inevitabilmente ricorre tanto in 

ciascuna scienza, quanto in qualsiasi ragionamento quotidiano», i postulati costituiscono precise 

richieste che «il lettore deve accettare accingendosi allo studio di una disciplina, affinché i 

ragionamenti successivi non suscitino obiezioni da parte sua» (Cit. in R. Tazzioli, op. cit., p. 66). 

93 H. Meschkowski, Mutamenti nel pensiero matematico, Torino 1973, p. 87. Come rileva giustamente 

Umberto Bartocci: «Logicismo, formalismo, crisi dei fondamenti, etc., sono tutti riconducibili 

nell'illustrato contesto ad esiti naturali del tentativo di espungere la geometria euclidea dai fondamenti 

della matematica» (U. Bartocci, op. cit., p. 24). 

94 È paradigmatico «il detto di Einstein che "la base assiomatica della fisica teorica… deve essere 

liberamente inventata"» (F.S.C. Northrop, La concezione della scienza di Einstein, in P.A. Schilpp 

(ed.), op. cit., p. 341). 

95 J.P. Changeux - A. Connes, op. cit., p. 16. 

96 Scrive, ad esempio, Roger Penrose: «La teoria ha due argomenti molto efficaci a suo favore e solo 

uno, di scarso rilievo, a sfavore. Innanzitutto, la teoria è sorprendentemente esatta rispetto a tutti i 

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152 

risultati sperimentali fino ad oggi ottenuti. In secondo luogo [...] si tratta di una teoria di straordinaria e 

profonda bellezza dal punto di vista matematico. L'unica cosa, che può essere detta contro di essa, è 

che, presa in assoluto, non ha alcun senso!» (Cit. in A. Zeilinger, Problemi di interpretazione e 

ricerca di paradigmi in meccanica quantistica, in F. Selleri (ed.), Che cos'è la realtà. Dibattito nella 

fisica contemporanea, Milano 1990, p. 123). 


98 S.W. Hawking - R. Penrose, The Nature of Space and Time, Princeton 1996, p. 116. 

99 E. Schrödinger, L'immagine del mondo, Torino 2001, p. 115. 

100 G. Bachelard, La dialettica filosofica dei concetti della relatività, in P.A. Schilpp (ed.), op. cit., p. 

511. 

101 H. Reichenbach, Relatività e conoscenza a priori, Bari 1984, p. 59. 

102 Cit. in F. Selleri, La fisica del novecento. Per un bilancio critico, Bari 1999, p. 94. 

103 W. Heisenberg, La tradizione nella scienza, op. cit., p. 127. 

104 G. Gamow, Trent'anni che sconvolsero la fisica, Bologna 1966, p. 107. 

105 Scrive il logico americano Alonzo Church: «Noi non attribuiamo alcun carattere di unicità o di 

verità assoluta ad alcun sistema logico particolare… possiamo considerare l'analogia di una geometria 

tridimensionale utilizzata nella descrizione dello spazio fisico… può esservi, e in realtà vi è, più di una 

geometria il cui uso è lecito nella descrizione dello spazio fisico. Analogamente, esiste senza dubbio 

più di un sistema formale che può essere utilizzato come logica, e di questi sistemi uno può essere più 

proficuo o più comodo di un altro; non si può, però, dire che uno sia giusto e l'altro sbagliato» (Cit. in 

J.D. Barrow, op. cit., p. 43). 

106 G. Bachelard, La valeur inductive de la Relativité, op. cit., p. 99. 

107 G. Bachelard, Il nuovo spirito scientifico, op. cit., p. 39. 

108 Ibidem, p. 50. 

109 Ibidem. 

110 H. Bouasse, La question préalable contre la théorie d'Einstein, Paris 1923, p. 18. 

111 Ibidem, pp. 18-20. La trad. it. è a cura di M.R. Abramo in Gaston Bachelard e le fisiche del 

novecento, Napoli 2002, pp. 21-2. 

112 G. Bachelard, L'expérience de l'espace dans la physique contemporaine, Paris 1937, p. 42. 

113 E. Cassirer, Determinismo e indeterminismo nella fisica moderna, Firenze 1970, p. 243. 

114 H. Bouasse, op. cit., p. 17. 

115 W. Heisenberg, La tradizione nella scienza, op. cit., p. 137. 

116 F. Selleri, Introduzione, in F. Selleri (ed.), La natura del tempo, op. cit., p. 22. Dinanzi al 

voltafaccia dell'Einstein maturo che cambia rotta e fa una "inversione a U" sul tracciato 

epistemologico intrapreso negli anni memorabili, Max Born - sbigottito e dispiaciuto per la «tragedia» 

di aver perso «il nostro capo e portabandiera» - ammette: «Dobbiamo accettare il fatto che anche nella

fisica, come in tutte le altre attività umane, le convinzioni fondamentali vengono prima del 

ragionamento» (M. Born, Le teorie statistiche di Einstein, in P.A. Schilpp (ed.), op. cit., p. 68). 

117 P.W. Bridgman, La logica della fisica moderna, Torino 1965, pp. 83-84. 

118 M. Mamone Capria, La crisi delle concezioni ordinarie di spazio e di tempo, in M. Mamone Capria 

(ed.), op. cit., p. 347. 

119 R. Descartes, Regulae ad directionem ingenii, in Opere filosofiche, vol. I, a cura di E. Garin, Roma- 

Bari 1991, p. 64. 

120 H. Dingle, Science at the Crossroads, London 1972, p. 13. 

121 U. Bartocci - R.V. Macrì, Il linguaggio della matematica, op. cit.. 

122 H. Dingle, op. cit., p. 130. 

123 P.J. Nahin, op. cit., p. XV. 

124 F. Selleri, La causalità impossibile. L'interpretazione realistica della fisica dei quanti, Milano 

1988, p. 45. 

125 P.W. Bridgman, op. cit., p. 52. Ciò viene tradotto all'interno dell'immagine scientifica del mondo 

come un continuo susseguirsi di teorie rivoluzionarie senza arrivare mai alla verità: una «corsa che 

non avrà mai fine» (F.A. Levi, Esplorazione del tempo e dello spazio, Milano 1981, p. 126), quando 

invece lo stesso artefice della nuova visione del mondo si affannava per trovare la chiave "definitiva". 

Ciò fu osservato distintamente da Wolfgang Pauli, il quale a proposito della tenacia e dell'inventiva di 

Einstein a garantire ogni anno una nuova teoria unitaria scrisse: «È interessante dal punto di vista 

psicologico che per qualche tempo la teoria corrente sia ritenuta dal suo autore "la soluzione 

definitiva"» (Cit. in R. Highfield - P. Carter, Le vite segrete di Albert Einstein, Padova 1994, p. 190). 

126 Un approfondimento si ha in R.V. Macrì, Relativismo e pensiero debole: la perdita del fondamento, 

«Episteme», n.1, 2000. 

127 L'esasperato formalismo matematico che accompagna l'immagine scientifica del mondo nella nostra 

epoca sembra voler spezzare il nesso storico ed epistemologico tra scienza e filosofia, dimenticando 

che la prima è figlia della seconda: «La filosofia e la scienza sono assai più intimamente legate che 

non credano gli scienziati che disprezzano la prima e i filosofi che ignorano la seconda» (A. Garbasso, 

"Scienza realistica", in Scienza e poesia a cura di J. de Blasi, Firenze 1934, p. 220). Bisogna dunque 

domandarsi perché per una parte considerevole della comunità scientifica l'opera di divulgazione è 

temeraria e temuta: per la paura legittima di inquinare ciò che è puro (matematico) o non piuttosto per 

la paura di scoprire in uno stato chimerico quello che si credeva matematicamente compreso? Può la 

(falsa) matematica ostruire il cammino ad una "umana" (o fisica, o filosofica) comprensione? A sentire 

lo stesso Einstein il pericolo non è illusorio: «Da quando i matematici hanno invaso la teoria della 

relatività, io stesso non la capisco più» (A. Sommerfeld, Per il compleanno di Albert Einstein, in P.A. 

Schilpp (ed.), op. cit., p. 54). 

128 Cfr. A. Pais, "Sottile è il Signore…", op. cit., cap.7 (7a.3), pp.158-159. 

129 Scrive Lewis Pyenson nel suo meritevole The young Einstein: the advent of relativity (Bristol - 

Boston 1985, p. 80): «Minkowski thought that by mathematising special relativity he clarified the 

essential physical features of Einstein's theory. Although Einstein accepted Minkowski's 

mathematisation as only a technical improvement on his own work, many other physicists and 

mathematicians attempted to extend Minkowski's formulation of matter and electromagnetism. Few 

realised that there were major differences between Minkowski's and Einstein's approaches to the 

principle of relativity». Per quanto riguarda l'influenza dei matematici su Einstein, in particolare della 

Scuola di Göttingen, oltre al suddetto testo di Pyenson si cfr. anche S. Walter, Minkowski, 

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154 

Mathematicians and the Mathematical Theory of Relativity, in H. Goenner et al. (edd.), The 

Expanding Worlds of General Relativity, Birkhäuser 1999. 

130 Cit. in L. Pyenson, op. cit., p. 28. 

131 I. Newton, Arithmetica universalis, 2ª ed., 1728, p. 193. 

- - - - - 

[Una presentazione dell'autore si trova nel numero 1 di Episteme] 

"RVM" 

* * * * *

Did Einstein Claim That Nature Has Mathematical Structure? 

(Jarosław Mrozek) 

Abstract 

This paper is an attempt to analyse some of Einstein's utterances concerning the relationship 

between mathematics and the world and its ontological structure. The author tries to interpret, 

in a non-standard way, Einstein's standpoint expressed in the words: as far as the proposition 

of mathematics refer to reality, they are not certain; and as far as they are certain, they do not 

refer to reality. Einstein's words prove that he rejected a possibility of direct correspondence 

of mathematics and the world. Therefore the author of the paper questions the view according 

to which Einstein claimed that nature is mathematical. It seems that Einstein's words can be 

interpreted as claiming the possibility of applying mathematics to the study of nature, about 

which we don't need to assume that it is mathematical. Such an approach better explains the 

successes as well as failures of applications of mathematics. Mathematically 'indifferent' 

nature can be examined to some degree using mathematical methods and it can also resist 

these methods. Thus the hypothesis of amathematicality of nature is closer to the 'scientific 

practice' of naturalists. 

* * * * * 

Albert Einstein was probably the most outstanding physicist of the XXth century. His 

scientific authority is so great that - although he wasn't a professional philosopher, his 

philosophical views deserve full attention. It is known that Einstein was an advocate of a 

realistic standpoint in ontology - he maintained that the world exists and that in its essence it 

is deterministic. As regards his epistemological views, I would like to expose his conviction 

that it is possible to get to know the world and that it can be understood thanks to the harmony 

present in the world. Einstein expressed his conviction in an aphorism: Raffiniert ist der 

Herrgott, aber boshaft ist er nicht (God is sophisticated, but he is not malicious). It is just this 

possibility of getting to know the world which, despite its complexity, seems to Einstein to be 

the greatest mystery of epistemology - bordering on a 'miracle'. 

The reported Einstein's utterance sometimes has a 'stronger' interpretation. This aphorism is 

treated as Einstein's expression of mathematical structure of the world. Physics - as a science 

examining nature - uses mathematics as its tool. For this to be possible - in accordance with 

this interpretation - nature must be mathematical, that is, it must possess the structure 

corresponding to the structure of mathematics. God, while 'creating' the world, was 

sophisticated, creating it as a highly complicated and complex system, but he wasn't 

'malicious' because the structure of the world can be deciphered using theoretical 

(mathematical) means available to man. 

Indeed, in the philosophical works of Einstein we find fragments and phrases, which can be 

considered as utterances about the mathematical character of nature, for instance: 'nature is 

the realisation of what is the simplest to think of as regards mathematics' 1 . However other 

utterances of Einstein show that he didn't find mathematicality to be an immanent 

characteristic of nature. Einstein - in my opinion - treated the issue of the ontological structure 

of the world rather in the categories of intelligibility or rationality of the world. Nevertheless, 

we cannot exclude other interpretations of Einstein's ideas. Besides, he encourages 

philosophers to treat distrustfully the declarations found in the works of scientists, claiming 

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(in a slightly different context): if you want to learn from physicists theoreticians something 

about the methods they use, I propose to stick to this rule: Don't listen to their words, but 

watch their deeds 2 . I think that by tracing Einstein's practice of applying mathematics to 

physics, an attentive researcher can feel encouraged to adopt a slightly different approach to 

mathematics. The argument supporting such a possibility is that, when confronted with the 

question "[h]ow can it be that mathematics, being after all a product of human thought which 

is independent of experience, is so admirably appropriate to the objects of reality?" 3 , Einstein 

answers it without referring to the mathematical structure of the world. 

Einstein characterizes mathematics as a science whose theses are absolutely certain and 

unquestionable, favouring here a widespread conviction that the status of mathematics differs 

from the status of natural sciences. According to him mathematics is a formal-logical science, 

not empirical. In this context, for Einstein as a physicist and a philosopher, the usefulness of 

mathematics in the examination of the world is just amazing. If Einstein shared the view 

about mathematicality of nature, there wouldn't be anything surprising there. Everything 

would be clear. Why can we refer mathematics to reality? - because nature has mathematical 

structure; why do we apply mathematics in natural sciences? - because it is mathematics that 

is the 'key' to the knowledge of the world of nature. Einstein, however, gives a different 

answer: "[i]n my opinion the answer to this question is, briefly, this: as far as the propositions 

of mathematics refer to reality, they are not certain; and as far as they are certain, they do not 

refer to reality" 4 . 

It seems that Einstein's words can be interpreted as a viewpoint claiming that it is possible 

to apply mathematics to examine nature, about which we need not assume that it is 

mathematical. It follows from the suggestion that if mathematical propositions refer to reality, 

they are not certain. If nature were mathematical, then - as I understand Einstein - referring 

mathematical propositions to it wouldn't lead to the loss of their certainty because then the 

whole operation would occur between isomorphic domains - nature having mathematical 

structure and mathematical theories. With such an approach, the only problem could be to 

discover, identify or construct a suitable - for a given area of reality - mathematical theory 

which would provide notions for the adequate modelling of physical processes. 

Let's consider this issue 'from the point of view' of mathematics - as long as propositions are 

certain, they don't refer to the world. Mathematical propositions refer to the possible formal 

relations between mathematical entities, which we approach mentally and then they are 

apodictic. The certainty of its theses is a result of the previously accepted premises and the 

agreement as to the acceptable methods of reasoning. It is, thus, aprioric in the 

methodological sense - it can develop autonomously and it is most often created 

independently of external or extramathematical influences. Mathematics as such cannot say 

anything about objects imagined or real. However let's notice that such an approach to this 

issue excludes only the possibility of direct reference of mathematics to the world. It doesn't 

follow from it that mathematical propositions should not be referred to reality. It is possible 

and - as mathematical natural science shows - very fruitful. 

However the application of mathematical propositions leads to the loss of certainty (if we 

refer mathematical propositions to reality, they cease to be certain). But it is not the reason 

that would make it impossible to refer mathematical propositions to the world. Einstein in 

'practice' shows that although mathematical propositions in themselves don't refer to reality, 

with the help of suitable physical procedures they can be applied in order to grasp the 

characteristics of natural reality, gaining real meaning. However it should be remembered that 

in such a case mathematical propositions lose their absolute certainty. Mathematics applied to 

physical phenomena cannot guarantee by itself the truthfulness of conclusions to which it

leads by making use of a deductive method appropriate to it. It operates, after all, on 

unfamiliar ground. In the 'kingdom' of physics there applies methodology which is suitable 

for an empirical science - that means standards and rigours of justification and acceptance of 

propositions, different than in formal sciences. Therefore mathematical propositions, showing 

some possibilities of such and not a different behaviour of a physical system, on the ground of 

physics are not able to predict the real course of a phenomenon as this course can be 

ascertained by means of methodological criteria, appropriate to the domain of natural 

sciences. 

Summing up, Einstein's standpoint concerning the relation between mathematics and the 

external world can be formulated like this. What gives some content to mathematical notions 

does not belong to mathematics but is a physical interpretation. Therefore Einstein in his work 

of applying mathematical methods introduces some 'medium' between mathematics and the 

world. This intermediary field, in which mathematical structures and really existing nature's 

structures meet, is obviously physics. Reconstructing Einstein's standpoint expressed by the 

words: as far as the proposition of mathematics refer to reality, they are not certain; and as far 

as they are certain, they do not refer to reality, we can state that instead of abstract 

considerations of the relation between mathematics and the world, in his scientific work 

Einstein in fact considers the triple connection: nature - physical theories - mathematics, 

because mathematics itself does not refer to reality. 

In this light, if the issue of the structure of reality itself is concerned, it shouldn't be 

approached dogmatically. In particular, with reference to Einstein's standpoint, we could 

hypothetically assume that natural reality is neither mathematical nor non-mathematical, it is 

simply amathematical (similarly as it is not moral or immoral, but simply amoral). Such a 

neutral approach to the problem of nature's structure has its advantages. Thanks to this it is 

possible, in my opinion, to avoid the difficulties of realistic standpoint, as well as overcome 

the hurdles of instrumental interpretation of mathematics' applications. Mathematically 

'neutral' nature can - to some extent - be 'approached' with mathematical methods, as well as - 

to some extent - resist these methods. 

In this context, successes and failures of applications of mathematics become well 

understood. Naturalists know that to apply mathematics effectively, a lot of effort is needed to 

'tailor' mathematical methods so that they 'work' in accordance with the accepted premises. 

Let's mention here at least the problem of infinite remains, appearing in the quantum theories 

of the field, which are removed by ad hoc 5 mathematical means, or Hawking's attempts to 

eliminate, on the ground of the quantum theory of gravitation, the boundary conditions for the 

Universe 6 , described by Robert Mathew as 'mathematical hocus pocus' 7 . Obviously such 

'inconvenient' facts are not exposed by the enthusiasts of effectiveness of mathematics in 

natural sciences, but they can be traced in the whole history of mathematics' applications in 

physics. 

Suspending the judgement as to the issue of mathematical structure of nature, we don't 

exclude at the same time that some of its aspects can be subjected to mathematical 

description, are 'approachable' or 'interpretable' mathematically. Amathematicality of nature 

does not exclude a priori the elimination of mathematical methods from natural sciences. 

Mathematical methods, as outstanding physicists have shown in their scientific activity, 

supported by physical principles, can become a highly effective tool for expressing at least 

some aspects of the surrounding nature. 

It seems that Einstein's standpoint as to the issue of the relation between mathematics and 

the world contains a significant novum compared to classical approaches (Platonic, 

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158 

Aristotelian, Cartesian and Kantian). It is the treatment of the correspondence between 

mathematics and the world as the relationship which is generated in the course of the 

development of natural scientific theories applying mathematics. Such an approach does not 

require the acceptance of strong metaphysical assumptions about the nature and structure of 

the world and mathematics as it does not assume that correspondence of mathematics and the 

world is a guaranteed state, something existing in advance, a priori - but it treats this 

correspondence as something worked out in the process of knowledge development. 

In my opinion Einstein showed in his works that the epistemological role of mathematics is 

not just restricted to grasping - or not - the structure of the world in itself (as realists 

understand it) or only the external and intermediary participation in the articulation of the 

contents of natural scientific theories (in accordance with instrumentalist convictions). It 

seems that the process of examining the external world has a more basic and essentially 

creative character. It doesn't consist only in fitting mathematical categories to the examined 

object but rather in co-creating or constituting this object - that is reality. (The 'range' of this 

process is the simultaneous generation of mathematical categories). In this way the relation 

between mathematics and the world ceases to be only the juxtaposition of these two different 

domains and becomes a process, the effect of which is the epistemological grasping of reality 

by means of mathematical categories. Mathematicized physical theory makes use of the 

categorial apparatus worked out in formal sciences, in particular of mathematical notions and 

methods, however at the same time it still remains a physical theory, having 'contact' with 

physical reality. This contact ensures mathematical notions an operational scope by 

entangling them in physical meanings ( in the course of applying them) and in this way by 

assigning them real contents on the ground of natural sciences. 

The mechanism of effectiveness of mathematics is, as I think, conventional - adaptive and 

generally speaking it consists in, on the one hand, forcing physical aspects of reality to fit 

mathematical formulas and, on the other hand, creating mathematical theories that correspond 

to physical data or modifying these theories in order to get adapted to this data. There is 

nothing like prefect congruence between mathematics and the world - this congruence has a 

rather pragmatic character and is conditioned by these physical theories in a more basic way 

than it seems to us. 

Notes 

1 See, A. Einstein, On the Method of Theoretical Physics, Clarendon Press, Oxford 1933 

2 Ibidem 

3 A. Einstein, Geometry and Experience, in: A. Einstein, Ideas and Opinions, Crown Publishers, Inc. 

New York 1954, p. 233 

4 Ibidem, p. 233 

5 See. S. W. Hawking, A Brief History of Time: From the Big Bang to Black Holes, A Bantam Books, 

New York 1988 

6 Ibidem 

7 See, R. Matthews, Unravelling the Mind of God. Mysteries at the Frontier of Science, Virgin 

Publishing Ltd, 1992 

- - - - -

University of Gdańsk 

Institute of Philosophy and Sociology 

ul. Bielańska 5, 80-851 Gdańsk, Poland 

Jarosław Mrozek, (born 1955), assistant professor in Department of Logic, 

Methodology and Philosophy of Science, University of Gdańsk, Discipline: 

Philosophy of Mathematics, Philosophy of Science. M.A. - University of Gdańsk 

(1977), PhD - University of Gdańsk (1985); dissertation: Epistemological 

Aspect of Relation Between Mathematics and Outer World. Head of 

Department of Logic, Methodology and Philosophy of Science (1997 - 1999); Vdirector 

of Institute of Philosophy and Sociology, University of Gdańsk (1999 - 

2002), Member of Polish Society of Philosophy. Among others academical 

publications: Einstein's Conception of the Relation Between Mathematics and 

the World, The General Function of Mathematics in Physical Sciences, 

Cosmology and Anthropic Principle, The Problem of Understanding 

Mathematics. 

filjam@univ.gda.pl 

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160 

The Problem of Reciprocity and Non-Reciprocity 

in Special Relativity Theory 

(Francisco J. Müller) 

Abstract: The implications of the two relativistic postulates are analyzed in terms of their reciprocity 

and symmetry aspects. Whereas the first postulate entails a perfect equivalence of all frames, the 

second postulate, as reflected by the Einstein-Lorentz equations, implies an asymmetry of values (not 

of forms) that clashes not only with the first postulate equivalence but with the possibility of 

experimental verifications, all of which are "asymmetric" in each concrete case. A double index 

notation is proposed at the end, in order to show more clearly these asymmetries, and to interpret in a 

realistic way, the referential (physical) meanings of the four space/time variables. Lorentzian versus 

Einsteinian relativities are contrasted. The former seems to cope better with the asymmetric 

experimental realities. The latter only does so by subreptitiously changing the meaning of the physical 

variables. 

In the introduction of his 1905 relativity paper (1) Einstein gives a hint that the 2 nd 

relativistic postulate about the universal constancy of the speed of light might be "apparently 

irreconcilable with the former" postulate, that is, with the first Postulate about the formal 

validity of physical laws for all frames of reference. Few physicists have pondered why 

Einstein posited this dialectical contradiction at the very beginning of his paper. It is the 

purpose of this article to dig into this question. A superficial interpretation of the possible 

contradiction views it as the clash between the classical, or Galilean composition of 

velocities, and the counter-intuitive "scandal" that light seems to travel at the same speed for 

all relatively moving observers. But there are more hidden aspects to this problem. The 

prototype of this light "scandal" was provided by the null Michelson-Morley experiment. This 

experiment, however, have always been performed in a "proper frame", without even the 

possibility of observing it from the viewpoint point of a moving frame (for example, from the 

Sun)(2). Yet, the theory elaborated by Einstein, introduces a perfectly "reciprocal" treatment 

of the experiment, (in its equivalent gedanken version) both in a proper and in a non-proper 

frame. 

After all the theoretical work was done by Einstein, arriving at the Lorentz equations, 

the reciprocity and symmetry of such equations have been greatly studied and formalized. 

Group theory assimilated the equations as part of its program. This theory is perhaps the best 

mathematical tool to investigate such symmetry properties of physical phenomena as 

rotations, nuclear particles, relativity, Quantum symmetries, hypersymmetries, antisymmetries, 

etc. etc. 

Relativistic formalization versus physical realities 

An essential aspect of these formalizations is to consider variables like x,y,z,t with 

primed and unprimed characters. The operators, matrices, generators, etc. are said to 

"transform" one set of un-primed variables into the primed ones, and viceversa. Reciprocity 

and symmetry are, here, practically synonyms. Reciprocity, however, usually refers only to 

the relationship (also termed "inverse") between one set of variables and another 

"corresponding" set. In contrast, symmetry can be discovered within one such single set. For 

example the elements Aij and Aji are equal in a "symmetric" matrix or tensor. In 

contrast the word "anti-symmetric" has been used to described the case when Aij = 

-Aji . When the reciprocity simply consists in changing (+) and (-) signs some authors 

still consider it "symmetric", others "anti-symmetric" and some even "asymmetric".

Leaving the heavens of pure mathematics, the physical use of such primed and 

unprimed quantities have been mostly to denote variables pertaining to a "moving" 

versus a "non-moving"(resting) frame of reference. Yet, on account of the relativity 

principle and the equivalence of all frames (First Postulate), nobody takes seriously the 

labels "moving" versus "non-moving" any more. Being perfectly "interchangeable" or 

"reciprocal", the primes and unprimes become, again, a mere mathematical formality. 

This leads to the familiar interpretation of the Lorentz equations, for example, as a 

"rotation" in 4-dimensional space. To the performance of succesive Lorentz steps as 

mere multiplications in group theory. And to the "raising" of the time variable to an 

"equivalent" status as the space variables through the artifact of an X4 = ict terminology. 

This enables to write the "fundamental relativistic interval dS" in a very beautiful way. 

But the danger of all these mathematical myths is that, by taking them too 

seriously, (and isolating them from their referential meanings) the physical reality that 

they "signify" becomes more and more obscured , ignored and even confusing. This 

confusion applies especially to the concept of "event". 

The elusive "event" (physical versus mathematical) 

A first problem that arises in this respect is the nature, the uniqueness, or even 

the existence, of the "event" (the space/time point) that is being "observed", "seen", 

"transformed", by a certain number of observers, (minimally by two) in relative 

"motion". Mathematically speaking this event can be common to any set of reference 

frames, regardless of their "motions", because the world of Mathematics is intrinsically 

static and motionless. If we mark a point XY in the plane of a Cartesian system K and 

then refer that "same point" to another frame K' that has been "rotated" respect the 

first, there is absolutely no difficulty in expressing X' = RX and Y' = RY where R is the 

"rotation matrix". The original point does not "belong" any more to the K system as to 

the K' one. In fact, nothing has to move and, indeed, nothing has moved. 

But when we return to physical reality a given "event" is not only a set of 

coordinates, but a physical entity, a "happening", a phenomenon. This could be a 

Coulomb force between two (real) charges; or a photon being emitted or received, or a 

ticking clock, etc. Then it is dramatically important to distinguish in which frame the 

said entity or event is AT REST and in which it is seen as a "moving" reality. This 

physical event is certainly not interchangeable and non-reciprocal. In theory yes, we 

could set the physical entities in ANY of the two frames, but in each concrete experiment 

one and only one of the frames is the proper one. 

It is in this sense that the Lorentz equations yield "asymmetric values", although 

being formally symmetric (or anti-symmetric). Panofsky and Phillips, very well 

established authors of the 1960's, explicitly recognized this when they described the 

Lorentz contraction, X

162 

"moving" and "resting" are absolutely interchangeable and in that sense they are 

"trivialized" Yet, the primed and unprimed notation of formalized group and 

transformation theory only pays attention to such irrelevant tags, and is oblivious of the 

most important point: the residence of the unique physical reality that confers one 

frame the character of being "proper" and the other "non-proper". Even worse, by 

ignoring the residence of that unique physical event the primed/unprimed notation 

opens the way to the removal, altogether of the unique physical event. Then the scenario 

of the twin paradox is wide opened and all its concomitants debates start to proliferate. 

Let me expand on this. 

Methodological origin of the clock or twin paradox 

In the twin paradox the time of each twin plays the role of a proper time. Each 

twin's clock is resting in each twin's frame. Why should the "moving" twin return 

younger, when in its own proper clock nothing has absolutely happened according to the 

first relativity Postulate? From where comes the "asymmetry" of their times or "ages"? 

We know the standard relativistic answer: "from the fact that only the 'traveling' 

twin accelerated". And we know also the standard non-relativistic objection: 

"accelerations are as relative and as interchangeable as the velocities. If distances are 

relative and their first derivatives are so, why not their second derivatives?" "Because a 

force, indeed" answer the relativists, "must have been used by the 'moving' twin to 

produce the acceleration". But again the non-relativists accuse the relativists of 

introducing a "non-inertial" element in their theory (a force!), thus violating the logical 

presuppositions under which the whole Lorentzian deduction was made. This debate can 

keep going on and on. I do not pretend to end it here. But what I want to point out here 

is the origin of the debate, which is this: a mis-application of the Lorentz 

transformation. 

The Lorentz equations, at least as conceived by its original author in 1904 (5), 

were only geared to study how that unique physical reality of which I have spoken 

before, (an electron, a ray of light, etc), is "seen", or "measured" by TWO observers in 

relative motion. We can call this a ternary structure: two observers and ONE physical 

event. (2O1E for short). In contrast, the twin paradox scenario uses a binary structure: 

two clocks or "twins" in relative motion and no common event independent of their own 

clocks or "ages" to be studied or observed. Such a binary scenario leaves the theory 

totally empty and devoid of objective purpose. It is futile, in search of some objectivity, 

to speak of the twins as "observers" and the clocks as "events". That language is but a 

picturesque antropomorphism that has creeped only too much into relativistic 

textbooks. (Einstein himself is partially guilty of this antropomorphism when using 

expressions like: the observers "judge", or "ascertain", or "declare", etc, etc). 

Critical comment 

What, then, should we conclude here about the debates on the clock paradox? 

That they have been a waste of time. Relativists will keep insisting in their 

"asymmetrizing" acceleration factor, while non-relativists will insist in the intrinsic 

equivalence of all truly inertial frames. In reality, the struggle here is between the 

equivalence, reciprocity and formal symmetry that springs from the First Postulate on 

the one hand, and on the other, the (numerical) asymmetry that results from the Lorentz 

equations (2 nd Postulate) when applied to a concrete situation. Indeed, we have returned 

here to that "apparent contradiction" between the two Postulates that Einstein envisaged 

at the beginning of his paper. The fact that the Lorentz equations are in harmony with c 

= c for both (or all) frames does not remove the clash between the asymmetry of the

numerical values it predicts for the rest of the physical realities, in comparison with the 

perfect equality and equivalence predicted for those same realities by the First 

Postulate. 

In reality the reason why physicists do not perceive this methodological (even 

logical) "mis-match" between the two relativistic postulates is that they have gone too 

far into mathematics and have abandoned too much the real physical qualities. They 

imply, following Minkowski, that those qualities are mere "shadows", and only their 

mathematical connections in a four-dimensional (mythical) language remain formally 

invariant. 

In this respect it is frequently said that relativity theory ended the "mechanistic" 

philosophy of the etherists. But in reality relativity has "ended" all physical qualities, 

(electromagnetism included), in the name of pure games of kinematically related frames. 

This is not only mechanistic, but "geometristic". The world of relativity is, thus, a timeless, 

motionless world. And if we still remember Aristotle we will agree with him when 

he said that "if we do not understand motion we cannot understand Nature". So 

relativity does not "understand" Nature at all, since "nothing moves" in the relativistic 

eternal and timeless heavens. 

This critical comment, however, does not entail, in the least, that the effects 

experimentally tested like time dilation, mass increase, etc, are not real. But only that 

they cannot be predicted from a symmetristic, equivalential, reciprocating, version of 

relativity theory as Einstein's version. It seems that only the Lorentzian (nonsymmetristic) 

version of relativity makes sense. To consider this I will summarize the 

previous verbal analysis in a more concise and symbolic way, using a "double index" 

notation, a notation that I think has been long time overdue in relativistic textbooks. 

Analysis using a "double index" notation 

Let A and B be two frames of reference in relative motion. We shall not stipulate 

which is moving and which is not. Let any property T (like time) be labelled with two 

subindexes: the first indicating: where the event or object is; and the second by whom or 

in which frame the observation is made. Thus: 

1- T AA means: the "time" of an event in A as measured by A (a proper value) 

2- T AB means: the "time" of an event in A as measured by B (a non-proper 

value ) 

3- T BB means: the time of an event in B as measured by B (a proper value) 

4- T BA means: the time of an event in B as measured by A (a non-proper or a 

"coordinate" value) 

Whenever the two subindexes coincide, we have a proper value. Whenever they are 

mixed, we have a non-proper value (or "coordinate" value) The previous T variables 

should be understood as dT's in the case of time intervals. For simplicity I will use the 

single letter T . With this notation, and the additional symbol L(±v) for a Lorentz 

transformation we can express the First Postulate writing that: 

(I) TAA = T BB (valid also for all TCC , T DD , T EE , etc) 

And the 2 nd Postulate by means of the reciprocal Lorentz equations: 

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164 

(IIa) TAA =L(v)T AB 

(IIb) TBB =L(-v)TBA 

Notice that in the Lorentz equations the first subindexes have to be equal, 

because both frames, A and B are refering to a unique common object either in A, 

(Eq.IIa), or in B (Eq.IIb). Thus, an equation like T AA = L(v)T BA would be totally 

meaningless. 

Are all equations I and II applicable simultaneously in each concrete situation? 

Are all four "referential" parameters defined above simultaneously meaningful? Let us 

see the possible answers both in an Einsteinian (reciprocal) relativity and in Lorentz's 

(non-reciprocal) kind. 

For both versions of relativity, the First Postulate should be always applicable. 

Unfortunately, due to the limitations of the primed/unprimed notation, there is not even 

a way to express Eq-I as done above. To write T = T' with this purpose would be to 

invite total confusion when the Lorentz equations later yield T ≠ T' . Especially in this 

aspect we see the greater advantage of the double index notation. 

Now in the Lorentzian context equations II can only be applied one at a time in 

each case. Suppose we are dealing with (IIa), so that the event is proper in A and not 

proper in B, (regardless of which "moves" or not). Then TBB and TBA are "empty". No 

part of this experiment refers to them and, hence, no paradox arises. We could later 

repeat an "identical" experiment in B and apply (IIb), in which case TAA and TAB will 

represent nothing of "that" experiment. The conclusion of the experiment is simply, in 

the first case, that A has a proper time or "age" T AA and B sees it non-properly as TAB 

and in the second, reciprocal case, that B has a proper time or "age" TBB and A sees it 

non-properly as TBA . The two reciprocal cases do not "mix" or "apply" together in one 

single experiment. 

In Einsteinian relativity, however, both equations II are taken as perfectly 

reciprocal (which they are) and as applicable simultaneously but in a "mixed" way. 

(Typically this is the clock paradox bynary scenario) What happens here is that 

relativists speak of the "age" of each twin or clock, in their own proper frames. These 

"ages" should be denoted by TAA and TBB in the double index notation. That being the 

case, the only conclusion should be what the First Postulate establishes, namely that T AA 

= TBB . No possible asymmetric aging can arise. But relativists insist that one frame, for 

example A, is "really moving" and asymmetrically accelerating. Then they apply (IIa) to 

conclude that TAA = L(v)TAB , a result which they express verbally by saying that the 

"age" of twin A is smaller (younger) than the "age" of twin B. But the problem here is 

that TAB is not the proper "age" of twin B, but only the non-proper "view" or 

measurement that B has of A's age. The proper age of B is still TBB, a fact that relativists 

overlook simply because they lack the adequate double index notation that I am 

proposing here. 

Relativists "transform" conceptually the non-proper measurement TAB made by 

B, into the proper age TBB of B. This happens, as explained above, because in the bynary 

scenario there is no fixed, unique, common object to be observed. Then the subjectivity 

of each observer takes the place of the object to be measured. This is what produces the 

"mixing-up" of equations in Einstein's "symmetristic" relativity which I mentioned 

above. 

This unwarranted "transformation" of the physical meaning of the mathematical 

variables is, perhaps, the most persistent and irritating error both in Einstein's original 

paper and its descendants. Parameters like x,y,z, and ct that were used to describe the 

motion of a "light ray", are suddenly, without justification, used for representing the

"positions and times" of a moving clock or rod. Again this all can happen because the 

primed/unprimed notation used exclusively by relativists is totally "blind" to the 

referential physical meaning of the variables. The prime/unprime notation simply 

indicates "moving" vs "non-moving" systems, a tag that is perfectly equivalent, 

reciprocal and interchangeable. But the proper vs non-proper elements of the 

experiments are, in contrast, non-reciprocal and physically asymmetric. This physical 

asymmetry is the only thing that experiments can show and verify, a fact that means 

that in practice, only Lorentzian relativity, with its preferred ether frame, is the one in 

harmony with experiments. The only way that Einsteinian symmetristic relativity can 

cope with experimental facts is by converting itself to the Lorentzian scenario as each 

situation demands. A few examples of this suffices. 

The experimental asymmetries oppose Einstein's symmetristic relativity 

1 - The GPS community, for example, must use a reference frame fixed to the earth and 

not rotating with it, in order to account for the Sagnac effect that takes place between 

the GPS satellites and the terrestrial stations. This is an example of a preferred frame of 

reference, breaking all reciprocities and symmetries. Likewise, the gyrolasers, nowadays 

used in commercial aircraft, are based on the "asymmetric" times of flight of two 

opposing beams of light, S/(c+v) and S/(c-v), observed by proper observers corotating 

with the gyrolaser. Hence they can deduce the speed v from their observations. Again, 

Lorentz "wins" and Einstein "looses". 

2 - In the Hafele-Keating experiment the results did not show the symmetry they were 

supposed to show. Any school boy knows that the term v 2 /c 2 has even parity (+v and –v 

yield the same result). So clocks flying to the East must have behaved exactly like those 

flying to the West. But they did not. The clocks that flew westward were accelerated (!) 

respect the resting Washington clocks, while the eastbound clocks did show the expected 

time dilation. To explain these asymmetric results the authors had to adopt the 

"viewpoint" of observers fixed to the North pole, (ie, not rotating with the Earth, just as 

the GPS community does). Another triumph for non-reciprocal relativity. In adopting 

this "polar viewpoint" Hafele-Keating were implying that the observers at rest in 

Washington (themselves) could see what the North pole observer "should" have seen. If 

that is the case, then why use any relativistic transformation at all? Regardless of the 

sloppiness of Hafele-Keating's experiment it showed a remarkably "neat" violation of 

the symmetristic and transformational relativistic scenario. 

Final conclusion 

In reality what happens in all this is that when we have two really inertial, (noncommunicable) 

frames of reference, only one side of the story can be verified 

experimentally in each case. As mentioned above, we cannot perform the MM 

experiment from a non-proper frame, neither can we observe fast mesons, or for that 

matter relativistic electrons, simultaneously in the non-proper and proper frame. So 

physical reality, by selecting in each case a proper frame and not another, breaks the 

theoretical symmetry of Einstein's relativity. From all this two major conclusions can be 

derived: 

1 - Einstein's symmetristic theory can never be proven right because of methodological 

impossibilities. But then it cannot be disproved either, for the same reason. Relativists 

will always supply, in their favor, what the "imaginary" observer "must" have seen. 

Hence, strictly speaking, applying Popper's falsification methodology, relativity theory is 

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166 

not a scientific theory at all. It springs from ideal, impossibly symmetristic, thought 

experiments. 

2 - When only primed and unprimed variables are used everything works perfectly in 

the mathematical heavens of group theory. But when the more "messy" but physically 

more revealing double index notation is used we see how symmetristic relativity becomes 

asymmetric by subreptitiously changing the physical meaning of the variables.

References 

1) Einstein, A, "The Electrodynamics of Moving Bodies", (1905) Annalen der Physik, vol.17, 891. 

2) Attempts at performing MM's experiment with a star light as source are vitiated by the fact that 

once the light enters the lens of the apparatus it is re-radiated internally, hence, becoming again an 

inmediate "proper" source, just like a terrestrial one. 

3) Panofsky, W and Phillips, M "Classical Electricity and Magnetism", Addison-Wesley, Reading, 

Mass., 1962, pg. 291. 

4) Panofsky and Phillips, Ibid. pg. 292. 

5) Lorentz, H A, "Electromagnetic Phenomena in a System Moving with any velocity less than that of 

Light," Proc. Acad. Sc. Amsterdam, vol. 6, 809 (1904). 

- - - - - 

Francisco J. Müller is the actual President of the Natural Philosophy Alliance 

(see the section "Alternative Physics On Line" in this same volume of Episteme), 

and is known for a criticism of relativity grounded even on original 

experimental results (see point 16 in the second list of the quoted section). 

Varela Academy of Science and Philosophy 

8025 SW 15 St. 

Miami, Florida 33144 

U.S.A. 

fjmuller@bellsouth.net 

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168 

On the Impossibility to Describe the Fields of the System of 

Uniformly Moving Charges in the Frame of Special Relativity 

(Vladimir Onoochin) 

1. Introduction. 

In this article, we intend to discuss one point of foundation of the relativistic theory, 

i.e. the transformational properties of the scalar potential of the uniformly moving charges. 

The relativistic theory has the pretension to play a role of an absolutely true theory and this 

fact seems to be undisputable to such extent that some questions laying in the basis of this 

theory are treated as postulates or as direct consequences of the postulates. However, the 

special relativity is based on some experimental facts which cannot be derived from the 

postulates of the theory. The subject of this article is the analysis of the consistency of the 

relativistic transformations of the potentials with the experimental facts. 

Development of the classical electrodynamics at the end of XIX and beginning of XX 

century went in a way when the main attention was focused on seeking the transformations 

for the EM field while going from a frame at a rest to the moving frame. However, the 

expressions for transformed EM fields have not been studied with necessary thoroughness, 

namely, only the expressions for the fields created by single point charge were analyzed. But 

even while analysing these simple expressions some points are overlooked; by the way, these 

points form the basis of the special relativity. We will show that these 'holes' in basement of 

the special relativity make the latter to be incorrect. We start from well known Lorentz 

transformations. 

It is known from the special relativity that the coordinates in the laboratory frame and 

uniformly moving frame are connected by the Lorentz transformations: 

x − vt 

x′ 

= 

y ′ = y z = z 

2 2 

1 − v c 

2 

t − vx / c 

t′ 

= 

; (1) 

1 − v c 

′ 2 2 

and, correspondingly, the charge density and the scalar potential must transform as: 

ρ ′ 

ρ = 

; (2a) 

2 2 

1 − v c 

ϕ ′ 

ϕ = 

. (2b) 

2 2 

1 − v c 

In Eqs. (2), the quantities ρ ' and ϕ ' are defined in co-moving frame where the charge 

is at rest so the quantities j′ x and x A′ are equal to zero. 

If the above equations are fulfilled, then the electrodynamical quantities provide 

invariance of the physical laws in both frames. We emphasize that, despite of widespread 

belief, these equations are not postulates 1 , but they either must be proven or derived from the 

experimental data.

The first of equations (2) can be easily proven. Since the charge density of the 

elementary charge is described by the Dirac delta function, for uniformly moving charge the 

proof goes as follows: 

2 2 

( , t ) = δ ( x − vt ) δ ( y ) δ ( z ) = δ ( 1 − v c ⋅ x′ 

) δ ( y′ 

) ( ′ ) = 

ρ ( x, y, 

z, 

t) 

= δ r 

δ z 

= 

δ 

( x′ 

) δ ( y′ 

) δ ( z′ 

) ρ ( r′ 

) 

= 

2 2 

2 2 

1 − v c 1 − v c 

which agrees with the law of conservation of the total charge: 

∫ 

( x′ 

, y′ 

, z′ 

) 

; (3) 

ρ 

2 2 

ρ ( x , y, 

z ) dxdydz = ∫ 

1 − v c dx′ 

dy′ 

dz′ 

= q 

2 2 

. (4) 

1 − v c 

Validity of Eq. (2b) has been proven by Lorentz who solved the wave equation for the 

ϕ potential with its rhs describing uniformly moving elementary charge: 

⎛ 1 

2 

∂ 

⎜ 

⎝ 

2 

c 

2 

∂ t 

2 2 2 

∂ ∂ ∂ ⎞ 

− − − ⎟ ϕ ( x, 

y, 

z, 

t) 

= 4π 

ρ ( x − vt) 

2 2 2 

(5) 

∂ x ∂ y ∂ z ⎠ 

in relativistic approach (here, ρ(x – vt) is the density of the uniformly moving charge). 

Finally, we must show that solution of Eq. (5) has the following properties: 

- It transforms according to Eq. (2b); 

- It describes the Liénard-Wiechert and Coulomb potentials of the uniformly moving 

charge in co-moving frame and the laboratory frame respectively. 

2. Relativistic solution of the wave equation. 

Before starting the procedure of resolution, it must be noted that the wave equation 

with the extended source in its rhs cannot be treated as a well defined partial differential 

equation, because some physics is hidden there. This physics is that one cannot calculate the 

total potential created by the source as the integral of the potentials created by every moving 

infinitesimal element of the source. The reason of such a limitation in calculating the sum is 

that calculating the sum means collecting some information at the only point. But the speed of 

propagation of information is limited by the speed of light c. So during the process of 

collection of the whole information about the source, this source displaces itself and actually 

we cannot determine from what element of the source information comes at a given instant of 

time. 

This problem does not exist in pre-relativistic theories because according to them, the 

characteristics of the source do not change while going to another frame. But in special 

relativity all characteristics of the source, except for the value of the charge, do change. 

Formally we could make some suggestions regarding the changes of the parameters, however, 

when verifying the foundation of the special relativity, we have to use only quantities which 

can be measured directly. Taking into account the problem caused by the finiteness of the 

speed of propagation of information, we conclude that we must use the only way to find the 

solution in relativistic approach, i.e. we must go to co-moving frame where the source is at 

rest. In this frame, collecting information from all elements of the source becomes 

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170 

independent on the speed of propagation of information, because the problem reduces to the 

electrostatic task of finding the ϕ potential created by some extended charge. Then one returns 

to the original frame so expression for the ϕ potential is transformed too. This expression 

must describe the ϕ potential in the original frame. We should expect that all transformations 

during this procedure must satisfy to the requirements of relativistic invariance (covariance). 

Below we realize this procedure. 

According to the arguments given above, we go from the laboratory frame to the comoving 

frame for the charge where the charge is at rest, so: 

1 − 

1 

⎛ 1 

2 

∂ 

⎜ 

⎝ c ∂ t′ 

2 

∂ 

− 

∂ x′ 

2 

∂ 

− 

∂ y′ 

2 

∂ ⎞ 

4π 

ρ ′ ( x′ 

, y′ 

, z′ 

) 

− ⎟ ϕ ′ ( x′ 

, y′ 

, z′ 

, t′ 

) = 

∂ z′ 

2 2 

⎠ 

v c 

2 2 2 2 2 2 2 

v c 

1 − 

. (6) 

In opposition to most papers on transformation properties of the electrodynamical 

quantities, we keep the factor ( ) 1 − 

2 2 

1 − v c in both sides of Eq. (6), in order to show that the 

wave equations in two inertial frames differ one from another only by the constant factor. So 

the "principle of invariance" is fulfilled for Eqs. (5) and (6). 

Because the rhs of Eq. (6) does not depend on the time variable, the lhs should not 

depend on t' variable too so this equation reduces to Poisson-like equation (we now omit the 

factor ( ) 1 − 

2 2 

rest: 

1 − v c 

⎛ 

⎜ 

⎝ 

): 

2 

∂ 

∂ x′ 

2 

2 

∂ 

+ 

∂ y′ 

2 

2 

∂ ⎞ 

+ ⎟ ϕ ′ 2 

∂ z′ 

⎠ 

( x′ 

, y′ 

, z′ 

) = − 4π 

ρ ( x′ 

, y′ 

, z′ 

) 

. (7) 

Solution of Eq. (7) is known. It is the Coulomb potential created by the charge being at 

ρ ′ ( x′ 

, y′ 

, z′ 

) 

ϕ ′ ∫ r' − r' 

1 1 1 

( x ′ , y′ 

, z′ 

) = 

dx′ 

1dy′ 

1dz′ 

1 

1 

. (8) 

The final step is to return to the laboratory frame. By means of Eq. (2b), the scalar 

potential takes the form: 

ϕ ' 

ρ ′ ( x′ 

, y′ 

, z′ 

) 

1 1 1 

( x , y, 

z, 

t ) = 

= 

dx′ 

1dy′ 

1dz′ 

1 

ϕ 

2 2 

2 2 ∫ 1 − v c 1 − v c r' − r'1 

where the rhs of Eq. (9) should be expressed via the original variables 

calculating the integral. 

1 

; (9) 

x , y, 

z, 

t after 

But if we analyze the above procedure for the resolution of the wave equation, we find 

one strange point. For better understanding, we write step by step the above procedure in 

symbolic form. So these steps from Eq. (5) to Eq. (7) can be written as (we re-write Eqs. (2a) 

and (2b) as ρ = γ ρ ′ and ϕ = γ ϕ ′ ): 

Wϕ = ρ W γ′ ϕ ′ = γ ρ ′ Wϕ 

′ = ρ ′ 

; (10)

where W is the operator of the wave equation, sign means "the Lorentz transformations of 

the variables (and functions of these variables)" and sign ⇔ means "which is equivalent to". 

The second equation in this chain is equivalent to the third equation, since the "wave 

1 

operator" 2 

c 

2 

∂ 

2 

∂ t 

− 

2 

∇ is invariant under the Lorentz transformations, i.e. W' = W . 

The inverse procedure, i.e. transformation of the solution, to the original frame, should 

be written in symbolic form as: 

− 1 − 1 

− 1 − 1 

− 1 

( ) ' ρ ′ γ ϕ = ( W ) γ ρ ⇔ ϕ = ( ) ρ 

ϕ ′ = W W ' ; (11) 

where W -1 is the inverse wave operator. The chain (11) is correct if the "inverse wave 

operator" is transformed, under the inverse Lorentz transformations of the coordinates, as: 

− 1 − 1 

( ) ' = W 

W . (12) 

But Eq. (12) is incorrect because the integral operator: 

− 1 1 

W = ∫ dxdydz 

R − r 

; (13) 

is not Lorentz-invariant. So we obtain a strange result, i.e. if one makes inverse Lorentz 

transformations of Eq. (8), in analogy with the transformations of Eq. (5), one finds that the 

solution for the ϕ potential via the charge density ρ does not maintain its original form when 

transforming from one frame to the other. In different words, despite the form of the wave 

equation, which is covariant, the solution of this wave equation is not covariant. 

The problem can be stated in another way. One is able to calculate the value of the 

scalar potential in the laboratory frame by two methods. First, by treating the rhs of Eq. (8) as 

some mathematical expression, one can make the inverse Lorentz transformations of both 

integrand, taking into account transformation (2) , and the element of volume dV' , and then 

calculate the integral. The second way is to calculate the integral in the rhs of Eq. (8), i.e. to 

calculate ϕ as a function of x ′ , y′ 

, z′ 

, and then to make inverse Lorentz transformation to the 

variables x , y, 

z , taking into account that the quantity ϕ transforms according to Eq. (2b) too. 

The final results obtained by these two methods are different and this difference is 

caused by difference in sequence of mathematical operations used while calculating the 

potential. But because the final result cannot depend on the sequence of mathematical 

operations (namely, transformation of variables and calculation of the integral), some error 

must be hidden in the proof of the covariance of the scalar potential. 

ϕ ′ = q ′ 

This difference actually exists. For example, it is known that the Coulomb potential 

R′ 

cannot be transformed into the Liénard-Wiechert potential by using the first 

method, because, when transforming the charge q', which is invariant (q' = q), and 

denominator, one obtains: 

q′ 

ϕ ′ = 

ϕ = 

2 2 2 

x′ 

+ y′ 

+ z′ 

2 

( x − vt ) 2 2 

1 − v 

2 

c 

q 

2 

+ 

y 

+ 

z 

; (14) 

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172 

and the potential given by Eq. (14) is no the Liénard-Wiechert potential of the uniformly 

moving charge 2 . 

So, as we have seen above, there is some problem when trying to prove the covariance 

of the scalar potential of the single uniformly moving charge. But Lorentz used another 

method in proving the covariance of the ϕ potential 3 . He compared the relativistic solution 

(Eq. (9)) with the solution of the wave equation (5) obtained by the method of directly solving 

the wave equation [3] (Ch. 18.3), and he showed identity of both expressions. Below we 

analyze the method of Lorentz, and prove why these expressions are not identical. 

3. Direct solution of the wave equation. 

In this Chapter, we consider why Lorentz obtained the relativistic properties for the 

Liénard-Wiechert and Coulomb potentials. The solution of Eq. (9), for a charge with spherical 

shape in a frame where the charge is at rest, is given by the formula: 

q 

ϕ ' ( x ', 

y' 

z') 

= 

. (15) 

r' 

This solution is derived by expansion of the denominator in a series of spherical 

harmonic functions (Eq. (3.70) of [1]) in a region r > r0 , where r0 is effective radius of the 

charge. Since the charge has spherical shape, then all terms of the expansion, except the zero 

term, are equal to zero, and so we obtain (15). Inverse transformation of the potential (Eq. (2)) 

gives: 

' ( x′ 

, y′ 

, z′ 

) 1 

q 

( x, 

y, 

z, 

t) 

= = 

2 2 

2 2 

1 − v c 1 − v c 

ϕ 

ϕ ; (16) 

[ ] 2 / 1 

2 2 2 

x′ 

+ y′ 

+ z′ 

and after the Lorentz transformation of the coordinates we have: 

or 

ϕ ( x, 

y, 

z, 

t) 

= 

q 

4π 

ε 

0 

1 

1 − v 

2 

c 

2 

( x − vt ) 

⎡ 

⎢ 

⎣ 1 − v 

2 

2 2 2 2 

( x − vt ) + ( − v c )( y + z ) 

0 1 

2 

c 

2 

2 

1 

+ 

y 

2 

+ 

z 

2 

⎤ 

⎥ 

⎦ 

1/ 

2 

; (17) 

q 

1 

ϕ ( x, 

y, 

z, 

t) 

= 

4π 

ε 

. (18) 

The above expression is the well known expression for the LW potential of the 

uniformly moving charge. Thus, at least in one case, the relativistic approach gives the correct 

result, despite of the breakdown of the Lorentz invariance of the operator (13). Below we 

analyze why this is possible. In order to do it, we consider derivation of Eq. (5) by a method 

of "direct solution of the wave equations" ([3], Ch. 18.3). In this method, one does not use 

Lorentz transformation of the coordinates, but one introduces some physically reasonable 

assumptions while solving the wave equation with the source corresponding to uniformly 

moving charge. Obviously, the field created by such a source must follow this charge.

Therefore, the partial spatial and time derivative are not independent one of another, but they 

are linked by the relation: 

∂ 

= − v ⋅ ∇ 

∂ t 

. (19) 

This relation means that any parameter of the field changes, during the time interval 

dt, at the same value as while displacing to the distance –vdt along the direction of motion of 

the charge. Taking into account Eq. (19), we are able to transform the wave equation (5) to: 

⎛ ⎛ 

⎜ 

⎜ 

⎝ ⎝ 

2 2 2 2 

v ⎞ ∂ ∂ ∂ ⎞ 

− ⎟ + + ⎟ ϕ ( x, 

y, 

z, 

t) 

= − ρ ( x, 

y, 

z) 

2 2 2 

c ∂ x ∂ y ∂ z ⎟ 

. (20) 

⎠ 

⎠ 

1 2 

One can see that dependence of the potential on the time disappears in the rhs of Eq. 

(20) so actually Eq. (19) corresponds to the Galilean transformation of the coordinates: 

x → x − vt ; y → y ; z → z ; t → 

By change of variables: 

x′ 

= 

x 

1 − v 

y′ 

= y 

z′ 

= z 

2 

c 

2 

⎫ 

⎪ 

⎪ 

⎬ 

⎪ 

⎪ 

⎭ 

Eq. (20) can be reduced to the ordinary electrostatic Poisson equation: 

whose solution is: 

2 2 

( 1 − v c x′ 

, y′ 

z′ 

) 

2 

∇ ′ ϕ = − ρ 

, 

2 2 

1 ρ ( 1 − v c x′ 

, y′ 

, z′ 

) 

ϕ 

4π 

∫ r' − r' 

1 1 1 

( x ′ , y′ 

, z′ 

) = 

dx′ 

1dy′ 

1dz′ 

1 

1 

t 

. (21) 

; (22) 

; (23) 

. (24) 

We have in the lhs of Eq. (24) the scalar potential in the laboratory frame which, 

however, is still expressed via quantities defined in the co-moving frame. Inverse transition is 

made by changing the variables: 

1 − v 

2 

c 

2 

y = 

( x − vt ) 

y′ 

z = z′ 

= 

x′ 

⎫ 

⎪ 

⎬ 

⎪ 

⎭ 

. (25) 

So finally, we have for the scalar potential in the laboratory frame two solutions 

obtained in relativistic approach and by direct solving the wave equation. For better 

understanding, we re-write Eqs. (9) and (24): 

173

174 

1 

1 1 

ϕ = 

2 2 ∫ 4π 

1 − v c r' − r'1 

ρ ′ ( x′ 

, y′ 

, z′ 

1) 

dx′ 

dy′ 

dz′ 

2 2 

1 ρ ( 1 − v c x′ 

1, 

y′ 

1, 

z′ 

1) 

ϕ = 

dx′ 

1dy′ 

1dz′ 

1 

4π 

∫ r' − r' 

1 

1 

1 

1 

; (26a) 

. (26b) 

Because both the above equations are written for the same potential, we must have: 

1 

1 − v 

2 

c 

′ 

′ 

′ 

ρ ( 1 − v 

2 2 

( x1, 

y1, 

z1) 

1 

2 ∫ dx′ 

1dy′ 

1dz′ 

1 = 

r' − r' 

∫ 

1 

r' − r'1 

ρ ′ 

This will be the basic equation of our further analysis. 

c 

x′ 

, y′ 

1, 

z′ 

1) 

dx′ 

dy′ 

dz′ 

4. Analysis of the function describing the charge density. 

1 

1 

1 

. (27) 

This equation can be treated as some integral equation for the functions ρ and ρ ′ . 

Unfortunately, because these functions belong to different frames we are not able to compare 

them4 . However, we can get some information about these functions. Since ρ ′ describes a 

single charge being at rest, it must be represented by some function with spherical symmetry. 

By the way, the function ρ has not such a symmetry5 . But in order to satisfy Eq. (27) for any 

r′ , i.e. in such a way that the method of direct solution gives the same results as the 

relativistic approach, then it is necessary that the function ρ can be transformed to the form 

which has spherical symmetry. This can be easily proven by simple consideration. Actually, 

in order to satisfy Eq. (27), one can evaluate only the values of the function ρ defined in a 

limited region of the space, i.e. where the charge is located. Formally, the function ρ is 

defined in the whole space, however, for calculation of the integrals, only values of this 

function defined in limited region are essential. In opposition to this region of internal 

variables, the region where r′ is defined, and it is essential for the calculation of the integral, 

is much greater, since it must be the whole space. So the only possibility to choose the true 

form of the function ρ is to assume that this function can be transformed (in the integrand of 

Eq. (27)) into a symmetric one on the variables x ′ , y′ 

, z′ 

. Since when v = 0 the function ρ 

must degenerate into the function having spherical symmetry for the variables x , y, 

z , finally 

we have the functional equation for this function (we omit the signs "prime"): 

2 2 2 

2 2 2 2 2 Cρ 

[ ( ) 

] [ x + y + z ] 

1 − v c x + y + z = 

ρ 

2 2 

. (28) 

1 − v c 

It can be shown that this functional equation has two only solutions, i.e.: 

⎧ ρ = C 

⎨ 

⎩ ρ = C 

2 

2 2 2 2 

[ − ( x + y + z ) σ ] 

2 2 2 2 

( V ) θ [ ( x + y + z ) − r ] 

1 exp 

0 

. (29) 

In the previous formulae C and C1 are some constants, the constant C2(V) does depend 

on the volume V of the charge, r0 is the radius of the charge, and θ is the Heaviside step 

function. A parameter σ in the first solution of (29) corresponds to some "effective radius" of 

the charge. The second solution in Eq. (29) does describe the model of the electron used by 

Lorentz, where the charge is represented as a particle with the radius r0 and a uniform charge

distribution inside. When this charge moves, its size does contract in the direction of the 

motion, and, since the volume of the charge contracts too, the value of the charge density 

arises proportionally. After integration over internal variables, this solution yields Eq. (15). 

But it is a well established point in classical electrodynamics [3] (Ch. 18.1) that the 

only known parameter of the electron is its total charge equal to e, and any calculation of the 

EM fields and potentials based on some specific charge distribution inside the electron cannot 

be physically meaningful. So one of the fundamental points of the special relativity, i.e. the 

proof of the covariance of the scalar potential, is derived by using questionable assumptions. 

Actually, both charge distributions (29), necessary for the covariance of the scalar potential, 

are forbidden by quantum mechanics. As a matter of fact, quantum mechanics does not allow 

the existence of singular distributions (second distribution in Eq. (29) is singular on the 

boundary of the electron). But the first distribution in Eq. (29) must be caused by some 

potential of oscillatory type. However, it is not physically sound to suggest that the internal 

force (Poincaré tension) arises proportionally with the distance (in this case, the internal force 

would yield the potential of oscillatory type). 

We should remark at last that in classical electrodynamics, the elementary charge is 

described by some singular distribution, i.e. by the Dirac δ-function. It is known that this 

distribution has some representation, and despite the multitude of these representations, the 

final result cannot depend on the specific representation chosen to describe the elementary 

charge. However, we have that only the two specific representations (29) do satisfy the 

condition which is required on the shape of the charge in order that the scalar potential created 

by the charge of a given shape is relativistically covariant. So the existence of only two 

specific representations for the δ-function, instead of the existence of the whole multiplicity 

of them, in order to provide for the covariance of the expression for the scalar potential, must 

be mathematically incorrect. 

In conclusion, we obtain that the only relativistically correct method of establishing 

the connection between the LW and Coulomb potentials is relativistically non-invariant itself. 

Therefore, the relativistic connection (2b) between these potentials derived by Lorentz looks 

like an artefact, which is conditioned by applying the point like approximation (29b) of the 

elementary charge. But if we consider the connection between the LW and Coulomb 

potentials in a strictly mathematical way, and at very small distance, we obtain that Eq. (2b) is 

wrong. Therefore, the scalar potential cannot be treated as the zero-component of a relativistic 

four-vector. 

Notes 

1 Despite of this, in most textbooks on classical electrodynamics, relativistic covariance of the scalar 

potential is treated as a fact which does not need any proof. For example, in [1] (Ch. 11.9) it is noted 

that covariance of the vector and scalar potential follows from the covariance (invariance) 

requirements to all electrodynamical quantities. In [2] (Sec. 16), it is written without any explanations 

that the vector and scalar potentials form relativistic four-vector. 

2 The derivation of the LW potential from the Coulomb potential given in [2] (Sec. 63) is incorrect. 

Actually, while applying the Lorentz transformation to the lhs of chain (14), it is illegal to change the 

spatial quantity R' by c(t' - t1'). As a matter of fact, R' = c(t' - t1') is some equation, but not an identity. 

3 Actually, Lorentz operated with the fields but not with the potentials, however, the method is the 

same. 

175

176 

4 It is the main trouble of the special relativity that it is impossible to compare quantities which belong 

to different frames. 

5 This function must describe the charge contracted in the direction of the motion. 

References 

[1] - J. D. Jackson, Classical Electrodynamics, 2 nd edn (New York: Wiley, 1975). 

[2] - L.D. Landau and E.M. Lifshitz, The Classical Theory of Field, (Pergamon, Oxford, 

1975). 

[3] - W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, (NY, 1955). 

- - - - - 

Vladimir Onoochin was born in Gorgii region, Russia, in 1953. In 1990 he 

took a PhD degree in Physics at Ioffe insititue, St. Petersburg. He is actually the 

manager of radiophysics (spectrometers) project at Sirius Ltd, Moscow. His 

main areas of interest are: Electrodynamics of short ultrawideband (UWB) 

current and EM pulses; Development of the measurement equipment and 

measurement of the powerful EM pulses in 1 to 150 GHz frequency range; 

Pulsed power devices. Special points of interest are even some problems in 

classical electrodynamics usually omitted by mainstream physics, such as 

penetration of the EM fields through metallic shields, longitudinal EM waves 

and properties of the EM potentials in different gauges, etc.. To these topics the 

author has dedicated many research papers. 

"Vladimir Onoochin"

Introduzione 

Simmetrizzazione delle equazioni di Maxwell 

con l'introduzione del campo gravitazionale, 

un'idea bizzarra? 

(Sabato Scala) 

Sono passati circa 15 anni da quando, con un carissimo amico oltre che compagno di studi, 

affrontammo la preparazione dell'esame di Campi Elettromagnetici con il simpaticissimo oltre 

che preparatissimo prof. Giorgio Franceschetti. 

Fu proprio da una accattivante introduzione al suo libro dedicato a questa affascinante e 

complessa materia, che, un po' per gioco, nacque l'idea bizzarra che voglio proporre al 

paziente lettore. 

Il tempo passato e la ruggine accumulatasi per effetto della mia attuale professione 

interamente centrata sullo sviluppo software ben distante dai miei passati interessi, potrà farmi 

compiere più di un errore per i quali chiedo venia tenendo soprattutto conto che quanto 

propongo vuole essere semplicemente ciò che fu allora: un complesso gioco di fantasia. 

Onestà vuole, anche per inquadrare nella corretta luce il presente articolo, che narri anche del 

piccolo retroscena che ispirò l'idea di fondo del nostro "gioco" fisico-matematico. 

Era appena uscito un volumetto di fanta-storia estremamente affascinante dedicato al famoso 

"Esperimento Philadelphia". La storia mai confermata dai vertici militari americani, narra di 

un esperimento svoltosi alla fine del 1945 che, nelle intenzioni degli studiosi che vi presero 

parte, avrebbe dovuto consentire la "deviazione" della luce con la conseguente 

mimetizzazione di un qualsiasi oggetto consentendo, in pratica, di vedere ciò che si trovava 

dietro di esso e quindi rendendo invisibile l'oggetto frapposto. 

Il libretto, estremamente ben congegnato con tanto di "soffiate", di "scienziati dissociati", 

interviste, esperimenti preparatori, ecc., non sembrava affatto scritto da un semplice 

giornalista ma da qualcuno che aveva una conoscenza notevole di fenomeni elettromagnetici. 

Eppure qualcosa non quadrava: nel libro c'era praticamente tutto ciò che serviva per una 

succosa ricetta di fanta-fisica, ma senza la necessaria conclusione. 

L'idea di fondo, del testo, era basata sulla adozione di un campo elettromagnetico prodotto in 

una apparato contenuto in una misteriosa sfera, collegato ad un alternatore ed impiantato sulla 

nave che nel libro aveva il nome di Eldridge. 

Il nome, che nel libro si dice sia stato attribuito all'esperimento dagli allora vertici militari 

americani, è "Rainbow Experiment". 

La cosa che ci affascinò non fu tanto lo straordinario esito dell'esperimento - che provocò, a 

detta dell'autore, la reale sparizione della nave - ma i sub-effetti di quell'esperimento, narrati 

dall'autore con chiaro sensazionalismo e gusto dell'orrido. 

La nave sparisce, ma compare in un porto a vari chilometri di distanza e in pochi istanti, 

ritorna al suo posto. Alla sua riapparizione i marinai sono, in parte impazziti, in parte fusi con 

la materia del vascello, in parte scomparsi del tutto. 

Altra cosa interessante è la narrazione puntigliosa degli esperimenti che precedono quello 

definitivo, fatta utilizzando condensatori con dimensioni dell'ordine del metro, bobine giganti, 

e alternatori appositamente realizzati, il tutto condito con segnalazione delle frequenze di 

alimentazione, della capacità dei condensatori, della entità delle correnti impiegate, ecc. 

Tra gli effetti segnalati c'è il sollevamento degli apparati, la loro vibrazione e oscillazione con 

frequenza pari a quella dell'alternatore ecc. 

177

178 

Insomma il tutto, anche se mai in alcuna parte del testo viene riportato, sembra chiaramente 

dovuto alla generazione di un campo gravitazionale collegato ai campi elettrici e magnetici ad 

alta frequenza utilizzati per alimentare gli apparati. 

La variazioni nello spazio-tempo, anche se mai viene detto nel libro, sembrano dovute proprio 

agli effetti di un gigantesco campo gravitazionale tale da provocare la deviazione delle onde 

elettromagnetiche luminose intorno alla nave. 

Per dirla in sintesi, sebbene il testo non ne faccia mai riferimento, esso descrive gli effetti del 

sogno dei fisici di quegli anni (1945): l'unificazione dei campi. 

La simmetrizzazione 

Da qui veniamo a questa bislacca idea e alla ispirazione venutaci dal libro del prof. 

Franceschetti, che nulla mai seppe di questo nostro "gioco", visto il motivato timore di 

"saltare" la seduta d'esami per eccesso di "stupidità". 

Prima di tutto andiamo all'oggetto del contendere: le equazioni di Maxwell, vediamole nella 

forma differenziale: 

1) ∇ . D = ρ 

2) ∇ . B = 0 

3) ∇ × E = - ∂ B 

∂ t 

4) ∇ × H = J + ∂ D 

∂ t . 

Franceschetti faceva notare nel suo libro l'anomalia costituita dalla mancanza di simmetria del 

sistema di equazioni, evidente nell'assenza nella equazione 2) di un equivalente della densità 

di carica elettrica ρ che si trova nella equazione 1) , e nella equazione 3) di un equivalente 

della densità di corrente J che si trova nella 4) , per non dire dei segni con cui appaiono le 

due derivate temporali, una volta meno e una volta più. 

L'asimmetria ha un effetto fisico evidente che si rileva integrando la 1) e la 2): 

∫ ∫ ∫ (∇ . D)dV = Q 

∫ ∫ ∫ (∇ . B)dV = 0 . 

In pratica, mentre esiste in natura una entità chiamata "carica elettrica" (Q) , in grado di 

generare un campo le cui linee partono a raggiera da essa, lo stesso non si può dire per il 

campo magnetico, poiché non sembra esistere in natura la "carica magnetica". 

Nel libro si ipotizza esistente la carica magnetica ρm e si perviene alle seguenti equazioni: 

1') ∇ . D = ρ 

2') ∇ . B = ρm 

3') ∇ × E = Jm - ∂ 

B 

∂ t

4') ∇ × H = J + ∂ D 

∂ t . 

In esse è stata introdotta, come dicevamo, una ipotetica densità di carica magnetica ρm e la 

corrispondente densità di corrente magnetica Jm . Non esistendo il primo dei due termini (o 

quantomeno non essendo mai stata trovata la carica magnetica) risulta inesistente e quindi 

inessenziale anche il secondo. 

Unica anomalia nella simmetria, resta il segno meno nella derivata parziale rispetto al tempo 

per il vettore B. 

Da questa e da altre scarne osservazioni, tra cui l'einsteiniana "Dio non gioca a dadi!", ci 

ponemmo il problema di un possibile intervento di simmetrizzazione sulle equazioni che, 

però, includesse anche il campo gravitazionale. 

Cominciamo a far osservare le analogie tra il campo elettrico e gravitazionale partendo dalla 

legge di Coulomb che descrive l'intensità dell'interazione tra due cariche elettriche: 

Fq = 

1 

π ε 

4 0 

Q Q 

1 2 

2 

r 

ove ε0 = 8,854188 x 10 –12 Kg –1 m –3 s 2 C 2 . 

Questa espressione, formalmente, è simile all'intensità della forza di gravità che agisce tra due 

masse: 

Fg = G 

M M 

1 2 

. 2 

r 

Dalla equazione della forza di Coulomb si ricava quella del campo elettrico (scalare): 

Eq = 

1 

π ε 

4 0 

Q 

2 

r 

, 

mentre da quella della forza di gravità si ricava l'analoga espressione per il campo 

gravitazionale (scalare): 

M 

X = G 2 . 

r 

A questo punto, supponendo di voler creare un campo elettrico equivalente a quello 

gravitazionale, introducendo una carica "equivalente" alla massa, uguagliando le forze 

dovremmo far uso di un'equazione del tipo seguente: 

Qmequiv = κ0 M , 

ove κ0 sarà una costante tale che κ0 2 = 4πε0 G . 

Ricordando che G = 6,670 x 10 -11 Nm 2 Kg -2 , si ottiene: 

κ0 = 4,306 x 10 -10 CKg -1 . 

Introduciamo quindi una densità di carica equivalente ρmequiv definita come: 

179

180 

ρmequiv = κ0 ρk , 

ove ρk = densità di massa per unità di volume. 

Per esprimere un'equazione formalmente analoga a quella del campo prodotto da una carica 

elettrica anche per il campo gravitazionale è necessario introdurre anche un termine omologo 

all'ε0 , che chiameremo ζ0 , definito ovviamente dalla: 

ζ0 = κ0 / 4πG . 

La precedente equazione del campo gravitazionale (scalare) assume, quindi, la seguente forma 

(dove abbiamo abbreviato mequiv in meq): 

X = 

1 

π ζ 

4 0 

Q 

r 

meq 

2 

. 

Ricordando la relazione tra il vettore D e il vettore E , campo elettrico nel vuoto (all'interno 

di altri materiali è necessario moltiplicare per una costante ε tipica dello specifico materiale): 

D = ε0 E , 

per analogia definiamo un omologo vettore R associato al vettore X del campo 

gravitazionale: 

R = ζ0 X . 

A questo punto possiamo scrivere le equazioni del campo gravitazionale in forma 

differenziale, indicando, come detto dianzi, con ρk la densità di massa: 

5) ∇ . R = κ0 ρk = ρmeq 

6) ∇ × X = 0 . 

La seconda equazione si ricava ricordando che il campo gravitazionale è irrotazionale 

(conservativo), in pratica il lavoro che si compie muovendosi lungo un percorso chiuso è 

nullo (il lavoro lo si ottiene integrando la 6) ). 

Fin qui nulla di nuovo, salvo una forma diversa per le equazioni del campo gravitazionale. 

Ora supponiamo per un attimo che le equazioni di Maxwell possano essere messe insieme a 

queste aggiungendo qualche termine di collegamento. Supponiamo anche che la forma delle 

equazioni di Maxwell contenga già la "forma" in cui appariranno tutti i termini di 

collegamento. Intendiamo con ciò dire che ci dovranno essere dei termini omologhi dei 

termini J , ∂ D 

che appaiono nelle predette equazioni. Questo vuol dire che dovremo 

∂ t 

introdurre, ove manca, un termine Jk omologo della densità di corrente elettrica J , ed un 

altro termine gravitazionale omologo del termine (differenziale) corrispondente al contributo 

del vettore D . Il tutto andrà fatto supponendo che il termine differenziale per il vettore R 

dovrà comparire con segni alternati + e – , in modo che il complesso delle equazioni presenti 

una certa simmetria matematica. Fermi mantenendo i termini ρm e Jm già introdotti da 

Franceschetti e comunque inessenziali (a valore nullo), a causa della inesistenza della carica

magnetica, non resta che introdurre una densità di corrente di massa Jk che si affiancherà alle 

densità di corrente J e Jm . In buona sostanza i termini nuovi che affiancheremo a quelli già 

presenti a destra del segno di uguaglianza nelle equazioni di Maxwell - nella forma con gli 

apici - saranno Jk e una sorta di densità di corrente di massa di spostamento ∂ R 

. Bisogna 

anche tenere ovviamente conto della necessaria omogeneità dimensionale delle quantità 

fisiche che si sommeranno tra loro, per il che sarà necessario introdurre, oltre alla costante 

κ0 , anche un'altra costante λ0 , che ragioni di "simmetria fisica" fanno presumere di poter 

definire come: 

λ0 = 

ove c = 

1 

4π 

ε 

magnetica). 

ε 

0 

1 

0 

c 

μ 

0 

= 

μ 0 2 -2 -1 c ~ 30 Kg m C s , 

4π 

è la velocità della luce nel vuoto ( μ0 indica, come usuale, la permeabilità 

In definitiva, ecco come si presenterebbero le equazioni unificate ottenute per estensionesimmetrizzazione 

di quelle di Maxwell con l'introduzione del campo gravitazionale: 

7) ∇ . D = ρ 

8) ∇ . B = ρm 

9) ∇ . R = ρmeq 

10) ∇ × E = λ0(Jk + ∂ R 

∂ 

11) ∇ × H = J + ∂ D 

∂ 

t ) - Jm - ∂ 

t - Jk - ∂ 

R 

∂ t 

B 

∂ t 

12) ∇ × X = κ0(Jm + ∂ B 

∂ t ) - κ0λ0(J - ∂ D 

) . 

∂ t 

Dalle equazioni si vede come i tre termini di corrente, uno per ciascuno dei 3 campi, 

compaiono alternativamente nelle 10), 11) e 12) insieme ai termini differenziali dei tre campi 

R , D , B (che appaiono sotto forma di derivate parziali rispetto al tempo), con i segni più e 

meno in forma ciclica. Questa ipotesi di simmetrizzazione spiegherebbe anche l'anomala 

presenza del segno meno nelle equazioni già ampliate da Franceschetti con l'introduzione dei 

termini magnetici. 

Non resta che verificare se: 

a) le equazioni producono effetti che non hanno a quel che si sa un equivalente fisico, 

nel qual caso il nostro discorso cadrebbe senz'altro; 

b) le equazioni generano effetti che hanno qualche rispondenza in fenomeni noti ma 

non ancora spiegati, o ne prevedono di ancora non noti che potrebbero però essere reali. 

∂ t 

181

182 

In pratica non resta che verificare la "sostenibilità" del precedente sistema di equazioni nel 

mondo reale, dopo di che "divertirsi" a dedurne eventuali effetti pratici ancora sconosciuti. 

Coerenza delle equazioni con fenomeni fisici osservati 

Cominciamo con considerazioni di carattere generale. 

In assenza di correnti di massa e di variazioni del campo gravitazionale le equazioni classiche 

di Maxwell restano invariate poiché: Jk = 0 e ∂ R 

= 0 . 

∂ t 

Ferma restando la costanza della massa nelle normali situazioni sperimentali, le variazioni 

possono esser dovute unicamente ad azioni dinamiche e quindi a movimenti di masse (flussi 

di massa). 

Quali sono le masse in movimento, coinvolte nei fenomeni elettromagnetici? 

Sappiamo che la corrente elettrica è dovuta ad un flusso di elettroni all'interno di campi 

elettromagnetici, di conseguenza un flusso di elettroni produce sia una corrente elettrica 

grazie alla carica dell'elettrone, sia una "corrente di massa", grazie alla massa dello stesso 

elettrone. Calcolando la divergenza della 11) , e ricordando che la divergenza di un rotore è 

sempre uguale a zero, si ha: 

∇ . (∇ × H) = (∇ . J) +(∇ . ∂ D 

∂ t ) - (∇ . Jk) - (∇ . ∂ R 

) = 

∂ t 

= (∇ . J) + ∂ ( ∇ . D) 

- (∇ . Jk) - 

∂ t 

∂ ( ∇ . R) 

= 0 , 

∂ t 

la quale diventa, in virtù delle equazioni 7) e 9) : 

(∇ . J) + 

∂ ρ 

∂ t - (∇ . Jk) - 

∂ ρ 

meq 

∂ t 

= 0 . 

Passando all'integrale di superficie si ottiene: 

I + ∂ Q 

∂ 

t - Ik - ∂ 

Qmeq 

= 0 . 

∂ t 

In questo caso sembrerebbe negata la legge di conservazione della carica elettrica, che si 

esprime nella seguente formula: 

I = - ∂ Q 

∂ t , 

ma si ottiene una sorta di conservazione di "carica totale": 

13) I - Ik = - ∂ 

Q ∂ Qmeq 

+ . 

∂ t ∂ t 

Ricordiamo inoltre che, essendo la massa dell'elettrone pari a: m e = 9,1091 x 10 -31 Kg , e il 

termine moltiplicativo 4πε0G pari a: 1,8544 x 10 -21 Kg –3 m -1 s 2 C 2 N , per la quantità totale di 

massa di elettroni che attraversano la sezione del conduttore nell'unità di tempo si ottiene un 

termine moltiplicativo dell'ordine di grandezza di un 10 -51 che, per quanto numerosi siano gli

atomi all'interno di detta sezione, rende totalmente irrilevante da un punto di vista quantitativo 

il termine correttivo nella precedente legge di conservazione della carica totale. 

Poniamoci, ora, nella ipotesi di assenza di cariche coulombiane in movimento (corrente 

elettrica), e di presenza di un campo magnetostatico. L'equazione di conservazione della 

carica totale prende adesso questa forma: 

14) Ik = - ∂ 

Qmeq 

. 

∂ t 

Ricordando ancora una volta il valore numerico della costante moltiplicativa 4πε0G , quando 

una massa di 1 Kg attraversa una superficie unitaria in 1 secondo, si otterrebbe una corrente di 

"massa equivalente" pari a 6,18 10 -21 A, praticamente non misurabile. Questo conferma 

l'applicabilità del principio di conservazione della carica coulombiana come ottima 

approssimazione della equazione generale della conservazione della carica totale anche in 

presenza di masse in movimento. 

Altra legge che parrebbe violata è quella della irrotazionalità del campo elettrico in un campo 

magnetostatico che si ricava integrando la 10) : 

∫ E . ds = λ0Ik . 

In buona sostanza si otterrebbe la previsione che una massa in movimento produce un campo 

elettrico perpendicolare alla direzione del movimento, e disposto con simmetria circolare 

intorno alla massa. Ovvero, che mettendo una massa in movimento attraverso una spira chiusa 

si produce un campo elettrico nella spira, e quindi una corrente. 

L'osservazione fatta in precedenza, però, ci porta ad affermare che la irrotazionalità del campo 

elettrico in un campo magnetico statico resta sostanzialmente valida, cioè con buona 

approssimazione, fintantoché non entrano in gioco masse in movimento dell'ordine di 10 12 

tonnellate, in grado di produrre, correnti di 1 micro Ampere. 

In altre parole, ammettendo per un attimo che le equazioni siano valide, non si può ottenere 

corrente apprezzabile semplicemente facendo passare per esempio dell'acqua all'interno di un 

tubo. 

Un problema serio è invece posto dalla 12) , che nega la irrotazionalità del campo 

gravitazionale (vedi 6) ) in presenza di campi elettrici e magnetici non statici, ferma restando 

la inesistenza di correnti magnetiche create da un monopolo magnetico, e quindi l'identità Jm 

= 0 . La 12) prevede nuovi inattesi fenomeni fisici, perché, se è vero, come abbiamo appena 

visto, che gli effetti dei moti di masse su campi elettrici e magnetici sono sostanzialmente 

inapprezzabili, viceversa per quelli dei campi elettromagnetici sui moti delle masse (sul 

campo gravitazionale) sarebbe vero esattamente il contrario. 

Effetti delle equazioni unificate sulla possibilità di creare un campo gravitazionale a 

partire da campi elettromagnetici 

Vediamo come si trasforma la 12) scrivendola in forma integrale: 

15) ∫ X . ds = - κ0λ0 I + κ0 ∂ 

∂ 

(flusso di B) - κ0λ0 (flusso di D) . 

∂ t ∂ t 

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Supponiamo di voler realizzare un apparato elettromagnetico che sfrutti la 15) per generare un 

campo gravitazionale opposto a quello terrestre, in pratica un apparato elettromagnetico per la 

levitazione gravitazionale. 

Considerando i termini al secondo membro, ci vengono offerte due possibili vie: 

1 - Sfruttare il termine di corrente e quindi adoperare una corrente continua. 

2 - Sfruttare i termini di flusso elettromagnetico e quindi adoperare generatori di corrente 

alternata in grado di generare campi elettromagnetici tempovarianti. 

La prima soluzione parrebbe quella più abbordabile anche per la semplicità degli apparati 

composti da un generatore di corrente continua ed una bobina. 

Sarebbe, infatti, sufficiente far circolare una corrente opportuna, in una spira circolare per 

produrre un campo gravitazionale orientato perpendicolarmente al campo della spira e, quindi, 

in grado di farla sollevare. 

La presenza del termine moltiplicativo κ0λ0 , purtroppo, rende impraticabile questa soluzione. 

Supponendo, infatti, di essere in presenza di campi elettrostatici, e considerando il campo X 

prodotto costante in intensità e direzione lungo il piano della spira (questa è in realtà solo una 

approssimazione, in quanto il campo gravitazionale è perfettamente verticale al piano della 

spira solo al centro di essa, mentre tende a ruotare intorno al conduttore quando ci si allontana 

dal centro) la 15) può essere scritta come segue: 

X ∫ ds = X 2πR = κ0λ0 I , 

da cui: 

X = κ0λ0 I/2πR . 

A questo punto, ricordando che g = 9,8 m s -2 (ovvero N/Kg) è l'accelerazione di gravità media 

sulla terra, e supponendo di disporre di una spira di raggio R = 1 m , se ne ricava che la 

corrente necessaria per produrre il sollevamento sarebbe pari a: 

I = 6,28 x 9,8 / (30 x·4,306 x 10 -10 ) = 4,76 10 9 Ampere , 

che è purtroppo un valore del tutto incompatibile con la dissipazione per effetto Joule che 

affligge i tradizionali conduttori, oltre che una corrente difficilmente generabile. 

Il problema potrebbe forse essere risolto nell'ambito della tecnologia dei superconduttori, ma 

vogliamo vagliare alternative differenti e tecnologicamente più agevoli. Ripieghiamo, quindi, 

sull'uso di campi elettrici e magnetici tempovarianti, soffermando la nostra attenzione sul 

termine legato alle variazioni nel tempo del flusso magnetico. Anche in questo caso, per poter 

generare un campo X opposto alla direzione della attrazione gravitazionale terrestre, si può 

pensare di ricorrere ad una spira "magnetica" circolare di raggio r , e nuovamente 

supporremo X costante (indipendente cioè da ds , pur consci del fatto che questa 

approssimazione è valida solo nei pressi del centro della spira). Nell'attuale ipotesi il campo 

X ha una direzione ortogonale al piano della spira e dipende unicamente dal tempo, essendo 

indotto dal flusso dei campi elettromagnetici tempovarianti. Estraendo X(t) dall'integrale a 

sinistra della 15), tale termine diviene pari a: 2πr X(t) . A questo punto non resta che 

progettare la spira magnetica in grado di produrre le variazioni di campo che appaiono a 

destra della equazione 15). 

Per generare un campo siffatto possiamo pensare di adoperare un solenoide toroidale avvolto 

su ferro. Questo accorgimento ci consente di "amplificare" l'effetto del termine μ0

(permeabilità magnetica nel vuoto, che vale 1,2566 x 10 -6 m Kg C -2 ), che nel nostro caso va 

moltiplicato per un termine aggiuntivo μr , una costante pura che per il ferro ha un valore di 

circa 800. Indicheremo con μferr = μ0 μr il termine che sostituisce la permeabilità magnetica 

nel vuoto, per avvolgimenti su ferro. Vediamo subito perché un simile dispositivo potrebbe 

rispondere, in linea di principio, alle nostre esigenze. Ogni spira dell'avvolgimento genera, 

percorsa da corrente, un campo magnetico ortogonale alla spira. Possiamo avvolgere le spire 

seguendo il "cerchio magnetico" che desideriamo realizzare. Ciò che si ottiene è, appunto, una 

bobina a forma di toro circolare. Indichiamo con Ns il numero di spire che formano la 

bobina, con R il raggio del toro e con r il raggio di ciascuna delle spire minori che avvolte 

formano il toro, e passiamo a calcolare il campo magnetico indotto dalla corrente I(t) . 

Partendo dall'integrale della 11) , calcolato nella ipotesi che D ed ed R siano costanti, si ha: 

∫ H . ds = I(t) . 

Questa equazione è applicabile a ciascuna delle spire circolari che formano l'avvolgimento. 

Le linee del campo H divengono, per simmetria, circolari e coassiali e quindi il campo 

scalare H complessivo indotto è pari a: 

H(t) = Ns I(t) / 2πr , 

da cui: 

B(t) = μferr H = μferr Ns I(t) / 2πr . 

Se utilizziamo un generatore di corrente alternata con pulsazione ϖ0 si ottiene per la I(t) 

l'espressione sinusoidale: I(t) = I0 sin(ϖ0t) , e quindi: 

B(t) = μferr H = μferr Ns I0 sin(ϖ0t) / 2πr . 

A questo punto torniamo alla 15). Sappiamo che con correnti ordinarie il primo termine di 

corrente, a sinistra, può essere trascurato; inoltre trascuriamo, per ora, anche la derivata 

parziale di D rispetto al tempo, che andrà comunque riportata in conto alla fine del calcolo, 

poiché questa componente nasce per induzione ogni qual volta si generano campi magnetici 

tempovarianti, ed è inseparabile da essi (con la conseguenza che il rendimento complessivo 

del nostro "motore antigravitazionale" cala considerevolmente, tenuto conto del fatto che il 

lavoro associato al generatore del campo gravitazionale verrà in parte dissipato dalla 

resistenza del conduttore ed in parte impiegato per la generazione del campo indotto ma 

indesiderato D ). Ecco la forma che prende l'equazione, ferma restando l'ipotesi di 

indipendenza di X(t) da ds : 

2πR X(t) = κ0 ∂ 

(flusso di B) . 

∂ t 

Applicando ad essa il valore (scalare) di B(t) prodotto dal toro circolare si ottiene: 

2πR X(t) = [κ0 μferr Ns I0 ∂ 

∂ t sin(ϖ0t)] / 2πr . 

Da qui si ottiene: 

4π 2 rR X(t) = κ0 μferr Ns I0 ϖ0 cos(ϖ0t) , 

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186 

e quindi in definitiva: 

16) X(t) = κ0 μferr Ns I0 ϖ0 cos(ϖ0t) / 4π 2 rR . 

Per avere un'idea di come vanno quantitativamente le cose, supponiamo di utilizzare un toro 

di raggio R = 6 m , avente sezione circolare di raggio r = 0,005 m , e conduttori a sezione s 

= 0,001 m (sicché il numero di spire massimo ottenibile con un solo avvolgimento sarà: N s = 

2πR / s = 37700 ). Un siffatto toro avrà un volume pari a: 

V = πr 2 x 2πR = 2 π 2 r 2 R = 2,95 x 10 -3 m 3 , 

e una massa che si deduce dal valore precedente moltiplicandolo per la densità del materiale 

di composizione. Sebbene l'avvolgimento sia su ferro, mentre il materiale di conduzione 

sarebbe, in generale, di rame, supporremo per semplicità che tutta la struttura toroidale sia in 

ferro, sicché, indicata con Dferr la densità volumetrica di questo materiale, che considereremo 

pari a 9,7 10 3 Kg/m 3 , la massa complessiva risulterà pari a M = Dferr V = 28,7 Kg . 

Tornando al nostro punto, per sollevare il toro sarà necessario produrre un valore massimo di 

X(t) (che si ottiene considerando la condizione di picco del coseno, cioè quando questo 

raggiunge il suo valore massimo pari ad 1) pari al richiamato valore "critico" 9,8 N/Kg . 

Possiamo ricavare quindi la necessaria frequenza di alimentazione partendo dall'espressione 

del campo prodotto: 

X = κ0 μferr Ns I0 ϖ0 / 4π 2 rR = 9,8 , 

la quale implica: 

ϖ0 = 2πf = 4π 2 rRX / κ0 μferr Ns I0 (f = frequenza) , 

ovvero: 

f = 2πrRX/κ0 μferr Ns I0 . 

Ricorrendo ad una corrente di 1 Ampere si ottiene, per il generatore di corrente, che la 

frequenza di alimentazione necessaria per il sollevamento è di circa 110 Mhz. 

Ci sarebbe però un altro problema da risolvere. Essendo la corrente alternata di tipo 

sinusoidale, più che sollevarsi, il nostro veicolo sarebbe soggetto ad una vibrazione verticale 

di altissima frequenza, quale quella precedentemente stimata. L'alimentatore del sistema non 

può essere quindi puramente sinusoidale, ma andrebbe adoperata, semmai, una sinusoide 

raddrizzata con le "gobbe" troncate al primo quarto. L'operazione di "raddrizzamento" della 

sinusoide si può ottenere con l'uso di un ponte di raddrizzamento e di un filtro opportuno. 

Ecco una immagine dell'apparato proposto:

Si porrebbe, a questo punto, pure la questione dello spostamento dell'eventuale macchina 

volante nelle diverse direzioni. Una possibile soluzione sarebbe quella di costruire una cupola 

tale che le linee di forza del campo gravitazionale prodotto siano, punto per punto, ortogonali 

ad essa. Sulla cupola, poi, andrebbero alloggiati gli apparati per produrre il campo 

gravitazionale di compensazione. Un'idea potrebbe essere quella di ricoprire la cupola con 

una serie di solenoidi toroidali compositi di piccole dimensioni, ma si potrebbe anche tentare 

di utilizzare il campo elettrico, e quindi l'ultima componente della 15), approfittando inoltre 

del "piccolo" vantaggio offerto dal fattore moltiplicativo λ0 . La soluzione proposta consente 

di creare da un lato lo spostamento dell'apparato in qualunque direzione, dall'altro consente di 

riutilizzare i piccoli solenoidi toroidali per ridurre le vibrazioni del "velivolo", alimentandoli, 

magari, con una corrente sfasata di 90 gradi rispetto a quella che alimenta il solenoide 

toroidale principale. Ecco un'immagine dell'apparato proposto in sezione: 

Non è difficile riconoscere, nella macchina, la classica forma a sfera schiacciata di un UFO, e 

non può, sempre rimanendo nel fantastico, non tornare alla mente l'apparizione dei primi di 

questi oggetti intorno agli anni 50. Il vero problema è che la frequenza di alimentazione 

sembra difficilmente compatibile con la tecnologia dell'epoca, quindi il mistero resta, anche 

se è interessante notare che questo tipo di apparecchio potrebbe produrre effetti molto simili a 

quelli che solitamente vengono associati agli avvistamenti di UFO, vediamone alcuni. 

L'elevata frequenza genera correnti indotte, e quindi può provocare bruciature o carbonizzare 

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composti biologici (piante, animali, etc.) che si avvicinino all'apparato in funzione, 

esattamente come accade in un forno a microonde. La gravità inversa prodotta dall'oggetto 

provocherebbe una forza repulsiva gravitazionale nella parte inferiore di esso, e quindi lo 

schiacciamento di superfici (ad esempio manto erboso) pur senza che il sistema vi si sia 

fisicamente poggiato. La parte superiore della sfera, invece, presenterebbe una forza 

gravitazionale attrattiva che produce una compressione dell'aria con conseguente 

riscaldamento, rendendo possibili anche fenomeni di luminescenza. La compressione dell'aria 

indotta nella parte superiore potrebbe a sua volta provocare fenomeni di diffrazione, rendendo 

vaghi i contorni dell'ipotetico veicolo. 

Infine, il sistema può interferire con sistemi elettronici, provocando disturbi radio o inducendo 

correnti tali da distruggere gli strumenti, o bloccarne temporaneamente il funzionamento. 

Possono, in questo caso, venire in mente i blocchi dei motori di normali autoveicoli, spesso 

segnalati nel corso di avvistamenti, a causa della interferenza per induzione elettromagnetica 

con le bobine degli spinterogeni. 

L'esperimento Rainbow: possibile? 

Visto che ci siamo già "screditati" abbastanza agli occhi del paziente lettore, arrivando a dare 

una "spiegazione" razionale alle fantasticherie ufologiche, perché non ritornare alla fantasia 

primitiva da cui eravamo partiti? 

Veniamo, quindi, all'esperimento Rainbow che ci ispirò, quasi oltre 15 anni fa, le bizzarrie 

che abbiamo esposto. Da un punto di vista puramente teorico, disponendo i solenoidi su una 

sfera, anziché su una cupola, come per il famoso esperimento, si potrebbe generare un campo 

antigravitazionale centrato sul centro della sfera. Se, in linea di principio, i solenoidi sono 

alimentati ad alta frequenza e con intensità di corrente elevate, il campo antigravitazionale 

potrebbe provocare una deviazione della luce verso l'esterno del campo, e non verso l'interno 

come accade, ad esempio, nei pressi di un campo gravitazionale tradizionale ed attrattivo 

intenso quale quello di un buco nero. 

Inutile dire che, proseguendo sulla via di speculazioni quasi fantasiose, ci sarebbero effetti 

anche sullo spazio-tempo. Sempre in teoria, mentre nei pressi di un campo gravitazionale 

attrattivo di notevoli dimensioni il tempo scorre più lentamente, in un campo 

antigravitazionale artificiale il tempo scorrerebbe più velocemente, facendo apparire "il 

mondo esterno" praticamente fermo. La stravaganza considerata consentirebbe lo spostamento 

della nave a velocità che per il mondo esterno sarebbero pressoché istantanee! Esisterebbero 

anche delle ulteriori particolari anomalie, dovute alla distanza dal centro della sfera che 

produce il campo. Infatti, il tempo, evidentemente, scorrerebbe più veloce man mano che ci si 

avvicina al centro della sfera, come dire in buona sostanza che l'interno della sfera 

viaggerebbe più velocemente della parte esterna della nave, con conseguenze difficili da 

immaginare. 

Altro, straordinario, risultato sarebbe la possibilità di costruire una macchina del tempo che, 

vista la possibilità di generare campi gravitazionali inversi, potrebbe scorrere al contrario 

consentendo viaggi nel passato, e non solo quelli nel futuro già contemplati dalla relatività 

einsteniana!! 

Soltanto un'idea bizzarra? 

E' con mia somma meraviglia che, solo pochi giorni or sono, durante una delle mie 

peregrinazioni attraverso le autostrade telematiche, mi sono imbattuto in una sconcertante 

teoria, peraltro estremamente ben congegnata, e con basi logiche che vanno assai oltre la mia 

semplice idea di simmetrizzazione. Ebbene, la teoria espone risultati ed equazioni non molto 

dissimili da quelle illustrate in questo lavoro. Essa porta il nome del fisico tedesco Burkhard

Heim (scomparso, purtroppo, il 14 gennaio del 2001), ed è reperibile in linea al seguente 

indirizzo: 

http://www.mufon-ces.org/docs/heimphysics.pdf , 

relativo al documento: The Physics of Burkhard Heim and its Applications to Space 

Propulsion, by Illobrand von Ludwiger, M.Sc., realizzato per la presentazione al primo 

Workshop Europeo sulla Field Propulsion, 20-22, Gennaio 2001, University of Sussex, 

Brighton, GB. 

Sintetizzarla in maniera corretta è pressoché impossibile, ma possiamo delineare le linee di 

fondo ed il percorso logico seguito da Heim. L'obiettivo che si è posto lo scienziato è stato 

quello di comprendere se le equazioni della Relatività Generale di Einstein potessero essere 

combinate e rese compatibili con quelle della fisica quantistica, adottando opportuni 

accorgimenti matematici ed in particolare una apposita matematica che fosse in grado di far 

transitare dallo spazio dei tensori della fisica dei sistemi macroscopici a quello della 

quantizzazione dello spazio-tempo, e quindi a ciò che Heim chiama spazio dei "selettori" per 

la fisica quantistica. Il tutto senza interruzioni o rotture, ma con un unico sistema di equazioni. 

Ebbene, Heim non solo riesce nel suo intento, ma lo fa introducendo uno spazio ad 8 

dimensioni ove, alle 4 tradizionali (3 per lo spazio ed una per il tempo) se ne aggiungono altre 

4 virtuali. Uno spazio che potremmo definire "spazio delle configurazioni", ove sono allocate 

tutte le possibili forme della realtà, le dimensioni aggiuntive facendo riferimento al piano che 

descrive la probabilità dei cambiamenti di stato. Le equazioni spiegherebbero non solo la 

possibilità di considerare la Relatività e la Meccanica Quantistica come applicazioni 

particolari di esse, ma anche di desumere in maniera automatica, quali loro soluzioni, 

l'esistenza di 4 tipologie di particelle: fotoni, neutroni, cariche elettriche e gravitoni, di cui 

Heim calcola, sempre in base alle sue equazioni, il valore esatto delle rispettive costanti. 

Ma non finisce qui. Le equazioni applicate allo cosmologia consentono di interpretare ciò che 

appare come espansione dell'universo quale effetto della espansione del metrone (quanto di 

spazio) e del cronone (quanto di tempo), e quindi di calcolare il momento iniziale 

corrispondente alla nascita dell'Universo (la teoria non prevede alcun Big-Bang). 

Quello che, però, è più rilevante ai nostri fini, è la applicazione di questa teoria alla fisica 

dell'elettromagnetismo, che porta alle equazioni di seguito riportate: 

Ove: 

Γ = campo gravitazionale 

µ = mesofield 

α = permettività gravitazionale nel vuoto (1/4πγ = 1.19 × 10 9 s²kg/m³) 

γ = costante di gravitazione universale ( γ = 6.67422 × 10 -11 m³/s² kg) 

ß = 1/αc² (9.34 × 10 -27 m/kg) 

c = velocità della luce (3 × 10 8 ms) 

je = densità di corrente elettrica 

jm = densità di corrente di massa . 

Heim aveva lavorato, fino al 1954, presso il Max-Planck-Institut di Goettingen, che 

abbandonò a causa di un grave handicap che lo privò dell'uso degli occhi e delle mani. Tra il 

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1979 e il 1984 pose mano ad una voluminosa opera (699 pagine) in cui espose l'intera teoria. 

Quando uscì il volume praticamente nessuno ricordava che Heim già nel 1959 era divenuto 

famoso proponendo un nuovo sistema di propulsione astronautico. 

- - - - - 

[Per una presentazione dell'autore si rimanda al suo articolo pubblicato nella 

prima parte di questo stesso numero di Episteme] 

sabato.scala@libero.it

Abstract 

Recent Developments in the Relativistic Electrodynamics 

Controversy 

(Gianfranco Spavieri, Miguel Rodríguez and Edgar Moreno) 

In this paper we consider the controversial facets of two tests that are supposed to show 

experimental evidence against the accepted standard electrodynamics based on special 

relativity. The first refers to the detection of longitudinal electromagnetic forces in current 

carrying conductors, and the second represents a modified version of the Trouton-Noble 

experiment for which a non-null result has been found. Although the first test is inconclusive, 

the positive result of the second, if it is really such, is surprisingly in agreement with standard 

electrodynamics. 

1 - Introduction 

* * * * * 

Classical electrodynamics is in a slow but continuous evolution and some of the recent 

advances are the results of discussions that have been going on for decades. In recent times 

many papers have been published on themes related to the so called "electrodynamics 

controversy." This is a scientific controversy between physicists in favor of the standard 

relativistic interpretation of classical electrodynamics and physicists that favor an approach to 

electrodynamics based on coordinate transformations different from the Lorentz 

transformations and, thus, negate the validity of special relativity. 

In this paper we consider, both from a theoretical and experimental point of view, two aspects 

of this ongoing controversy, namely: the detection of longitudinal forces on current elements 

[1-8] and an experiment of the Trouton-Noble type [10-16] which, supposedly, leads to a nonnull 

result, in contrast to the traditional view exposed in many textbooks. 

Before going into the details, we would like to make a general comment on the reliability of 

the papers that deal with this type of conflicting aspects of fundaments of physics. As it has 

been remarked by several epistemologists and experts in the philosophy of science, most 

physicists assume spontaneously a partial position in these discussions. The remark is that 

some experimentalists are tempted to, and in fact do, try to arrange the experimental set up in 

such a way that the data are trimmed or slightly modified in favor of expected or desired 

results, which would corroborate their own visions or theories. Moreover, it is not uncommon 

to find out that theoreticians may have selected from the existing theory formulas or partial 

approaches that lead to a theoretical result in agreement with their vision, most of the times 

neglecting "unintentionally" other formulas or approaches that would lead to opposite or 

different results. 

We believe that the majority of physicists deal with controversial issues with serious and 

frank attitude, so that the effects of "unintentional" modification of experimental data and 

manipulation of theoretical models is probably limited and, hopefully, do not alter 

significantly the objective physical results. Nevertheless, some of these controversies, which 

generally imply the waste of a lot of time, would not subsist if physicists were a little more 

scrupulous in their research. Moreover, some physicists, either in favor the official, standard 

view of accepted theories or not, assume generally a rigid and dogmatic attitude that often 

prevents discussion and advances. Sometimes this attitude prevents the research of issues that 

later are recognized as real fundamental unsolved problems of modern physics. 

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With this in mind, we try to address in an objective way the two experimental topics 

mentioned above, being our impartiality somewhat assured because, although the predictions 

of opposing theories are clear, we are not completely in favor of the expected standard 

prediction. 

Two groups of researchers performed recent experiments on these topics. The novelties of the 

experiments, which make them interesting from a theoretical point of view, are: 

- In the case of detection of longitudinal forces, a time varying current has been used 

[3], unlike other previous experiments where the current was steady-state [1-2, 4-6]. 

- In the case of the Trouton-Noble experiment, the parallel plate capacitor was not 

shielded from external electric fields [13], unlike previous experiments of this type 

[10-12]. 

2 - Advances in the Controversy of the Longitudinal Forces on Current Elements 

This is an old discussion that sets as opposing theories or formulas, describing the force acting 

a current element, the Ampere law and the Biot-Savart law. 

The Ampere law reads 

i indmdn 

, 2 

( r ) 

Δ Fm, n = − k m 

(1) 

m, 

n 

where im and i n are the currents flowing in the current elements of length dm and dn 

respectively, r is the distance between the two elements, and k is a dimensionless geometrical 

function that takes into account the direction of current in each element. 

An important feature of this law is that the action and reaction principle holds for the 

interaction between two current elements. Moreover, besides the usual forces perpendicular to 

the current elements, this law predicts also the existence of longitudinal forces, i.e. forces 

acting on a current element in the direction of the current. 

The Biot-Savart law reads 

Δ F = i dm 

× B , 

(2) 

m, 

n m n 

where Bm is the magnetic field due to current element dn , given by the Laplace formula 

μ 

dB 

n = ( in 

dn) 

× 

4π 

For this law, the forces are always perpendicular to the current element. However, this law 

does not comply with the action and reaction principle between two current elements. 

Nevertheless, both laws give the same result when the interaction is extended to the complete 

circuit and the action and reaction principle is not violated. 

Several of the experiments that try to discriminate the two laws experimentally have been 

discussed in Ref. 4-5, 7. It has been remarked that the theoretical advantage of the Ampere 

law is that it complies with the action and reaction principle. Although some more refined 

discussion should be in order on this theoretical aspect, the final impression we have, from an 

experimental point of view, is that a point in favor of the Ampere law has not yet been made. 

In this article we consider the results of a recent experiment by Graneau et al. [3] who claim 

to have proven the existence of electromagnetic longitudinal forces. Their experimental set up 

r 

( r 

n, 

m 

n, 

m 

) 

3 

. 

(3)

consists of a closed circuit where a high intensity time-dependent current I is induced, as 

shown in schematically in Fig. 1. In this experiment, a capacitor is charged at a very high 

voltage and then discharged when connected to the electric circuit where a current I = I(t) is 

induced. A small section R of the circuit is isolated from the rest of the circuit by two air 

gaps, Gu and Gd, so that the rod R can move up and down if a net force acts on it in the 

longitudinal direction. 

Graneau et al. observed that the rod moves, during their tests, and it reaches a height h that 

depends on the maximum intensity of the current and also on the difference between the 

lengths of the up and down gaps, Gu and Gd. Their data indicate that the net force, which 

makes the rod reach the height h, is zero for a symmetric set up, when Gu = Gd, while the 

force and the height h increases progressively up to a maximum value when, progressively, 

one sets Gd < Gu. 

Thus, Graneau et al. conclude that their experiment proves the existence of electromagnetic 

longitudinal forces and favor Ampere's law. An extended article refuting their conclusions has 

been recently submitted for publication [8]. Here we give some of the arguments used for the 

rebuttal and use this occasion to make some other comments about this controversy with the 

aim to provide suggestions for other tests of electrodynamics where time-dependent fields are 

used. 

Qualitatively, our explanation of the results of Graneau et al. is the following. The net force 

exists but it is not of electromagnetic nature. When the current I of very high intensity is 

induced in the circuit, most of the power P = RcI 2 is dissipated via the Joule effect in the air 

gaps where the electrical resistance Rc is higher than in the rest of the circuit. The air in the 

gaps reaches a high temperature and pressure, generating a gas expansion, like a small 

explosion that acts on the inner surface of the mobile rod R. 

However, the air in the smaller gap Gd is relatively more confined than the air in the upper 

gap Gu. Molecules, radiation energy, electrons, etc., of the expanding ionized air, will bounce 

back and forth many more times between the inner walls of the gap Gd than of Gu, before 

they leave the gap. Thus the pressure exerted in the smaller gap is more effective than that in 

the larger gap. It is this pressure difference that generates the net upward force that pushes the 

rod at a height h. 

The details and a quantitative description of this mechanism are given in Ref. 8 where it is 

shown that the dependence of h with the length Gd is in good agreement with the 

experimental data and in better agreement with the the experimental results than the 

predictions of the Ampere law, as calculated by these authors. Thus, we believe that the 

experiment here considered is not conclusive and cannot be taken as an experimental proof of 

Ampere's law. 

Some considerations are in order here that can help to address the controversy on what are the 

real forces acting on charges or current elements. 

The novelty of this experiment is that it is conducted in non steady-state conditions, since the 

current varies with time. In this circumstance, the vector potential A(t), associated with the 

time varying current, also varies with time. Since A(t) can be in the direction of a current 

element, the force –q dA/dt = qE, where E is the induction electric field and q the charge 

associated to a current element, may also be in the direction of current elements. 

Generally, the circuit is neutral so that besides the moving charge q there is also a stationary 

charge –q in the current element, and there should be no net force. But, if the rod R 

accumulates a net charge during the extreme conditions of the test, a longitudinal force could 

be acting on R, even though it is probably small in this set up. 

However, the interesting point in the case of time-dependent fields is that one realizes that, 

contrary to the usual steady-state conditions where the Biot-Savart law is generally 

confirmed, there is no mention in the literature of experiments dedicated to the detection of 

forces acting on charges or current elements due to time-dependent induction fields. 

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194 

When the phenomenon of induction is applied to a closed loop we have many direct 

verifications of the law of induction, or Faraday's law, in terms of the emf, 

emf = ∫ E ⋅ d 

, 

induced in the loop, which has an integral form. In this common case, there are forces acting 

in the direction of the current but only the resultant on the closed loop is being tested in terms 

of the induced current or voltage difference. The differential force acting on a current element 

or a part of a loop is not being tested in the usual induction experiments. 

Thus, what has not been tested experimentally is not only if these induction forces are the 

same for charges at rest or in motion (as the moving charges in a current element), but if the 

induction forces act at all in an isolated stationary charge that is not part of a closed circuit. 

One reason why the experimental results for the last mentioned case are not obvious, even for 

standard relativistic electrodynamics, is that the action and reaction principle does not hold for 

the interaction between a coil producing a time varying magnetic field and an isolated charge 

(this is the so called Shockley-James paradox, solved in Ref. 9). Theoretically, there should be 

a force –q dA/dt acting on the isolated charge. However, the existence of a possible reaction 

force on the coil has been the source of controversial discussions [9]. 

There is a pragmatic reason why these problems related to time-varying fields are mentioned 

here. From an operational point of view, it may be easier experimentally to detect possible 

discrepancies with classical electrodynamics for isolated static charges than current elements. 

In fact, a current element is mainly a theoretical concept that is difficult to realize 

experimentally, as all the objections and drawbacks of the experiments on longitudinal forces 

performed so far has shown. While an isolated charge is a theoretical concept realized 

experimentally in many set ups, such as the experimental proof of Coulomb law, and it should 

be easier to handle without ambiguities. 

Thus, our suggestion and belief is that the electrodynamics controversy may achieve more 

interesting and definite results if it shifts its attention to the possible tests of electromagnetic 

interactions with time-dependent fields of the type mentioned above. 

3 - A New Experiment of the Trouton-Noble Type 

With the same spirit that motivated the mentioned papers [4] and [5], we believe that it is 

worth reconsidering here one of the tests of classical electrodynamics, the Trouton-Noble 

(TN) experiment, that has been recently discussed in the literature. 

The outcome of the TN experiment has been considered a null result for decades. Trouton and 

Noble wanted to verify that a charge moving with respect to the ether frame where the 

Maxwell equations were valid, would create a magnetic field. In order to check this 

hypothesis, they suspended a charged capacitor to a thin thread. Since the Earth (and the 

capacitor) was supposed to be moving with respect to the frame of the ether, the magnetic 

field produced by one of the charges of the capacitor in motion would act, via the Lorentz 

force, on the other charge producing a torque and an observable rotation of the apparatus. 

The experiment was first performed by TN [10] and later by Chase [11], and more recently 

and with a high sensitivity by Hayden [12]. The results of all these experiments indicate so far 

that the effect sought by TN does not exist. 

However, recently Cornille [13] has claimed that he performed a TN experiment with positive 

result and gives a number of reasons why the previous experiments failed while his 

succeeded. This result is surprising because it seems to defy the generally accepted 

interpretation of the TN experiment and of the standard, relativistic interpretation of classical 

electrodynamics.

In the present section we show that a test of the Faraday law in differential form can be 

related to an experiment of the TN type. Furthermore, we clarify the experimental limits of 

the original TN experiment and of that performed by Cornille. In a future paper we consider 

another test of the Faraday law in differential form and point out an interesting and unique 

experimental consequence of the validity of the conservation laws in electrodynamics. 

Without considering here Cornille's theoretical arguments in detail, we have noticed that 

Cornille's experimental set up differs from the others because he did not shield the suspended 

condenser from external electric fields. He also mentions that the magnetic field of the Earth 

cannot produce a torque because the charges of the capacitor are at rest in the laboratory 

frame of the Earth. 

We show that, theoretically and contrarily to the current belief, in specific experimental 

conditions an experiment of the TN type, consisting of a suspended charged capacitor, may 

succeed. In fact, according to the standard interpretation of Faraday's law of induction, a 

positive result is theoretically possible if the effect of the small magnetic field of the Earth on 

the capacitor is taken into account. 

However, the foreseen non-null result refers to the action of the external magnetic field of the 

Earth on the TN capacitor, which is actually rotating about the Earth axis in its diurnal 

rotational motion. It does not refer to the effect originally sought by TN and other theoretical 

effects considered by Cornille. 

Furthermore, the experiment of the TN type here considered, may provide a definitive 

quantitative test of the old theory of magnetic field lines ''cutting,'' which supposedly has been 

disproved qualitatively by the Kennard [14] experiment. 

In the final part of the paper we indicate the experimental conditions that lead to a positive 

result for an experiment of the TN type and comment on the experimental result of Cornille. 

4 - The Standard Description of the Faraday Disk 

The Faraday disk, as shown in Fig. 2, consists of a conducting disk rotating about its 

symmetry axis and connected to an electric circuit AECR with one end (A) on the axis at the 

center of the disk and the other end (R) in the form of a sliding contact touching the external 

circumference. When a magnet is placed near the rotating disk with its magnetic pole aligned 

along the disk axis, an induction current flows in the circuit. 

If the magnetic field B is uniform near the disk of radius R rotating with angular frequency ω, 

the electromotive force is given by 

1 

emf = ∫ E ⋅ d l = ∫ ( v× 

B) 

⋅ dl = wR 

2 

B 

i 

(4) 

2 

In many textbooks, result (4) is deduced from the integral form of Faraday's law taking into 

account the change of the magnetic flux as the material segment AR rotates in the presence of 

the field B. The integral form of Faraday's law cannot tell where, along AECR, the emf is 

induced. 

However, considering Faraday's law in differential form, the expression v×B represents the 

induction, effective field Ei seen by the charges co-moving with the disk along the segment 

AR. It is a consequence of the validity of the Lorentz force F=E+q v×B, written in a reference 

frame S, that indicates that the charge moving with velocity v in the presence of B and with 

E=0, experiences the field Ei=F/q= v×B. 

According to the transformations of the electromagnetic fields of special relativity, an 

observer in a reference frame S' instantaneously co-moving with a point of the disk 

experiences the fields B´≈B and E´≈ v×B. 

The observers of both frames S and S' agree that the emf is induced in the radial path of the 

disk and the description of the effect is essentially the same for S and S'. The same result is 

195

196 

obtained if the magnet is rotating with the disk or if a rotating conducting magnet alone is 

used as a Faraday disk. In fact, according to the standard relativistic interpretation of 

electrodynamics a cylindrical magnet can be thought of as made of a cylindrical current 

distribution, and the current and field produced by the current is the same even if the current 

loops rotate about the symmetry axis. 

Historically, the field lines of B were considered to have a precise physical reality. The 

potential difference generated across the radius AR was interpreted as due to the cutting of the 

magnetic field lines by the rotating metal. In the term qv×B, the velocity was interpreted as 

that of the charge with respect to the field lines, and not as the velocity of the charge relative 

to the reference frame where the magnetic field is measured. 

In the case of a Faraday disk formed by a rotating magnet, in the pre-relativistic 

interpretation, Faraday's hypothesis of 1851 -- in which he visualized the magnetic lines as 

fixed to the magnet and rotating with it -- was assumed. In this case, the lines will thus be cut 

by the external branch ECR and the emf is not induced in the disk but instead in the stationary 

part ECR of the electric circuit. In this interpretation v represents the velocity of the ''cutting'' 

field lines at the position of the ECR. 

Measurements of the induced voltage and/or current cannot discriminate between one theory 

or the other since in both cases the generated intensities are the same. In 1917 Kennard [14] 

achieved a breakthrough when he suppressed the ECR branch and was capable of measuring 

an induced potential difference along AR when the whole system rotated as a unit. Kennard's 

experiment consisted of a cylindrical capacitor and a coaxial solenoid. The induced 

electrostatic charge separation was measured by inserting an electrometer by means of two 

leads located along the axis. One of the lead was connected to the inner part of the capacitor, 

the other was connected to a radial wire reaching the outer part of the capacitor. When Tate 

[15] in 1922 reviewed the whole problem, he acknowledged Kennard's result and the implied 

disproof of the theory of rotating lines of force. 

Without negating the validity of Kennard's experiment, we point out some of its limitations. 

First of all the apparatus consisted, as in the case of the Faraday disk, of two parts in relative 

motion: the measuring device, or electrometer, at rest; and the rotating capacitor in motion. 

What is being measured is always a potential difference between the two parts and not the 

local field. The inner part of the capacitor had finite dimensions and one cannot exclude that, 

if the flux lines are rotating, they may induce a potential difference in the stationary part of 

the electrometer. Furthermore, the results are necessarily qualitative because of the difficulties 

of graduating the electrometer and eliminating additional electrostatic effect due to the air 

drag produced by the rotating parts. 

In an ideal experiment the measuring device should be co-moving with the rotating apparatus 

(magnet or solenoid) and measure the local electric field intensity, so that these objections no 

longer apply. This ideal situation is achieved with the set up of an experiment of the TN type 

that exploits the Earth rotation, as described in the sections below. 

5 - The Effect of the Magnetic Field of the Earth 

The magnetic field of the Earth (Fig. 3) is usually approximated by the equivalent field 

produced by a magnetic dipole placed at the center of the Earth of intensity mo=8.1×10 25 

gauss⋅cm 3 . Correspondingly, the magnetic field on the surface of the Earth varies from 0.3 to 

0.6 gauss depending on the latitude. 

The magnetic dipole is not aligned with the axis of rotation with which it forms an angle 

α≈14 ° , corresponding to a distance of about 1000 miles between the geographic and the 

magnetic pole. The radial component mosinα is quite smaller than the axial component 

mocosα, being sinα/cosα ≈ 0.22. In the following we consider first the effect of axial 

component and then show that, for our purposes, the radial component has no effect and can 

be neglected.

Let us consider the component aligned with the Earth axis with a dipole moment intensity of 

m=mocosα. To all respects, the Earth can be considered equivalent to a rotating magnet so 

that the results of Sec. 2 valid for the Faraday disk can be applied here. 

What is of interest here are the perpendicular and tangential components of B to the Earth 

surface. Taking the z-axis of frame S aligned with m, the components of the field B at a given 

latitude and longitude of the vector r are given by 

( r⋅ 

m) 

3r 

m 

B = − 5 3 

(5) 

r r 

By means of Eq. (5), one can find the field components that, because of the symmetry, do not 

depend on the longitudinal or azimuthal angle φ, but depend on the latitude θ . In analogy 

with the interpretation of the Faraday disk, a charge fixed on the Earth and rotating with it in 

the presence of the field B will feel the effective electric field Ei.=F/q=v×B. 

We consider now the effect of the small radial component mr=mosinα of the magnetic dipole. 

In the rest frame S, the radial component mr rotates with angular velocity ω. At a point r in 

space the magnetic field due to mr is a time-varying field and, by Maxwell's equations there 

must be also an induction electric field. In order to find this electric field, one can consider a 

moving inertial reference frame S' instantaneously at rest with a point rotating with the same 

angular velocity ω. We use special relativity but neglect retardation effects and relativistic 

corrections of order higher than v/c. In S' the magnetic field Br´≈ Br produced by mr is 

constant and there is no electric field. Transforming the fields one finds that the electric field 

in S is given by -v×Br. The Lorentz force due to mr acting on a charge fixed on the rotating 

Earth, is F=qE+qv×Br =q(-v×Br+ v ×Br)=0. Thus, the radial component mr does not have a 

net effect on a charge at rest on the Earth. 

The main difference between the effect of m and mr, is that m generates a constant magnetic 

field in S, while mr generates a constant magnetic field in S'. 

In conclusion, a charge fixed on the rotating Earth feels only the effect of the field B due to 

m, i.e. it experiments a field Ei.=F/q=v×B. 

6 - An Experiment of the Trouton-Noble Type in the Magnetic Field of the Earth 

Let us consider now a charged capacitor suspended by a thin elastic thread of torsion constant 

k as in the case of the Trouton-Noble experiment. The capacitor is generally described as two 

charges of opposite value q placed at the ends of an insulating rod and separated by a distance 

d, as shown in Fig. 4. 

In the following we assume the standard interpretation of electrodynamics which foresees a 

null result for the effect sought originally by Trouton and Noble. This was supposed to be a 

torque due to the self-action of the charges moving in the ether and generating a magnetic 

field with their motion. 

What we look for in the present experiment is the effect of the external magnetic field of the 

Earth on the moving charges. As discussed in the section on the Faraday disk, in the frame S 

the sought effect is due to the Lorentz force qv×B, in the frame co-moving with the charge the 

effect is due to the existence of the electric field qv×B. In order to detect this electric field, 

shielding screens around the capacitor must be avoided, as in the case of Cornille's 

experimental set up. 

With respect to frame S, the velocity v of the charges is in the West to East direction. The 

only torque on the capacitor about the axis of suspension is due to the component Bp of the 

magnetic field perpendicular to the Earth surface that produces a force F=qvBp lying on the 

plane of v and d, tangent to the Earth. The resulting torque is 

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198 

[ × ( q v× 

) ] = qvB ϕ 

τ = Bp 

pdcos 

r , 

where ϕ is the angle formed by the vectors v and d. 

This torque generates a rotation of the capacitor that tends to set d perpendicular to v. At the 

position of equilibrium the capacitor has rotated by an angle ε such that τ=kε. In order to 

verify that this angle is detectable with an apparatus of the Trouton-Noble type, we express 

the charge on the capacitor, for a parallel-plate capacitor, as q=CV and C=εoS/d. The result is 

that, when cosϕ = 1, 

ε o 

( vB ) 

SV p 

ε = . (6) 

k 

In order to estimate ε, we consider a location near the equator where the tangential velocity is 

greater, for example in Venezuela at 8 ° above the equator corresponding to θ=82 ° in Eq. (5´). 

In this case, with the radius of the Earth given by r=6.37×10 6 m and a velocity of 

v=ωrsinθ=445m/sec near the Equator, the perpendicular field component turns out to be 

Bp=0.17gauss directed toward the centre of the Earth and Ei=v×B≈ 7.5×10 -3 V/m. With a 

potential difference of V=2×10 4 Volt, a plate surface S=1m 2 and a torsion constant k=10 - 

8 kg⋅m 2 /s 2 , the torsion angle turns out to be of the order of ε≈0.13 radians≈7.5 ° , which is easily 

observable. 

7 - Conclusions 

We have considered two aspects of the electrodynamics controversy. 

The first aspect refers to the detection of longitudinal forces acting on current elements. We 

discuss the experiments by Graneau et al. and point out some weakness in the experimental 

set up that make it unreliable for this test. 

However, an interesting feature of the experiment performed by Graneau et al. is that timedependent 

fields have been used. This feature reminds us that there are no tests of the 

elementary laws on charges and current elements and that Faraday's law of induction has been 

tested with great accuracy but only in its integral form, on closed loops. 

Consequently, our suggestion is that the electrodynamics controversy should be directed 

toward testing the elementary forces relevant to the discussions on the Shockley and James 

paradox. 

The second aspect refers again to the test of the Faraday law in differential form. We have 

shown that the effects of the magnetization produced by the rotating Earth can be described in 

analogy with those produced by a rotating magnet. Thus, an apparatus of the TN type should 

lead to a non-null result and can be used to detect the small induction electric field Ei=v×B 

seen by an observer at rest on the Earth surface and co-moving with it in its diurnal rotational 

motion with a tangential velocity v=ω×r. 

This induction electric field is analogous to the local field supposed to be generating the emf 

observed in a closed electrical circuit in the Faraday disk. Therefore, this experiment can be 

used as a test of the Faraday law in differential form and as a quantitative test for the 

localization of the emf, which has been already qualitatively verified by Kennard. 

The non-null result reported by Cornille for his TN experiment -- with a high voltage of 

40×10 3 V -- seems to corroborate the existence of the small induction electric field Ei 

However, there are still some difficulties. 

First of all, Cornille's result is qualitative, as he observed a rotation of the apparatus tending to 

align along the velocity v, but did not measure the torque. He also states that the rotation is

unchanged by reversing the potential difference and concludes that the TN effect exists. If we 

discard the existence of the effect originally sought by Trouton and Noble, an explanation of 

the effect observed by Cornille can be attributed to an electrostatic induction of objects near 

the capacitor, which does not depend on the sign of the potential difference. 

In conclusion the experimental evidence for the localization of the emf is still uncertain and at 

most qualitative. However, the experiment described in this paper represents a theoretical 

improvement and its realization should be able to settle the question of localization -- and the 

questions raised by Cornille's experiment -- in a quantitative and definite way. 

Acknowledgments 

This research was made possible by a grant from the CDCHT (C-1015-00-05-B, ULA, 

Mérida, Venezuela). 

References 

1. P. Graneau, Phys. Lett. A 97, 253 (1983) 

2. T.E. Phipps and T.E. Phipps Jr., Phys. Lett. A 146, 6 (1990). 

3. N. Graneau, T. Phipps Jr., and D. Roscoe, Eur. Phys. J. D 15, 87 (2001). 

4. G. Cavalleri, G. Spavieri, and G. Spinelli, Eur. J. Phys. 17, 205 (1996). 

5. G. Cavalleri, G. Bettoni, E. Tonni, and G. Spavieri, Phys. Rev. E, 57, 1 (1998). 

6. P. T. Pappas, Nuovo Cimento B 76, 189 (1983). 

7. Cavalleri G., Spavieri G. and Tonni E., Hadronic J. 21, 459 (1998). 

8. G. Cavalleri and G. Spavieri, submitted to Eur. Phys. J. (2001). 

9. Y. Aharonov, P. Pearle, and P. Vaidman, Phys. Rev. A 37, 4052 (1988); G. Spavieri, 

Nuovo Cimento B 109, 45 (1994). 

10. Trouton F.T. and Noble H.R., Proc. Royal Soc., 72, 132 (1903). 

11. Chase C.T., Phys. Rev., 28, (1926). 

12. Hayden H.C., Rev. Sci. Instruments., 65, 788 (1994). 

13. Cornille P., Galilean Electrodynamics, 9, 33 (1998). 

14. Kennard E., Phil. Mag. 33, 179 (1917). 

15. Tate J., Bull. Nat. Res. Council, 4, 6 (1922). 

16. L. Nieves, M. Rodriguez, G. Spavieri, and E. Tonni, Nuovo Cimento B 116, 585 

(2001). 

Figure Captions 

Fig. 1. Scheme of the electrical circuit used by Graneau et al. for the detection of longitudinal 

electromagnetic forces. The mobile part of the circuit R moves up when a strong, impulsive 

electric current flows. 

Fig. 2. Scheme of the Faraday disk picturing the magnetic flux lines generated by the magnet. 

In the Faraday disk the emf is induced along the rotating material segment AR of the circuit. 

Fig. 3. Scheme of the magnetic field lines of the Earth. The Earth magnetization can be 

represented by a magnetic dipole placed at the centre of the Earth. 

199

200 

Fig. 4. A Trouton-Noble apparatus is suspended to a thin elastic thread. Due to the rotational 

motion of the Earth, the charged condenser moves with velocity v in the presence of the 

external magnetic field B. The Lorentz force F=qv×B acts on the charges ±q and tends to 

rotate the condenser until d is perpendicular to v. 

- - - - - 

FIG. 1

FIG. 2 

201

202 

FIG. 3 

FIG. 4 

- - - - - 

Centro de Astrofísica Teórica, Facultad de Ciencias, Universidad de Los Andes 

Mérida, 5101 - Venezuela 

spavieri@ula.ve 

[A presentation of the first two authors can be found in Episteme N. 3]

Dynamic Space Converts Relativity 

Into Absolute Time And Distance 

(Tuomo Suntola) 

Abstract 

A confusing feature in the theory of relativity is the use of time and distance as parameters in 

explaining the constancy of the velocity of light and the reduced frequencies of atomic clocks 

in fast motion and in high gravitational field. It is well known that a radio signal passing a 

mass center is delayed compared to a signal from same distance through free space. Instead of 

stating that the velocity of the signal were reduced the theory of relativity explains that time 

close to mass centers flows slower thus saving the basic assumption of the theory, the 

constancy of the velocity of light. Same is true for atomic oscillators and the characteristic 

absorption and emission frequencies of atoms, an atomic clock loosing time when in fast 

motion is not considered as running slower but as experienced slower flow of time. 

A key demand of a physical theory is its capability to create an understandable picture of the 

reality we observe. Instead of just introducing mathematical expressions for observations, a 

physical theory should explain the logic behind the phenomena observed. The old Ptolemy 

astronomy worked well for calendar and eclipses but failed in serving as a basis for a physical 

view of celestial motions. A key in Copernicus' findings was the realization of the observer's 

state in the system - instead of defining the observer's state as the origin at rest Copernicus 

identified the Sun as the origin of the planetary system with Earth orbiting and rotating like 

any other planet. Such a structure gave basis for a physical approach of motions in the system 

thus opening a new era for the understanding of the celestial mechanics and the laws of 

nature. 

The Dynamic Universe approach takes a further step in reorienting the observer. The 

observable three-dimensional space as whole is considered as a closed spherical structure with 

its dynamics determined by a zero energy balance between gravitation and motion in the 

structure. Such approach links local phenomena to the state and motion of whole space and 

gives physical explanations to several postulates like the velocity of light, the rest energy of 

matter and the Mach's principle. It also explains the dependence of the velocity of light on the 

gravitational environment and the dependence of the ticking frequencies of atomic clocks on 

the state of local motion and gravitation - not by distorting time and distance coordinates but 

in absolute time and distance. 

1 - Space as the surface of a 4-sphere 

* * * * * 

Many physicists have noticed the striking equivalence between the total rest energy of all 

mass in space and the gravitational energy of space estimated from Newton's gravitational 

energy as E ≈ GMΣ 2 /R where R = c/H is the Hubble radius. For further analysis of the total 

gravitational energy we need to assume certain geometry of space. A natural solution is a 

three-dimensional surface of a four-dimensional sphere. Following the ideas of Ludwig 

Schläfli, Georg Riemann and Ernst Mach, Einstein, Ref. [1] proposed such geometry in 1917. 

Einstein was looking for static space, which lead to the need of the cosmology constant to 

prevent shrinkage of the structure. Further, the fourth dimension was already reserved for 

time in the theory of relativity just completed. As the result, the spherical space was rejected. 

203

204 

Combining the idea of space as the surface of a 4-sphere to the mystery of the equality 

between the gravitational energy and the rest energy of mass in space suggests that space as 

the surface of a 4-sphere is in motion at velocity c in the direction of the radius of the 4sphere 

so that the energy of motion related to mass in space moving at velocity c along the 4radius 

is written like the energy of light as E = cp = c⋅MΣ c = MΣ c 2 (see Figure 1). 

−F’(g),t 

m 

R4 R" 

M" 

−F”(g) 

R4 

E”(g) 

E”(m) 

MΣ = 2ρπ 2 3 

R4 

Figure 1. The tangential shrinking force, F'(g),t, due to the gravitation of uniformly 

distributed mass in spherical space is equivalent to the gravitational effect, F"(g), of 

mass equivalence M" at distance R" from mass m along the 4-radius of the structure. 

The sum of the total energies of motion and gravitation in space is zero. 

A detailed mathematical analysis taking into account the four-dimensional geometry in the 

expression for the gravitational energy allows the zero-energy balance between motion and 

gravitation to written in form 

2 

2 GGEM Σ 

M Σ c0 

− = 0 

(1) 

R 

4 

where GE = 0.776 is a geometrical factor resulting from the integration of the gravitational 

energy throughout the three-dimensional surface of the 4-sphere, Ref. [2]. 

When solved for the velocity of space, c0, in the direction of the radius of the structure we get 

c 

0 

GGEM Σ GM " 

= ± = ± (2) 

R R" 

4 

which means that for maintaining the zero energy balance in space the velocity of expansion 

or contraction along the 4-radius is linked to the gravitational constant, total mass in space 

and the actual length of the 4-radius. For a mass density 5 ⋅10 −27 [kg/m 3 ], which is 0.55 times 

the Friedmann critical mass, and the 4-radius of space R4 = 14⋅10 9 light years, the numerical 

value of c0 in equation (2) is equal to c0 = c = 300 000 km/s. The latter form of equation (2) 

applies the mass equivalence M" of space at distance R" in the fourth dimension, in the 

direction of the 4-radius of three-dimensional space (see Figure 2). When applied to mass 

object m equation (1) means that the rest energy of matter can be explained as the energy of 

motion due to the expansion of space along the 4-radius. 

The buildup and release of the energy of matter in space can be described as a zero-energy 

process from infinity in the past through singularity to infinity in the future. In the contraction 

phase mass obtains its velocity against the release of gravitational energy like in free fall and 

in the expansion phase the energy of motion obtained in the contraction is converted back to 

the gravitational energy.

M" 

R" 

dM 

D 

x,y,z 

m 

Im 

Figure 2. The integrated gravitational effect of all 

the mass in space on a mass object m can be 

described as the gravitational effect of mass M" at 

distance R" along the imaginary axis inside closed 

space. 

In the expansion phase, the radial motion of space works against the gravitation of the 

structure, which means that the radial expansion velocity is gradually diminishing. The 

relative reduction of the expansion velocity in the present state of the Universe is about 

Δc0/c0 = 4⋅10 −11 /year. It turns out that the frequencies of atomic clocks and the characteristic 

wave numbers of the spectral lines of atoms are directly proportional to the internal 

momentum due to the motion of space at velocity c0. Accordingly, the reduction of the 

velocity of light is not detectable in measurements based on the readings of atomic clocks. 

−∞ 

Energy of motion 

contraction expansion 

∞ 

−∞ 

Energy of gravitation 

time 

Figure 3. Contraction and expansion of space and the 

corresponding evolution of the energies of motion and 

gravitation. In the contraction phase, the 4-radius of space goes 

from infinity to zero. In the expansion phase, after singularity, the 

radius increases from zero back to infinity. Zero total energy is 

preserved through the entire process. 

∞ 

205

206 

2 - The fourth dimension 

The shocking message of equations (1) and (2) is that the velocity light appears as the velocity 

of all mass in the fourth dimension. Same message is hidden in the line element in Lorentz 

coordinates or Minkowski metrics which in local homogeneous space can be expressed as 

or in vector form as 

( ds ) ( cdt ) ( dx) ( dy ) ( dz ) 

2 2 2 2 2 

= − + + + (3) 

ds = icdt 

+ dx + dy + dz 

(4) 

where c instead of dt is expressed as a vector in the fourth dimension, mathematically shown 

as the imaginary direction. Following the concept of space as the three dimensional surface of 

a 4-sphere, c in equation (4) does not mean motion in space but motion of space, i.e. motion 

that all matter at rest in space is subject to according to equation (2). Accordingly, the rest 

momentum of a mass object in space is 

p4 = i mc 

4 

(5) 

i.e. momentum in the fourth dimension which, when summarized to a momentum p in a space 

direction gives the total momentum ptot relevant with the total energy of an object moving in 

space 

( ) 2 

E = c p = c p + mc 

(6) 

tot 4 tot 4 

2 

r 4 

Equation (6) shows the total energy of an object in the same format as given by the theory of 

special relativity, however, without the use of the Lorentz transformation as a correction of 

the coordinates. Equation (6) describes the total energy as the result of the orthogonal sum of 

momenta due to the motion of space and the motion in space. 

In fact, motion of space at the velocity of light along the radius of curvature is implicitly 

given in the Hubble law and the uniform expansion of space, which were not known at the 

time the theory of relativity was formulated. 

3 - Motion in spherical space 

Observing that any motion in spherically closed space is central motion relative to the mass 

equivalence of space in the fourth dimension, the gravitational acceleration in the fourth 

dimension is reduced due to central acceleration (Figure 4). The effect can be expressed as a 

reduction of work done by the object against the gravitation of the mass equivalence of space 

in the fourth dimension. The effect can be expressed in terms of a reduction of the internal 

mass mI responding to the gravitational interaction with the total mass in space 

( ) 

m m m 

2 2 

I = eff 1− β = 1− 

β 

(7) 

The reduction of the internal mass reduces the momentum of the object in the fourth 

dimension and, accordingly the "excitation" of the energies of motion and gravitation. It can 

be shown that such situation results in a reduction of the characteristic frequencies of atomic 

oscillators, i.e. the frequency of atomic oscillators moving at velocity β = v/c is reduced by 

factor 

2 

1− β as 

f f β 

2 

I = 0 1− 

(8) 

where f0 is the frequency of the oscillator at rest in the local energy frame. Equations (7) and 

(8) give direct physical meanings to the Lorentz factor - not as a correction of time coordinate 

but a factor reducing the internal energetic response of a moving object to the gravitation of

the total mass in space on the object. In terms of inertia this means that the buildup of kinetic 

energy when accelerating an object to a velocity in space involves the work done in reducing 

the gravitational energy due to all mass in space. 

Im 

R” 

FC=mv 2 /R” 

Fg =−GmM”/R” 2 

=−Eg/R” 

M” 

Figure 4. (a) As central motion relative 

to the center in the fourth dimension, 

motion in space reduces the gravitational 

effect of the total mass described 

by mass equivalence M" in the fourth 

dimension. 

v 

R" 

F"i(a) = χmradc 2 /R” 

v = c 

F"g = −χmradc 2 /R” 

Figure 4. (b) For an object moving at a 

velocity equal to the velocity of space 

in the fourth dimension the gravitational 

effect of the total mass in space 

is fully counterbalanced by the centrifugal 

acceleration. 

4 - The effect of mass centers on the local velocity of light 

The idealized picture of completely symmetric spherical space assumes that mass is uniformly 

distributed all over the space. When mass is cumulated into mass centers in space the 

conservation of total gravitational energy demands that the "smooth" surface of an ideal fourdimensional 

sphere is tilted to form dents in the fourth dimension around mass centers in 

space. In tilted space also the direction of the fourth dimension is turned relative to the 

direction of the expansion, accordingly, locally the velocity of space in the fourth dimension 

is reduced in proportion to the tilting (see Figure 5). 

In a local gravitational frame the famous equation E = mc 2 shall written in form 

c 

M 

homogeneous space 

φ 

c0 

dr 

φ 

dr0 

c0 

Eδ = c0δ mc 

(9) 

Figure 5. In the vicinity of a mass center 

local space is tilted by angle φ relative to 

homogeneous space moving at velocity c0. 

Accordingly, the velocity of space, c, in the 

local fourth dimension is c = c0 cosφ . 

207

208 

where c is the local velocity of light in the gravitational state denoted by the gravitational 

factor δ and c0δ is the velocity of light outside the local gravitational frame, in the apparent 

homogeneous space of the local frame. The local velocity of light can be expressed in terms 

of the local gravitational state as 

⎛ GM ⎞ ⎛ GM ⎞ 

c = c0δ cosφ = c0δ ( 1 − δ ) = c0δ ⎜ 

1− ⎟ c0δ 

1 2 

rc0c ⎟ 

≈ ⎜ − ⎟ 

(10) 

⎝ 0δ 

⎠ ⎝ rc ⎠ 

where φ is the tilting angle of local space and δ the gravitational factor as expressed in terms 

of the gravitational constant G, M the mass of the central mass of the gravitational frame at 

distance r from the location of the object studied. 

Factor mc in equation (9) has the meaning of momentum in the local fourth dimension. The 

kinetic energy of free fall in a local gravitational frame is gained against a release of the rest 

energy of the falling object through the reduction of the local velocity of light. 

As a consequence of the reduction of the momentum in the fourth dimension the locally 

obtainable maximum velocity in space, the local velocity of light, and the frequencies of 

internal atomic processes are reduced. Motion in space reduces the frequencies of internal 

atomic processes through the reduction of internal mass, mass centers in space reduce the 

frequencies through a reduced velocity of light in tilted space. Combining effects of motion 

on the internal mass of an object and the effect of reduction of local velocity of light, the 

characteristic frequencies of an atomic oscillator moving at velocity β in gravitational state δ 

in a local gravitational frame can be expressed as 

2 

( 1 ) 1 

f = f − − (11) 

δ , β 0 δ ,0 δ β 

where frequency f0δ,β is the frequency of the oscillator at rest in the apparent homogeneous 

space of the local gravitational frame. 

Local tilting of space and the reduction of the velocity of light near mass centers have several 

interesting consequences. Light or radio signal passing a mass center is delayed due to the 

lengthened path and reduced velocity. Also, the path is bent due to the local deformation of 

space. A further consequence of the local deformation of space is that the main axis of 

elliptical planetary orbits is subject to a rotation observed as a shift in the perihelion of the 

orbit. 

5 - The system of cascaded gravitational frames 

Real space consists of cascaded gravitational systems such as our planetary system in the 

solar system, the solar system in the Galaxy, and the Galaxy in the local galaxy group. 

Following the zero energy principle, in cascaded gravitational systems the local velocity of 

light can be related to the velocity of light in apparent homogeneous space around the local 

dent and, finally, to the expansion velocity of hypothetical homogeneous space in the fourth 

dimension (see Figure 6). This also means that in a gravitational frame like the Earth 

gravitational frame the zero reference for the local velocity of light is locked to the shape of 

the local dent, the zero reference follows the orbital motion of the Earth around the Sun, i.e. 

the reference at rest "the local ether" for the propagation of light in the Earth gravitational 

frame is the Earth centered non-rotating frame (or Earth Centered Inertial frame in the 

language of the general theory of relativity). Based on the present knowledge of the 

gravitational systems Earth is bound to (the Solar system, Milky way and the local galaxy 

group), the local velocity of light on the Earth is about 1/10 6 (one per million) lower than the 

velocity of light in hypothetical homogeneous space where all mass were uniformly 

distributed.

Im0δB 

MB 

the apparent homogeneous space 

of the MB frame 

Re0δ B Imδ B=Im0δ A 

Imδ A 

MA 

m 

the apparent homogeneous 

space of the MA frame 

Re0δ A 

Figure 6. Apparent homogeneous space of the MA frame around 

mass center MA follows the direction of space in the MB frame as 

it were without the MA center. 

The assumption we made of space as a closed surface of a four dimensional sphere 

contracting and expanding by maintaining zero total energy leads to a number of phenomena 

we are used to know as relativistic effects. As a major difference to the theory of relativity we 

do not need to use the coordinate quantities, distance and time as parameters to explain the 

phenomena. 

In dynamic space, the effects of motion and local gravitation on internal atomic processes like 

the ticking frequencies of atomic clocks can be understood as consequences of the motion and 

local gravitation on the energetic state of the objects. More than that, we can understand why 

the velocity of light is the maximum velocity obtainable in space and how the inertia of mass 

linked to the total mass in space. 

We do not need to assume that time were different due to gravitational field to understand the 

delay and bending of light near mass centers or the gravitational red- and blueshift of atomic 

clocks and electromagnetic radiation. We can honor the coordinate quantities as constant 

measures in all observations. The velocity of light is not a constant but a function of the local 

gravitational state. 

In a complete form, taking into account the cascaded gravitational frames the equation for the 

rest energy of an object shall be written as 

2 

0 ( 1 ) 

n 

i= 

0 

( 1 i ) 1 

2 

i 

Eδ = mc − δ ⎡ δ β ⎤ 

∏ − − 

⎢⎣ ⎥⎦ 

(12) 

where m is the mass of the object, c0 is the expansion velocity of space. Gravitational factors 

δi describe the effects of the gravitational states of each gravitational frame in its parent frame 

and factors βi = vi /ci the motions of the local frame in the parent frames. On the Earth, the 

local velocity of light can be estimated to be c ≈ 0.999999 c0. Taking into account the effects 

of the cascaded system of gravitational frames the frequency of atomic oscillators can be 

expressed as 

n 

2 

( 1 ) 1 

fδ , β = f0 

Π ⎡ − δ 

i 0 

i − β ⎤ 

= ⎢ i 

⎣ ⎥ 

(13) 

⎦ 

where f 0 is the frequency of the oscillator in hypothetical homogeneous [see equation (11) as 

reference]. 

209

210 

6 - Expansion of space occurs everywhere 

By linking the energies of motion and gravitation through the zero energy principle, the 

spherically expanding space allows (or demands) the expansion of space also to occur within 

local gravitational systems. In the Earth − Moon system this means that out of the 3.8 cm 

annual increase in the Earth to Moon distance 2.8 cm is due to the expansion of space and 

only 1 cm due to the tidal interaction. 

In cosmological scale the propagation of light follows a spiral path, characterized by equal 

velocities in the fourth dimension with the expansion of space and the propagation observed 

in space (see Figure 6). 

p=h0/λ ⋅c 

R4=R4(t) 

Figure 6. At cosmic distances the propagation 

path of light appears as a spiral in four 

dimensions. 

The precise geometry of space and the defined propagation path of light in spherical space 

allows the derivation of the Hubble law and the redshift versus magnitude dependence 

without arbitrary parameters needed in the standard cosmology model. The Hubble law 

obtains the forms 

D R D 

4 z = and v = c0 

1− 

D R4 R4 

where the optical distance of the object, D, is the integrated tangential component of the light 

path from the object to the observer, which is the distance traveled by light in space. 

Inherently, equation (14) is consistent with the definition of the redshift in the general theory 

of relativity. 

The energy flux of an object with redshift z can be expressed as 

F 

( obs ) 1 

= 2 F z z + 1 

( e) 

( ) 

corresponding to magnitude versus redshift relationship 

( ) 

(14) 

(15) 

m = m0 + 5log z + 2.5log z + 1 

(16) 

Equation (16) gives a perfect match to the observed redshift − magnitude dependence of 

supernovas as shown in Figure 7. Accordingly, recent confusion regarding the redshift versus 

magnitude observations becomes solved without any new assumption or parameter, the 

prediction derived from the dynamic spherical space is shown as the solid curve in Figure 7, 

also showing recently published observations on supernovas.

apparent magnitude 

26 

22 

18 

F/F0 = 1/[z 2 (1+z)] 

14 

0.01 0.1 redshift (z) 1 

Figure 7. Apparent magnitude as a 

function of redshift in the range 

z = 0.01 to 1. The dots show 

observations reported by Perlmutter 

et al. , Ref. [5]. 

7 - Doppler effect and gravitational redshift of electromagnetic radiation 

The combined gravitational shift of atomic oscillators and the Doppler effect of 

electromagnetic radiation in a particular gravitational frame has the form 

f = f 

( ) 

A B 

( GM r c ) 

( GM r c ) 

( 1 vˆ r ) 

( 1− 

β A vˆ A ⋅ rˆ 

) 

1− A 

2 

1− 2 

β A − β B B ⋅ ˆ 

B 

1− B 

2 

1− 

2 

β B 

Equation (17) can be derived from the classical Doppler effect by taking into account the 

effects of gravitation and motion on the frequencies of oscillators. 

In the general theory of relativity the Doppler equation corresponding to equation (17) has the 

form, Ref [3], 

f = f 

( ) 

A B 

B 

1− 2GM 

r c − β 

2 2 

A A 

1− 2GM 

r c − β 

2 2 

B B 

( 1− 

β B vˆ B ⋅ rˆ 

) 

( 1− 


) 

In the Earth gravitational frame the difference between equations (17) and (18) is too small to 

be detected (for example, in the famous Scout D experiment, Ref. [4], the difference between 

equations (17) and (18) is of the order 10 −18 . 

When related to the frequency of the transmitter, fA, equations (17) obtain the form of the 

classical Doppler equation 

f = f 

( ) 

A B 

A 

( 1− 

β B vˆ B ⋅ rˆ 

) 

( 1− 


) 

where the effect of the velocities of the transmitter and receiver βA and βB are velocities in the 

local rest frame. 

8 - Discussion 

The Dynamic Universe approach is an "energy based" description of observable reality 

instead of the "metrics based" description given by the theory of relativity. Unlike the theory 

of relativity, the Dynamic Universe is derived starting from structure and zero energy balance 

of whole space and then, by conserving the energy balance in the system, derived into local 

phenomena. Such approach relates all local phenomena to the energetic state of whole space, 

which can be found to result in the effects generally referred to as "relativistic effects". The 

DU approach re-establishes the classical meanings of time and distance, which as coordinate 

211 

(17) 

(18) 

(19)

212 

quantities, are not used as parameters in explaining observations. The DU approach gives 

precise predictions to phenomena covered by the theory of relativity and the standard 

cosmology model. In addition, the DU approach explains the origin of inertia and the Mach's 

principle, the nature of mass as the substance for the expression of energy, and the physical 

mechanisms of the effects of motion and gravitation on the frequencies of atomic oscillators. 

It also describes the buildup and release of the rest energy of matter in the contraction and 

expansion of space in the zero-energy process of spherical space from infinity in the past to 

infinity in the future, Ref. [2]. 

References 

[1] Einstein, A., Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, 

Sitzungsberichte der Preussischen Akad. d. Wissenschaften (1917) 

[2] Suntola, T., The Dynamic Universe, A New Perspective on Space and Relativity, Suntola 

Consulting Ltd., ISBN 951-97938-6-0 (2002), www.sci.fi/~suntola 

[3] Baker, M.L., Jr., Astrodynamics, Academic, New York (1967) 218 

[4] Vessot, R.F.C., Levine, M.W. et al., Phys. Rev. Letters, 45, 26 (1980) 2081 

[5] Perlmutter, S. et al., 1998 AAS Meeting Jan 1998, Washington DC 

Tuomo Suntola, Dr. Tech. 

Senior Scientific Advisor 

Fortum Corporation 

POB 100, 00048 FORTUM, Finland 

http://www.sci.fi/~suntola 

tuomo.suntola@fortum.com 

- - - - - 

Tuomo Suntola was born in Finland in 1943. Helsinki University of 

Technology, M. Sc. (1967), Ph. D. (1971), Scientist at State Research Centre, 

VTT, (1971-1973). Development of humidity sensor for Vaisala Oy (Humidity 

measuring instruments based on Humicapã sensors are still world market 

leaders in humidity sensing and monitoring). Chief Scientist Instrumentarium 

Oy/Lohja Corporation (1974-1987). Development of Atomic Layer Epitaxy, 

ALE, for manufacturing of electroluminescent thin films. Development of flat 

panel display product and production machinery, implementation of the 

technology into commercial activity. Managing director of Microchemistry Ltd, 

a research company in Neste Group (1987-1997). Development of solar cell 

technologies, extension of the use of Atomic Layer Epitaxy to the manufacturing 

of heterogeneous catalysts and a research tool for surface chemistry. Direction 

of the ALE technology and machinery to semiconductor applications, start up of 

business activity on Atomic Layer Deposition ALD for semiconductor 

manufacturers. Microchemistry Ltd's ALD business was merged into ASM

(Holland) in 1998. ALD technology has become a main stream technology for 

nanoscale semiconductor devices, (e.g. Applied Materials, Veeco, IPS, Genus). 

Senior Scientific Advisor and R&D Fellow, Fortum Corporation since 1997. 

Docent at Physics Department of Tampere University of Technology since 1975. 

Lectures on semiconductor physics 1972-78. Member of the Finnish Academy of 

Technology, TTA since 1983, board member 1988-93. Board member of the 

Mentor Program since 1999. Deputy board member in the Foundation of 

Technology in Finland since 1991. He holds patents and has published widely 

in the fields of material science, thin film technology, and surface chemistry. 

[See even the presentation of Dr. Suntola's book which is published in the first 

Section of this same number of Episteme] 

213

214 

Introduction 

Nature of Energy, Light, and Einstein's 

Light-Principle in Special Theory of Relativity 

(Paramahamsa Tewari, B. Sc. Engg.) * 

With the discovery of positron (1932), a unique phenomenon of annihilation of matter 

(electron and positron) was observed. In this process, both the particles lose their mass, 

charge, and existence, producing annihilation-radiation, that is, light. An essential fact 

revealed through annihilation is that light is the last phenomenon of energy-effect before 

electron and positron lose their basic properties. Therefore, in order to understand the nature 

of light produced, an exact knowledge on the nature of charge and mass, and their distribution 

in the structure of the particles is essential, so as to gain deeper insight of the physical process 

of conversion of mass and charge into light, and to avoid any erroneous conclusion in the 

interpretation of this phenomenon. Further, light produced by thermal radiation is also 

considered emitted by orbital electrons in atoms, though, the structure of the electrons is not 

affected in this process. Light is some form of energy; and energy, from mass-energy 

equation, is expected to have proportionate mass. Therefore, understanding the origin of mass 

and charge in the electron structure is the first crucial step in determining the real nature of 

energy and the annihilation-light. 

Apart from the basic properties of light, that is energy-content, wavelength and frequency, the 

process of its transmission in absolute vacuum is equally important. In post relativity era, 

space medium, when considered without electromagnetic fields, is believed an empty 

extension (void) and, yet, light is supposed to be somehow transmitted in this void of 

nothingness. Such an assumption presupposes that the properties of mass, inertia, charge, and 

energy, possessed by matter, are independent of spatial reality, that is, the energy constituting 

matter is not derived from space. But, a comprehensive theory that explains creation of mass, 

inertia, charge and energy, say, in electron-structure; and that pinpoints the very source of 

universal energy and its fundamental nature, is nonexistent in contemporary physics. 

In this article, creation of electron from space, postulated to be fluid and nonmaterial in my 

earlier works [1,2,3] has been first described; mass, charge, energy and basic fields in the 

electron structure and the medium of space are briefly analyzed and defined; and from the 

observed conversion of mass and charge in the annihilation process, nature of the 

annihilation-light has been determined. With the new physical picture of the annihilationlight, 

shown here to be the most fundamental light-effect in the universe, conceptual errors in 

the current understanding of the nature of light have been pinpointed. Einstein's lightprinciple 

in special theory of relativity has been examined for its correctness. 

Mass and Charge of Electron 

The property of mass of electron has been shown [1,2,3] to originate from the medium of 

space - postulated to be a nonmaterial medium with fluidity, incompressibility, continuity, 

homogeneity, mass-less ness, and zero-viscosity. That is, none of the properties, except 

fluidity, possessed by matter, exists in space. The only property of the fluid-medium of space 

(hereafter, referred as "space") is a limit to its velocity of flow and also to the angular velocity 

of rotation (ω) when circulating in a vortex. Fig.1 shows an irrotational vortex of space which 

has opened up at the center into a dynamically stable spherical void due to the postulated 

limiting ω, which is also the maximum velocity gradient, c/re, where "c" is the limiting flow

of space (maximum velocity-field), and "re" is the radius of the spherical interface enclosing 

the void. 

A diametrical cross section of the vortex (Fig.2) shows an inward maximum accelerationfield 

c 2 /re; this inward radial acceleration of space prevents dilation of the vortex and results in 

dynamic stability. The vortex described above is the electron structure. 

215

216 

The mass of electron is defined as volume-integral of space-velocity within the interface, just 

prior to the creation of electron; and can be derived (Fig. 1) considering a differential element 

of volume: dV = (π re 2 sin 2 θ) re dθ, since, space, equivalent to this volume, is forced out at 

velocity ω re sin θ during the creation of void when the speed of space in circulation reaches 

c, and angular velocity becomes ω. Mass of the elemental volume from above definition: dM 

= dV (ω re sin θ). Integral over the spherical volume within the interface gives, θ varying from 

0 to π 

me = (4π/3) re 3 c. (1) 

Mass has the dimension of [L 4 / T], and in CGS unit, it has been derived 3 : 

gram = 8.6 x 10 6 cm 4 /s. (2) 

Charge of electron is defined as the surface integral of space velocity on the spherical 

interface. Considering the elemental surface: dA= (2π re sinθ) re dθ, and charge on it: dQ = 

[(2π re sin θ) re dθ] ω re sin θ. Integrating over the whole interface, θ varying from 0 to π 

qe = (π/4) 4π re 2 c. (3) 

The charge has the dimension of [L 3 /T], and in CGS unit, 

CGSE = cm 3 /s. (4) 

With the use of (1), inward gravitational field (g) due to mass of electron at a radial distance r 

from the electron center has been derived 1,2,3

where k is 1/s 2 . 

g = (k/4πc) me / r 2 (5) 

With the use of (4), inward electric field (E) due to charge of electron at a radial distance r 

from the electron center has been derived 1,2,3 

E = -c 2 re 2 sin 2 θ / 2 r 2 . (6) 

Basic constants derived [1,2,3] are: Coulomb's constant, with electron as the unit of charge, is 

c/4π; dialectic constant of vacuum: ∈ = π / 2c; permeability-constant: μ0 = 2 / πc; electron's 

intrinsic angular momentum: L= (4/5) me c re; magnetic moment of electron: μ = (3/4) qe c re; 

Planck constant 1 for electron: h = (4/5) me c re. All these constants show proportionality to c, 

which quantitatively proves the postulated universality of c. 

Energy in Electron Structure 

Qualitatively, most basic state of universal energy is defined as "dynamic space in linear, 

accelerating, or circulating motion". 

The central void at the electron center is field-less and hence energy-less (Fig. 3a), whereas, 

as per the modern concept of electron - a point-mass and a point-charge - energy is distributed 

all the way up to the center (3b). 

The latter leads to the following serious problems: 

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218 

(a) energy in the electrostatic field of an electron becomes infinite at r = 0; 

(b) electron can emit and absorb energy. 

With the central void at the electron center, minimum value of r is re, and not 0; thus avoiding 

the integration of energy to reach an infinite value. Also, the energy-less center of electron 

cannot emit energy (photons); neither can it absorb energy, because, the interface of the 

electron with space-circulation at limiting speed, is impervious to all external interactions. 

The distribution of energy in the structure of a stationary electron starts from its interface and 

spreads throughout the universal space as gravity and electrostatic fields. During motion, 

acceleration, or rotation of electron around a center, relative to space, the gravitational and the 

electrostatic energy is seen [1,2,3] as electromagnetic energy or light (discussed later). 

Energy of Electron Creation 

Refer to Fig. 1. As explained earlier, a differential element of disc with volume: dV= π re 2 sin 2 

θ re dθ, has mass: dM = dV (ω re sinθ) = c π re 3 sin 3 θ dθ. The area at the interface of the 

elemental disc, 2π re sin θ re dθ, is subjected at each point to an inward radial acceleration 

field: af = (ω re sin θ) 2 / re sinθ = c 2 sin θ / re, where c = ω re. Supposing, the elemental disc 

collapses under the above inward acceleration-field to zero radius. The work done in this 

process will be: 

dE = dM af (re sin θ) 

= (c π re 3 sin 3 θ dθ) (c 2 sin θ / re) (re sinθ) = π re 3 c 3 sin 5 θ dθ. 

Integrating over the whole interface where θ varies from 0 to π 

E = (4/5) [(4π/3) re 3 c] c 2 , 

which, from mass-equation (1), becomes 

E = (4/5) me c 2 . (7) 

The 'work done' is the energy produced due to the displacement of the inward acceleration 

field from the interface to its center; this energy fills up the void, and should be equal to the 

energy required to create the void at the electron center. Thus, the energy required for the 

creation of electron from (7) is (4/5) me c 2 . 

Medium of Space, and its States 

Fig. 4(a) shows the most basic state of space-a static non-viscous fluid, incompressible, 

continuous and mass less. This is the most basic substratum of the universe, existing eternally. 

In Fig. 4(b) dynamic space is depicted. The flow-velocity of space is termed as velocity-fieldthe 

most fundamental field, which produces all energy fields (Fig. 4c), that is, gravity, 

electrostatic, magnetic, nuclear, and electromagnetic. The solar system exists in the universal 

dynamic space with fields and matter (Fig. 4c) created by the galaxy.

Creation of Electron 

The process of creation 2 of electron is shown in Fig. 5. 

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220 

In a space vortex (irrotational) when the angular velocity of rotation reaches the limiting ω, 

space breaks down into a spherical void due to being subject to the highest velocity gradient 

c/re, as discussed before. The radial outward flow of space, creating the interface, takes place 

at the limiting speed c, and halted after a time interval re /c, because that is the maximum 

volume of the spherical void possible for dynamical stability. Since the fluid space is 

incompressible, a spherical shell of radial width re, with outward pressure 3 in it, is created 

concentric with the interface (void), and is transmitted in the universal space at the limiting 

speed c, thus energizing the universe gravitationally. Due to the incompressibility of space, at 

a sphere of radius r, there will be actual displacement (radial) of space points (Fig. 6), which 

will create gravitational potential there proportionately. This potential will exist as long as the 

void exists at the electron center.

Annihilation Process 

There can be two electron vortices, with their velocity fields (in between them), opposite in 

direction, or in the same direction (Fig. 7a,b). 

There is only one fundamental particle [1,2,3], electron, which, looked from the other end of 

its axis, is a positron. Positive and negative charges are relative concepts. Electrical attraction 

221

222 

between an electron and a positron can be determined from (6) from which Coulomb's 

equation has been derived [1,2,3]. Qualitatively, the unidirectional velocity fields between an 

electron and a positron (Fig.7a) cause attractive electrical force drawing the particles together. 

In this process, the spherical interfaces of the particles can be imagined to finally superpose 

each other (Fig. 7c); thus stopping the oppositely directed space-circulations around their 

interfaces, and leading to the collapse of their central voids and annihilation of the particles. 

Consequently, as experimentally observed, light is produced. 

Fundamental Nature of Light 

It is evident that the void-interiors of the electron and positron, being energy-less, cannot emit 

any kind of energy (photon). The energy (velocity and acceleration fields) in the vortex 

structure of these particles pervades the whole universal space before annihilation; and 

following annihilation, the process of dying (reducing to zero) of the electromagnetic and 

gravitational potentials of the particles, initiating from their superposed interfaces, is seen as a 

pulse, or a single shell of light (Fig.8). 

When the interfaces of the particles superpose, there is only one spherical-void common to 

both; space flows radially at its maximum speed c into the void (Fig. 8); the duration of 

collapse, Δt = re / c. During this time interval, a shell of radial width, Δt c, that is, (re/c) c = re, 

is formed, and transmitted outward at speed c relative to space. The transmission of the shell 

is a process that de-energizes the space medium, erasing for all the time the gravitational and 

electrostatic potentials that were created at the time of creation of the (now non existent) 

electron and positron. The spherical shell produced due to dying of potentials-a process of deenergizing 

of space substratum consequent to the electron/positron annihilation-is the 

fundamental light. 

The gravitational field of electron is radial and uniformly distributed on its interface (Fig.9).

Therefore, the effect of light due to dying-gravitational-potential will have spherical 

symmetry. Whereas, the maximum electrostatic fields of these particles, is confined mostly to 

the diametrical plane at right angles to the axis of rotation (Fig.1); hence, maximum effect of 

light produced due to dying-electrostatic-potential will be confined within this plane. 

Wavelength and Frequency 

The wavelength of annihilation light (Fig.8) is equal to the electron radius. This light, with a 

single shell, cannot have the concept of frequency applicable to it. In case there are several 

annihilations taking place at a point, one after the other, without absolutely any time gap 

between the successive annihilations, then the frequency can be defined as the nos. of shells 

formed in unit time. Also, if the time for the formation of a single shell is Δt, then frequency f 

can be defined as: f = 1/Δt, keeping in mind, however, that this mathematical operation does 

not mean that the single light-shell has the property of frequency as per the conventional 

definition of frequency mentioned above. When light is produced due to atomic vibration 

(Fig.10), the frequency of light is determined by the nos. of atomic oscillations in unit time, 

assuming that the oscillations are continuous [2,3]. 

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Fig. 10 

The shell of light produced in annihilation, as well as a light -shell produced in atomic 

vibration have their centers fixed with the source (assumed stationary relative to space), while 

the wave front with a fixed wavelength (radial) is transmitted at speed c relative to space. In

the modern concept of light, the photon, postulated as a "packet of energy", is understood to 

have its center moving at speed of light relative to the source. It is not clear as to how the 

concept of frequency is related with a photon; though, physical picture is not possible, 

perhaps, a photon wobbles transverse to its line of motion, a number of times say, f, in a unit 

time, while traversing at speed c relative to the source. And, if that is the possible physical 

picture, then, "f" will have meaning for a photon (with indivisible energy quantum, hf) only 

after it has traveled for a unit time having wobbled f times! Again, the specific characteristic 

of a photon that determines its wavelength remains obscure. Though, it is well known that the 

classical concepts of wavelength and frequency are inapplicable for a photon in quantum 

physics, in the absence of a physical picture, there occurs a serious conceptual error, leading 

to a mathematical discrepancy in the very basic relationship between energy and frequency in 

the Planck energy equation as pointed out below. 

Planck Energy Equation 

Based on the concepts of Maxwell-Hertz, that electromagnetic (light) energy is given off from 

electrical oscillators, Planck believed that the orbiting electrons inside the atoms of a glowing 

solid-emitter radiated electromagnetic waves in different quantities, the frequency being 

determined by the vibration of the oscillator. The classical picture was revised by Planck 

based on his observed experimental fact when he assumed that an oscillator, at any instant, 

could have its total energy (potential, kinetic) only as an integral multiple of the energy 

quantity hf, where h is a universal constant (experimentally determined) and f is the frequency 

of vibration of the oscillator. Thus, the light energy can be absorbed or emitted in an 

indivisible quantum of magnitude hf. Planck energy equation is: 

It can be also written as 

E = h f. (8) 

E / f = h. (9) 

It is seen from (9) that "h" is the energy associated with one oscillation of the vibrator, on the 

following basis. 

It has been shown elsewhere [2,3] that a time varying gravitational potential at the surface of 

an atom produces light (Fig. 10); and that one shell of light produced due to atomic vibration 

has energy close to the experimentally determined value of h. Though Planck believed that the 

oscillator emits its own energy (kinetic, potential) possessed by it structurally, by deriving h 

from the varying gravitational potential in space external to the oscillating atom (Fig.10), a 

new fact has been brought to light: that the "least energy" produced (in each shell of light) is " 

E / f". Therefore, the quantity "h f" is, actually, the energy contained in f-numbers of 

successive light- shells produced by the oscillator in unit time, and cannot be an "indivisible 

quantum" of light-energy available at an instant, which Planck assumed. 

Further, as stated earlier, the structures of the oscillators, either electrons or atoms, are not 

suited to absorb or emit energy-a serious misconception continuing since Maxwell's 

theoretical conclusion that oscillations of electric current leads to a loss of energy from the 

system in the form of electromagnetic waves. The modern concept that heat and light energy 

get detached from the oscillating atoms is corroborated in the following: " 4 …the collisions 

between atoms and molecules in a gas are said to be perfectly elastic. Although this is an 

excellent approximation, even such collisions are not perfectly elastic; otherwise one could 

not understand how energy in the form of light or heat radiation could come out of gas." But 

such a concept of energy absorption and emission is basically wrong with the vortex structure 

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of electron and atom. Even in 'oscillating electric current', the electrons cannot part with their 

structural energy (the velocity field in the vortex). 

The intrinsic angular momentum of electron derived from its vortex structure: L = (4/5) me c 

re; substituting the values of me and re, it is found [2,3] to be 7.5 times less than the Planck 

constant. However, for an average atom, Planck constant computed is close to the 

experimentally determined value [2,3]. 

The dimensions of h are that of angular momentum-same as the angular momentum of 

electron given above. Though, the angular momentum of electron is 7.5 times smaller than the 

accepted value of the Planck constant, the nearness of the two values may lead to a guess that 

the orbital electrons in the atoms are indeed the electric oscillators that produce light, as 

imagined by Planck and others, and as is also the prevalent concept. In this conjecture, 

however, following difficulty arises. 

An atom shows overall electrical neutrality in the region beyond the orbital electrons, where 

only the gravitational field of the atom should exist. On account of this, h has been computed 

theoretically with the considerations of the time-varying potential of gravitation alone [2,3]. 

This is not to say that a charged atom will not produce light; rather the value of h obtained 

from an assembly of charged oscillating atoms should be different, and so also the nature of 

light (frequency, wavelength) produced. 

Since the structure of light is shown to consist of successive shells, it can be said that light 

energy exists in quanta, where quanta is defined as "energy in each shell"; whereas, the 

kinetic energy of a moving body, which is proportional to the velocity of the body that can 

continuously vary, can not have quanta of energy. Any generalization coming out of Planck 

energy equation, and leading to the concept that all forms of energy occur in quanta, is 

therefore erroneous. 

Black Body Radiation 

In a hollow cavity, the equilibrium distribution of electromagnetic radiation energy, 

experimentally obtained, shows that at low frequency the energy is proportional to f 2, while at 

high frequency there is an exponential drop. Whereas, the theoretical energy distribution as 

per Rayleigh-Jeans law gives excessive energy for higher frequency, such that if integrated 

over all frequencies the total energy becomes infinite. Though, classical mechanics places no 

limit to the frequency of the mechanical oscillators (atoms), a limit to the oscillator's 

frequency is imposed by the motion of the fluid-space submerging the atomic vortices 

(oscillators). The displacement of the atoms from their mean positions displaces space, which 

has a limiting speed c. If an average radius of atoms is taken as taken as 1.5 x 10 -8 cm, the 

displacement of an atom on either side of its mean position up to a length equal to the radius 

will involve total displacement relative to space as 3x10 -8 cm. Time required for the fluid 

space to move up to this length at its maximum speed is: 3x10 -8 cm/(3x10 10 cm/s) = 10 -8 s. The 

nos. of light shells produced in one second due to this atomic oscillation will be 10 18 /s, which 

is the frequency of the light produced. Thus, maximum frequency of the oscillators in thermal 

radiation, excluding X-rays and gamma, should be limited to about 10 18 /s. It can therefore be 

inferred that the exponential fall of energy distribution in cavity at higher frequencies is due 

to the reaction from space at higher oscillation frequencies. The classical concept that to 

determine the total energy within a cavity (black body radiation), integral has to extend over 

all the frequencies is based on a misconception that atoms oscillate in the void ness (reaction 

less) of space and hence there can be no limit to their frequency of oscillation. 

Explaining Photoelectric Effect - Einstein's Error 

In the vortex structure of atom (Fig.11), the vortices of the orbital electrons, interlocked with 

the velocity fields of the atomic vortex, are carried round the nucleus as explained earlier.

As is well known, the outer orbital electrons, if interacted with light of appropriate 

wavelength, are released in photoelectric effect. It is now believed that the photoelectrons 

absorb energy from the incident light for their release, and also for the kinetic energy that 

they possess. On this phenomenon, the following new aspects are to be taken into account. 

As stated before, absorption of energy by an electron is, structurally, impossible. The orbital 

electron, already in circulating motion, possesses kinetic energy due to the velocity field of 

the atomic vortex. This energy is computed: The nuclear radius of an average atom is, r n = 

2.37 x 10 -9 cm. Like an electron, the nucleus too has its axis of rotation and, hence, the 

maximum electrostatic field is confined in a circular vortex in a plane (more or less), at right 

angles to the axis of rotation. In the irrotational vortex, space-circulation velocity falls 

inversely as the radius of rotation. In the electron vortex, in the diametrical plane transverse to 

the axis of rotation, c re = constant. Applying this relationship also on the nuclear surface, 

c re = un rn (10) 

where un is the maximum tangential velocity of space on the nuclear surface in the 

diametrical plane at right angles to the axis of rotation. Substituting in (10) the known values 

of c, re, and rn = 2.37 x 10 -9 cm, we have 

un = (3x10 10 ) 4x10 -11 / 2.37x10 -9 = 5x10 8 cm/s. (11) 

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This velocity, as stated above, falls in the atomic vortex (around the nucleus) inversely as the 

radius of space rotation. Assuming the radius of rotation of the outermost orbital electron to 

be 10 -8 cm, the space circulation-speed, which is also the tangential-velocity of the orbital 

electron, will be 

v = un (2.37x10 -9 cm) / 10 -8 cm =(5x10 8 cm/s) 2.37x10 -1 =1.2x10 8 cm/s. (12) 

The kinetic energy of the orbital electron is 

E kin = (1/2) me v 2 = (1/2) 10 -27 (1.2x10 8 ) 2 = 7.2X10 -12 erg. (13) 

The experiments show that the kinetic energy of the photoelectrons is about 8x10 -12 ergs, 

which is so very close to the value obtained above (13). It is thus seen that Einstein mistook 

the source of the kinetic energy of the photoelectron, thinking that it came from the incident 

light; whereas, the reality is that the velocity field in the atomic vortex projects the electron 

after the incident light has triggered its release, as explained below. 

Production of light due to oscillation of an atom has been mentioned before (Fig.10). We shall 

analyze here the displacement of an atom during its oscillation, and the radial flow of the 

surrounding space. An atomic nucleus, composed of independent electronic voids, closely 

packed, approximates to a "spherical hole" in space, central with the atom. The atom, during 

displacement equal to its diameter, leaves a "hole" in its previous location. This "hole" is 

filled due to radial flow of space at speed c, through the light's first wavelength λ, which gets 

formed. The time taken for this flow across the wavelength is λ/c; and the acceleration of 

space is c / (λ/c), which is c 2 / λ. Each successive wavelength, formed due to the oscillations of 

the atom, possesses the above inward acceleration-field across it (radial). Now suppose that 

the spherical wave front of one of these shells, during its transmission, meets an orbital 

electron of an atom. The orbital velocity v of this electron, is derived from the atomic vortex 

which subjects it to an inward acceleration v 2 / r, where r is the radius of its rotation. The 

electron is held by electrical force, created by the above inward acceleration towards the 

nuclear center. The acceleration field c 2 /λ, within the wavelength of the light shell that meets 

the orbital electron of the atom, is also inward, that is, towards the light source. For the 

electron to be released from the atomic vortex, the above two acceleration fields must be 

equal and opposite. Thus, 

c 2 / λ = v 2 / r (14) 

Or λ = c 2 r / v 2 . (15) 

Substituting the values: v = 1.2 x 10 8 cm/s obtained above (12); r = 10 -8 cm; c = 3x10 10 cm, 

the value of λ comes to, 6.25x10 -4 cm, which corresponds to the cutoff frequency of, 3 x 10 10 / 

6.25x10 -4 , that is, 0.48 x 10 14 cycles/s. (For metallic sodium, the threshold frequency is about 

5x10 14 sec -1 ). Considering the approximate nature of the assumptions on the orbital radius of 

electron, and the radius of an average size of nucleus, with which the space-circulation 

velocity around the nucleus and the orbital velocity of the electron were calculated; any better 

result from (15) to conform to the experimentally obtained value of threshold frequency is 

unlikely. For, the orbital radius of the electron, if supposed to be 10 -9 cm, rather than 10 -8 cm, 

the thresh hold frequency calculated from (15) will be closer to the experimental value. 

The additional information given by (15) is as follows. In atomic vortex, the velocity field 

falls inversely from the nucleus center; and therefore, the inner orbital electrons will have 

higher speed of rotation. On release by the incident light shell, these electrons will possess 

higher kinetic energy. It is seen from (15) that for higher value of the electron's speed v, the 

wavelength λ is smaller. It is thus concluded that with higher frequency of the incident light,

the photoelectrons released will show higher kinetic energy. This is an experimentally 

observed fact. 

The above analysis shows that the concept of the photon-nature of light, with an indivisible 

quanta of energy possessed by each photon, is a case of the most serious misconception, 

which led Einstein (who was a believer in the emptiness of space, as evident from the 

formulation of special theory of relativity) to wrongly treat light-energy, hf, as the 

instantaneous value (when in reality, this energy is produced and accumulated in unit time); 

because this way, the kinetic energy of the photoelectrons, as observed experimentally, could 

be explained without going deeper into the structure of the atom (that became known later 

about 1912 through Rutherford's experiments) to determine whether the photoelectrons have 

any other source in the atomic structure that imparts kinetic energy to them at the time of their 

ejection from the atoms. 

Though, Planck integrated together the energy of f nos. of shells erroneously, he still believed 

that light energy is distributed uniformly over an expanding set of wave fronts. In contrast, 

Einstein conceptualized that the energy of light is not distributed evenly over the whole wave 

front, as the classical picture demanded; rather it is concentrated or localized in discrete small 

regions. With the help of both these energy integration and concentration operations, the right 

order of magnitude of the kinetic energy of the photoelectrons, as observed experimentally, 

could be achieved at an instant in the quantity hf . 

For better understanding of the physical significance of the "indivisible quanta", we take the 

following example: Consider the case of a light source producing successive spherical wave 

pulses or spherical shells of light with frequency f, say 10 15 /s and wavelength 3x10 -5 cm. In 

one second, the energy produced by f nos. of shells will be hf, that is 6.62x10 -27 erg s x 10 15 /s 

= 6.62x10 -12 erg. Now, if it is desired to make the energy "hf" indivisible, then the independent 

shells produced successively in one second become indistinguishable, and the new imaginary 

wavelength of this light will become: λf = (3x10 -5 ) cm x 10 15 = 3x10 10 cm; while the 

frequency will be one, that is, only one wavelength of this large width of 3x10 10 cm will be 

produced in one second. The quantum physics will accept the energy of this new shell of light 

as calculated above, but not the new wavelength and frequency. It will accept the energy 

content of this new shell of light for explaining the photoelectric effect; and will reject the 

wavelength and frequency because the hidden inconsistencies in the photon model will come 

to the fore. 

Without any physical picture, clarity and meaningful explanations, some of these ambiguous 

conceptions on the fundamental nature of light laid foundation to quantum physics. 

Shortest Wavelength of Light 

As is known, in positronium, the electron and positron circle each other, till annihilation; this 

happens due to interaction of their vortices. At the final instant preceding annihilation, the 

rotation of the particles will reach the limiting speed c, because this is the speed that space has 

on the interfaces of the particles. In (15) the value of v will be equal to c. Also the distance 

between the centers of the particles being 2re, the value of r in (15) will be 2re. Substituting 

these values in (15), the shortest possible wavelength of light is 

λs = c 2 (2re) / c 2 = 2 re = 2 (4 x 10 -11 cm)= 8 x 10 -11 cm. (16) 

The shortest wavelength of light in the universe is produced consequent to the annihilation of 

electron and positron. 

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Interaction of X-rays with Atoms 

High-speed electrons, projected inside a vacuum tube and stopped by its walls produce Xrays. 

Here, each electron on impact and almost instantaneous-rebound leaves a "spherical 

hole" of the size of electron-void at the point of its contact with the wall, to be filled in with 

the space flowing nearly at speed c. This process is somewhat similar to the light produced 

during annihilation because, here too, the potentials in space associated with the electron at 

the instant of impact, die away, producing (which is seen as) X-rays. From each point of 

electron's contact with the wall, a spherical shell of light expanding at speed c will arise. 

Though the energy distribution on the wave front of the shell will fall inversely as the square 

of the radius of the expanding shell; yet, this shell after transmitting for some distance and 

with depleted energy-density on its wave front, on meeting an atom of a metal, releases an 

electron possessing kinetic energy almost equal to the kinetic energy of the first electron that 

produced the X-ray pulse. Indeed, the principle of energy conservation cannot explain this 

phenomenon because the same is not relevant here. Recognizing that light has the nature of 

successive shells, and in each shell, across the wavelength, exists an "acceleration field" of 

constant magnitude independent of the energy density in the wave front; the release of the 

electron, as discussed earlier in the case of the photoelectric effect, is attributable to this 

acceleration field, rather than to the energy density in the X-ray's wave front. If however, the 

explanation is sought with the idea of energy exchange between the X-ray and the ejected 

electron, this effect is most puzzling. In the words of Sir William Bragg: 'It is as if one 

dropped a plank into the sea from a height of 100 feet, and found that the spreading ripple was 

able, after traveling 1000 miles and becoming infinitesimal in comparison with the original 

amount, to act upon a wooden ship in such a way that a plank of that ship flew out of its place 

to a height of 100 feet.' Yet this effect was not utilized to support the wave nature of light. It 

was argued that the X-rays when passed through a gas, ionize only few molecules, and had 

the rays had the wave-property many more molecules should be ionized since the wave will 

meet all the molecules. This argument does not hold good with the shell nature of light; 

because, the acceleration-field in the X-ray shell has to be in opposition to the acceleration 

field of the orbital electron, that is, both the opposing acceleration fields must be in line for 

effective nullification of the electron's bond in the atomic vortex; which requires that the 

orbital electron, at the instant when it meets the light-shell (wave front), should be moving 

tangential to it. Obviously, such a disposition of the light shell and the electron can be only in 

rare encounters and, hence, the numbers of the ionized molecules with one shell of light are 

expected to be limited. Thus it is seen that wave nature (or more precisely shell nature) of 

light can explain the ionization of gases by the X-rays satisfactorily. 

Bohr's Theory of Atomic Radiation 

As per classical electromagnetism, electric charges in acceleration will radiate energy, and 

hence the orbital electrons in the atom will lose energy due to which the emitted radiation 

should continuously change. However, the existence of sharp spectrum lines, are not in accord 

with the above prediction of the classical theory. As a solution to this problem, Bohr 

postulated different 'energy states' for an atom, such that when it falls from a higher to the 

lower energy state, it emits a photon with energy hf as per Planck's energy equation. 

As discussed before, in the space vortex structure of the atom and electron, the orbital 

electrons have already their fixed orbits. These electrons, carried by the vortex around the 

nucleus, can neither lose any energy (structural, potential or kinetic) due to orbital motion, nor 

change their orbits due to strong bond created by the velocity fields in between the nucleus 

and the electrons; because 'losing energy' by an electron signifies 'losing part of its vortex 

structure'. Further, these electrons make negligible contribution to the gravitational potential

of the atom that, as seen before, produces light due to its time variation [2,3]. Moreover, the 

basic error of Bohr lies in the application of the concept of Planck's indivisible energy quanta 

hf, in equating the same with the differential energy between the two energy states, composed 

of the sum of the kinetic energy of the orbital electron and the electrical potential energy of 

the proton-electron system; this is because, as mentioned before, the energy 'hf' is the quantity 

produced in a unit time, whereas, the energy released due to difference between two energy 

states of Bohr (even if the energy states are supposed to exist) is instantaneous. 

The Compton Effect 

Compton's experiments are said to confirm that photon is a concentrated bundle of energy. 

The experiment consisted of a beam of X-rays of known wavelength falling on graphite 

block. He measured the intensity of the scattered X-rays with respect to their wavelength. His 

conclusion is that the X-rays are not waves but several photons each with energy, "h f". A 

photon, in his experiment, collides with a "free" electron in the graphite block, like the 

collision of billiard balls. He treats in his mathematical analysis the "free electron" as the one, 

which is not bound with the atom of the graphite block, and is at rest. The collision of photon, 

assumed with a free electron, has the following implication. 

As is well known, X-rays can damage molecules and ionize gases; and like in photoelectric 

effect, will extract electrons bound in atoms. In the latter case, even if the outermost orbital 

electron is released, its own kinetic energy in the atomic vortex, as discussed before, will be 

about 10 -11 erg. By assuming the collision of the X-ray with a "stationary" electron, the initial 

kinetic energy of the electron prior to its release from the atom has been neglected. In any 

case, one cannot assume that the X-ray interacts only with a "free and motionless" electron. 

This kinetic energy of about 10 -11 erg will be larger for the inner orbital electrons, which rotate 

at greater speed. For, an inner orbital electron, with an average speed of three times the speed 

of the outermost electron, will increase the above kinetic energy to about 10 -10 erg. The 

quantity of energy, accounted in Compton's experiment against the kinetic energy of the recoil 

electron, is about the same order of magnitude; the concept behind is that the electron's recoil 

energy comes from the energy of the incident X-ray photon. If an X-ray of frequency 10 17 is 

used during the experiment, its energy as per Planck energy equation will be; hf = 6.6x10 -27 x 

10 17 = 6.62x 10 -10 erg, which is not far from the above figure of the kinetic energy of the 

ejected electron that it would have had in the vortex of the atom due to its rotation prior to the 

release. On account of neglecting the initial kinetic energy of the released electron, and 

matching this figure with the indivisible energy quanta, Compton's conclusions on the photon 

nature of X-rays become erroneous. The misinterpretation of Compton experiment - that Xrays 

is not of wave but photon-nature - led to a misleading picture of photon, both 

qualitatively and quantitatively. 

Another misconception in the above experiment is to believe that a bullet-like photon after 

striking an electron rebounds with a reduced frequency. Evidently Compton believed that a 

single photon has a frequency; that it oscillates, perhaps, across its line of motion. As stated 

earlier, frequency for light would be meaningful only if it is defined as the numbers of waves, 

photons or shells, produced per unit time. But, in case of a single photon, its wavelength is not 

known in a physical way except for the mathematical expression c / f, which leads to an 

imaginary large wavelength of 3 x10 10 cm, and a single frequency, described earlier. 

Compton's interpretation of his experiment together with the basic concept of relativity that 

all kinds of energy should have mass, made photon to possess hypothetical mass, momentum 

and inertia, while the most fundamental cause for its observed uniform motion at the constant 

speed of light remained unknown. 

From the relevant literature, it is seen that Compton's arguments to assign momentum to a 

photon run as follows: As per the classical wave theory of light, if a body fully absorbs the 

energy E from a parallel beam of light, then a linear momentum E/c is transferred to the body. 

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Based on this Compton, using Planck Energy equation E= h f, derives momentum, p, for an 

individual photon 

p = E / c = h f / c = h / λ. (17) 

But the "radiation pressure" on a body is otherwise explainable by the interaction of light shell 

with the gravity field of atom without absorption of light energy [4]. The classical physics is 

equally wrong in the concept of absorption and emission of light energy. Further, the use of 

Planck Energy equation makes a single photon to possess enormous energy, that is, 10 16 times 

the actual energy, if we use light of frequency 10 16 /s, because in reality, the energy of a single 

shell of light is, 6.62x10 -27 erg, as determined by Planck Constant. 

It is seen that the concept of "energy quanta" misguided Compton too (after Einstein and 

Bohr) in the interpretation of his experimental results. 

Constancy of the Speed of Light in Special Theory of Relativity 

Einstein postulated that different observers, moving at uniform velocities relative to each 

other and to a source of light, should find their measurements of the speed of light to be the 

same, provided they use a defined reflection procedure. Let us suppose that light consists of 

several particles of energy (energy-as conventionally interpreted today, such that there is little 

difference at quantum level between matter and energy) say, electrons with properties of mass 

and momentum, being projected from a light source at random in all directions so as to form a 

uniform spherical distribution. The observers can choose any one of these particles for the 

test. A particular observer, moving in the same direction as his chosen particle, will find its 

speed different from the measurement of the other observer who is moving against the motion 

of the particle, as per classical relativity. Similarly, if light is imagined as a swarm of photons, 

each with mass, momentum and kinetic energy (as believed to day), being emitted from the 

source at random without any constant interval between the two successive photons from the 

same atom, the Galilean relativity will indeed be applicable, similar to the above-cited 

example of the shower of electrons; and the two observers will measure different velocity for 

the same photon. But, as shown before, the structure of light is that of successive shells of 

mass-less energy with a constant time-interval between the fronts of the adjoining shells 

emitted from each atom, as determined by the atom's vibration. It's the time-interval of 

emission between the successive shells that determines the frequency of light; whereas, in the 

earlier example of the photon-model of light, the frequency of light is a mere mathematical 

quantity, E/h, having no relationship with the timings of emission of the two successive 

photons from the same atom. It is this haziness on the physical picture of the frequency and 

wavelength of a photon that leads to misinterpretations of the results of several experiments 

devised to check the above postulate of special relativity. The following simple analysis, 

almost trivial, supports constancy of light-speed measurements by different observers in 

relative uniform motion postulated by Einstein. 

In Fig.12 a source of light S (stationary with respect to space) from which a single spherical 

shell of light, produced consequent to the annihilation of an electron and a positron located in 

S, is transmitted at a constant speed c relative to the medium of space.

When the wave front of this shell meets the eye of an observer O, who is also stationary 

relative to the static space, let him record this instant assuming that his time is the same as that 

of any other observer (universal time) who may even be in motion relative to space. Let him 

also record the instant when the tail end of the shell passes away from him. If λ is the radial 

width of this light-shell (wave length of this shell of light is re, equal to the electron radius), 

then, from the ratio of λ and the time difference between the above two instants, say t1, the 

observer can calculate the speed of light from the relation 

c = λ (1/ t1) = λ / t1 (18) 

because, light-effect is postulated to be transmitted within the wavelength at constant speed c 

relative to the stationary space. Let S produce similar shells in succession such that the tail 

end of a shell coincides with the front of the following shell. If the nos. of shells received by 

O in unit time is f, he will calculate the distance covered by f nos. of shells in unit time as fλ, 

and time duration as ft1. With the ratio of these two quantities he will get the value of c, same 

as before. It is seen that the measurement of the light velocity across one wavelength is the 

same as across any of the successive wavelengths, provided the successive shells are similar 

with no interruptions in between. Now let O move with a uniform velocity v relative to the 

static space towards S, and record his timings across one shell. Because his velocity relative to 

the light shell now is v + c, time elapsed across one shell will be 

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t2 = λ / (c + v) (19) 

which is shorter than t1 measured earlier. The moving observer's eye interacts with the lighteffect 

within the approaching shell for a shorter duration now and, hence, he sees the 

wavelength as: 

λm = length through which the light effect is transmitted in time t2 

= c t2 = c λ/ (c + v). (20) 

The nos. of shells meeting the eye of the observer in unit time from (19) will be 

fm = 1 / t2 = 1 / [λ / (c + v)] = (c + v) / λ. (21) 

The moving observer can now determine the light speed from (20) and (21) as: 

Speed of light = λm fm = [c λ / (c + v)] (c + v) / λ = c. (22) 

From (18) and (22) it is seen that the observer, in moving as well as stationary states, finds 

that the speed of light is constant; and he reaches this conclusion without sacrificing the 

traditional concept of time. 

In the well-known experiment of Sagnac, a beam of light is split into two halves that travel 

around closed identical paths (reflected through mirrors) in opposite directions, and combined 

again in a detector to examine their interference pattern. The rotation of the apparatus 

produces shift in interference fringes as a function of the angular velocity. From (20) and (21) 

the reflecting mirrors along one path, rotating opposite to the light beam, will 'see' shorter 

wavelength and, proportionately, more of light-shells in unit time (frequency); while the 

mirrors rotating in the same direction as the light beam in the other path, will see longer 

wavelength and lesser nos. of the light-shells in the same time interval. On account of this, the 

wavelength as well as the frequency of the two beams reaching the detector will be different 

and, consequently, a shift in the interference fringes will occur. The product of the 

wavelength and the corresponding frequency for each path of the beam remaining the same, 

the mirrors placed in the two paths (observers) will find the same value of the velocity of 

light. Therefore, on rotation of the apparatus, appearance of the shift in the interference 

fringes in Sagnac's experiment should not be taken to mean that the light has different speeds 

(relative to space) along the two paths. 

The above interpretation of Sagnac experiment can be confirmed by increasing the nos. of the 

reflecting mirrors in each path; in which case the shift in the interference pattern should 

increase. 

The effect of light at a space point involves creation of light shell there from the already 

existing gravitational potential at that point, and its further transmission. This process repeats 

continuously as the light shell traverses each point in space. In the various experiments, set up 

to determine the light speed, only transmission aspect of light is taken into account, neglecting 

the process of the formation of the wavelength-the radial spread of light. That is why a "ray" 

of light, supposed to be continuously issuing forth from the source, is erroneously supposed to 

have instantaneous reflection from a mirror, and also instantaneous interaction with the eye of 

the observer; as if the wavelength is zero. Due to this misconception, it does not become 

apparent that a moving mirror reflects light of wavelength different from what it receives; and 

a moving observer too sees light of wavelength different from what he sees the same light to 

be, when stationary relative to space. 

Considering Einstein's treatment of special relativity, in the moving frame of reference (with 

respect to the stationary one) the reflecting mirror for the light signal located at the X- axis,

should also be moving at uniform velocity like the observer; the ray of light (replaced by 

annihilation light source, sending out light-shells one after the other) from the origin of the 

axes towards the +X axis in this frame of reference will be reflected by the moving mirror at 

an increased wavelength and decreased frequency, as shown above; and the observer, because 

of his motion opposite to the reflected ray, will find the wavelength of this light decreased 

and the frequency increased proportionately. In the stationary frame of reference, the 

stationary observer receives the reflected ray of the same wavelength as that of the ongoing 

ray. Thus, the observers in both the reference frames find the reflected ray having the same 

wavelength. Since their time is the same as the universal time, the nos. of shells per unit time, 

that is the frequency of the light ray, will be equal for both of them; hence, they get the same 

velocity of light irrespective of the motion of the moving observer. 

Fresenel, around 1820, postulated ether-drag in a moving material medium and increase in 

light velocity on account of this. His ether-drag is close to the velocity-field that gets 

associated with the moving molecules of matter-responsible for momentum [2,3]. 

Transmission of light along the motion of the medium will increase the wavelength, whereas, 

it's opposite direction will decrease it. As the respective frequencies also will proportionality 

change, the velocity of light in both the directions of light will remain the same. This subtle 

aspect, that despite changes in wavelengths the speed of light will be the same, had not been 

taken note of. Fizeau's experiment to measure speed of light in flowing water detected 

changes in speed because he based his conclusion on fringe-shift that will occur when unequal 

wavelengths are superposed. 

In the assumed void-ness in space of 20 th century physics, which provides no explanation to 

the creation of matter and fields, speed of light too has no medium, either for its creation or 

for transmission; in fact in a medium of nothing ness, matter and light cannot exist. Therefore, 

if the velocity of light measured by different observers in uniform relative motion with respect 

to each other has to be the same as postulated in special theory of relativity, the spatial-reality 

and shell-nature of light require recognition. With this proposed conceptual shift on the basic 

nature of the absolute vacuum and the nature of light, the relativistic concepts involving 

changes in length and time dependent on the motion of the observers will become redundant. 

Light speed is Independent of the Motion of the Source 

Consider an electron with its vortex structure. At any point in space, the velocity field and its 

radial distance from the vortex center will determine the magnitudes of its gravitational and 

electrostatic potentials [1,2.3]. As discussed earlier, a displacement of the electron's center 

will produce changes in the potentials; such changes will occur during electron's motion, 

either uniform are accelerating. The equalization of potentials due to self-action of space takes 

place at speed c with respect to space. Therefore, considering motion of electron at ordinary 

velocity, it can be assumed that the field structure of electron retains its original symmetry of 

distribution as before in static state. 

Let an electron and a positron, moving together at ordinary speed, under go annihilation. 

After collapse of the electron-void during annihilation, it loses mass, charge, and its existence; 

but, since the entire field distribution can not die instantly, the light shell produced continues 

its transmission relative to space with the point of annihilation as its center, independent of 

the speed of the particles prior to the instant of their annihilation. The point of annihilation 

and the surrounding field structure get fixed relative to space subsequent to the annihilation. 

On similar arguments it will be seen that light produced during atomic vibration is transmitted 

at speed c relative to space due to self-action of space to equalize the potential gradients. 

Further, since light shells are mass less entities, not emitted from within the electron or atom 

in the light source, they cannot carry the momentum of the source (light-producing particles, 

atoms and electrons in the constitution of the moving source of light). 

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Time Dilation 

The traditional concept of time was revised in special relativity. Though it has been shown 

above that with the shell-nature of light, the postulate of relativity on invariance of the speed 

of light in different frames of reference is supported, the following thought experiment reveals 

the fallacy of the often-quoted arguments 5 in support of time dilation. 

Fig.13 shows a platform in uniform motion with two observers A and B on it, and another 

stationary observer C on the ground. 

The relativist's view is that 'if the observer A lights a match-stick creating a flash, the observer 

B sitting opposite to him will think that the flash has directly come to him along the route PQ, 

whereas, the observer C will see the path along PQ 1 , since, during the time the flash has 

reached him, the platform has reached to a new location P 1 Q 1 R 1 S 1 . The path of the flash 

does not look the same to the two observers B and C. Since the flash is moving with A, it 

seems to B taking a longer path; and if the speed of light is to remain the same, the longer 

path must seem to take longer time: time must pass faster for C'. The misconception on the 

nature of light in the above statement is the presupposition that "the flash is moving with A". 

But is the flash really moving with the observer A? It has been shown above that the speed of 

light is independent of the motion of the source. Hence, the uniform motion of A cannot be 

imparted to the flash of light that he creates by striking a match. To further pinpoint the 

relativistic misconception on the motion of the flash along with A, let us suppose that A has 

with him an electron and a positron that undergo at some instant annihilation. As explained in 

the earlier section, the point of annihilation along with the field structure of the particles will

get fixed in space, while the observers A and B will move on. Supposing, B can see the point 

of annihilation P even prior to the instant when the light shell consequent to annihilation 

reaches him, he will see that P is shifting to his left due to his own motion (relative to space) 

to the right along with the platform; and by the time B reaches Q 1 , he will see that the light 

shell has taken the route PQ 1 to reach him; PQ 1 is the same length as seen by C. Therefore, the 

assumption of the relativist that the flash of light is moving with A is erroneous. Further, if the 

stationary observer C stands at D, where PQ 1 = PD, the light shell will reach both B and C at 

the same instant. 

It has been shown that the new concepts of 'time dilation' and 'simultaneity' are clearly 

superfluous in special theory of relativity, since, the invariance of the speed of light in 

different frames of reference in relative uniform motion follows otherwise from its very basic 

nature. 

Conclusion 

The ether was declared superfluous in special relativity without identifying and providing a 

substitute for a universal entity, which could create cosmic energy and matter. And in the 

absence of a basic theory of matter that alone can reveal the genesis of material properties 

(mass, inertia, charge), and the associated energy-fields including electromagnetic, any 

generalization that the laws of nature are invariant in respect of all inertial systems will 

certainly lead to a highly complex theorization, just as special relativity has come to be. But, 

despite that, discarding photon model of light, and with a nonmaterial fluid space, Einstein's 

Light-Principle-that the velocity of light is invariant in respect of all inertial system, is 

vindicated with the shell-nature of light, which light in reality is. 

Notes 

* Former Executive Director (Nuclear Projects), Nuclear Power Corporation, India. 

1 It has been shown that Planck constant is not a universal constant; and, theoretically, each atom has a 

Planck constant with slight difference in magnitude. Electron too has a Planck constant. 

2 Creation of electrons and positrons take place in the interiors of the stars and the galactic center, 

where space circulations reach the limiting speed. 

3 The word "pressure" is used in material fluid; for fluid-space another appropriate word is to be 

coined. 

4 The Feynman Lectures on physics, Feynman,Leighton, Sands; Vol. 1, page 10-9. 

5 "The Clock Paradox", Dr. J. Bronowski, Scientific American, February 1963, Vol. 208, No.2. pp. 

134-144. 

References 

1. P. Tewari, (1982), "Space is the Absolute Reality", Proceedings of ICSTA, International 

Publishers, East-West , Niederschocklstr, 62, 8044 Graz, Austria. 

2. P. Tewari, (1995), Beyond Matter - A Comprehensive Theory of the Material Universe, 

Editor: Wolfram Bahmann, Feyermuhler Str, 12, D-53894 Mechernich. 

3. P. Tewari, (1984, 1996), Beyond Matter, Crest Publishing House, G-2, Ansari Road, Darya 

Ganj, New Delhi - 110 002. 

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238 

4. P.Tewari, (2000), "Conceptual Error on the Fundamental Nature of Light-Phenomenon in 

classical electrodynamics, led to the Complexities in Quantum Physics", Journal of New 

Energy, Vol.5, No. 1.3084 E.3300 South, Salt Lake City, Utah 84109-2154. 

- - - - - 

Paramahamsa Tewari was born on January 6, 1937, and graduated in 

Electrical Engineering in 1958 from Banaras Engineering College, India, and 

held responsible positions in large engineering construction organizations, 

mostly in Nuclear Projects of the Department of Atomic Energy, India. He was 

also deputed abroad for a year at Douglas Point Nuclear Project, Canada. He 

retired in 1997 from his position as Executive Nuclear Director, Nuclear Power 

Corporation, Department of Atomic Energy, India, and is the former Project 

Director of the Kaiga Atomic Power Project. Fundamentals of physics attracted 

Tewari's imaginations right from the early school and college days. Over the 

last two decades his new ideas on the basic nature of space, energy, and matter 

have concretized into definite shape from which a new theory (Space Vortex 

Theory) has emerged. The theory reveals the most basic issue of relationship 

between space and matter precisely pinpointing that space is a more 

fundamental entity than matter. The physical significance of mass, inertia, 

gravitation, charge and light are revealed by extending the analysis in the 

theory beyond material properties and into the substratum of space, which 

again is broken down into fieldless voids, thus showing the limit to which a 

physical theory can possibly reach. The real universe is shown to be opposite to 

the current concepts of concrete-matter and empty space. The books that he has 

authored on Space Vortex Theory are: The Substantial Space and Void Nature 

of Elementary Material Particles (1977); Space Vortices of Energy and Matter 

(1978); The Origin of Electron's Mass, Charge Gravitational and 

Electromagnetic Fields from "Empty Space" (1982); Beyond Matter (1984). He 

has lectured as invited speaker in international conferences in Germany, USA, 

and Italy on the newly discovered phenomenon of Space Power Generation. For 

the practical demonstration of generation of electrical power from the medium 

of space, Tewari has built Space Power Generators that operate at over-unity 

efficiency, thereby showing that space medium indeed is the source of 

generation of basic forms of energy. 

http://www.tewari.org/ 

ptewari1@sancharnet.in 

[See even the presentation of Dr. Tewari's book which is published in the first 

Section of this same number of Episteme]

On the Space-Vortex Structure of Cosmic Bodies 

(Paramahamsa Tewari, B. Sc. Engg.) 

1. As per the recent recorded data on the solar wind close to the surface of the sun, the wind 

velocity varied from a minimum of about 380 km/s to the maximum of about 500 km/s, 

giving an average of 440 km/s [ http://soho.nascom.nasa.gov/ ; 48 hours of solar wind data on 

10 July 2002]. While the sun rotates axially at a peripheral speed of about 2 km/s at the 

equator in the plane at right angles to its axis, the reason for so high a wind velocity is briefly 

explained with the principles of space vortex theory. 

René Descartes, the great French philosopher and mathematician, in his Vortex Theory, 

postulated around the middle of the 17 th century that the solar system is a large vortex of ether 

(space) that he defined to be a "property less" fluid. And in this vortex, the planets were 

carried along their orbits with no relative motion between them and the surrounding ether. 

"He firmly denied that the earth moved (relative to the neighboring space medium), and 

asserted that it was carried along with its water and air in one of those larger motions of the 

celestial ether which produce the diurnal and annual revolutions of the solar system" 

[Pioneers of Science; Sir Oliver Lodge; Dover Publications, INC.]. His above concept was 

powerful enough to protect him against any possible persecution by the church which, unlike 

Galileo, did not occur. That Descartes was right in his principles is clear from the fact that in 

addition to the explanation and derivation of the most basic phenomenon of surface gravity of 

the sun and the planets, the genesis of the solar wind close to the sun's surface can also be 

computed with the principles of Space Vortex Theory (SVT) which has postulates very 

similar to the Cartesian Philosophy. 

In my paper "On Planetary Motion caused by Solar Space Vortex" [Journal of New Energy, 

Vol. 3, No. 2/3, August 1998], Kepler's third law was derived, showing that the orbital speed 

of a planet is inversely proportional to the square root of the distance from the sun's center. If 

v is the orbital velocity of a planet whose orbit is at a distance r from the sun 

v = k / (r) 1/2 (1) 

where k is a constant of the solar space vortex. 

Substituting the known value of the orbital speed of the planet Mercury (it can be any other 

planet also) and its distance from the sun in (1), k is determined. Now, using this value of k, 

and substituting in (1) the sun's radius for r, it is calculated in the paper referred above that: v 

= 436.7 km / s. This shows that in the near hood of the sun's surface, its gaseous matter will 

be subjected to a maximum average velocity of 436.7 km / s, due to fluid-space circulation 

around the sun in the solar space vortex. The above computed value is so very close to the 

recorded data (440 km / s) mentioned above. 

The existence of the solar space vortex and the reality of the space-circulation gets proved (in 

the earlier paper) by deriving the surface gravity of the sun as: gs = v 2 / Rs, where v is the 

space velocity calculated above, Rs is the radius of the sun and gs is its surface gravity. The 

value of 274 m / s 2 obtained through the above calculations is exactly the same as accepted to 

day. 

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240 

It is most unlikely that through any other contemporary physical theories so accurate 

quantitative results and physical explanations revealing the genesis of the solar wind can be 

had. 

2. The Space Vortex Theory deals with the fundamental structural relationship between the 

universal matter and the space of the universe. 

Postulating the medium of space as a nonmaterial fluid, with a limiting flow and rotation 

when in vortex motion, it is shown that the universal matter cannot exist, or be created, in the 

absence of a dynamically real (energetic) space, as the only source of primordial energy. A 

circulating fluid-space creates energy and matter as its own vortices. The following are some 

essential aspects of this theory. 

- The most fundamental state of energy is an accelerating volume of the fluid-space. 

- The electron is identified as the only fundamental particle of matter - an irrotational vortex 

of space with a limiting speed (speed of light relative to the absolute vacuum) of rotation. 

- The property of "mass" (introduced in the Newton's laws of motion) of electron is shown to 

be due to a discontinuity in the energy distribution (field-less-void) in its vortex-structure at 

the center, rather than due to some kind of densification and continuous distribution of energy 

at the electron's center, as generally supposed currently. The property of inertia exhibited by 

matter follows from an "inward acceleration field" from the circulating-space acting towards 

the electron-center due to the existence of the central void in its structure. 

- The most fundamental field is "velocity field" defined as the velocity of a fluid-space-point, 

when space is in linear or circulating motion. The "charge" and "mass" of electron are shown 

proportional to the limiting value of this velocity field. The direction of spin in the electron's 

space-vortex determines the nature of electric charge; positive are negative. 

- A "gravitational potential" in space is created with the breakdown of the fluid-space in the 

electron's vortex-structure during its creation. Thermal radiation (light) from a vibrating atom 

is caused in space by a time-varying gravitational potential of the atom-only remotely 

connected with the orbital electrons in the atom as believed today. 

- All the universal constants, presently known, have been derived with a single universal 

constant (speed of light) and the electron radius.

- Surface gravity of the Earth, the Sun and the other planets, has been theoretically derived 

with a hitherto unknown formula in celestial mechanics. 

- A new electrical repulsive force operating between the Sun and the planets that maintains 

stability of the planets in the solar system has been found. The orbital radii of the planets have 

been accurately determined with a new equation that uses this electrical repulsive force. 

- The constancy of speed of light as measured by different observers in relative motion is 

supported (special relativity), while time dilation is concluded to be superfluous. 

- A serious misconception on the basic nature of light and, consequently, inappropriate use of 

Planck constant in photoelectric effect and atomic structure, are shown to be the cause that led 

to the present complexity and incomprehensibility of the quantum physics. 

- An unambiguous proof of the operation of the electrical forces of repulsion and attraction 

among cosmic bodies has been provided recently with the observation of the colliding 

galaxies; It was predicted that if two galaxies are drawing closer and closer, then this would 

be due to an electrical attractive force, and for that to exist, the galaxies in question must have 

opposite directions of their spin. 

- A decisive proof of generation of output electrical power more than the input has been 

achieved in a new system of power generation, thus showing a clear cut violation of the 

Lenz's law (law of conservation of energy). 

If indeed this pair of galaxies are drawing closer, then their spin directions 

will be opposite; the attractive force will be electrical (in addition to gravity). 

It would be of interest to know precisely the spin directions, 

as this will prove the existence of electrical forces too between cosmic bodies. 

3. This last comment is concerning the recent press news from NASA on the picture of 

colliding galaxies (NGC 4676) sent back by the Hubble Space Telescope's new camera. 

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242 

You can see above a picture enlarged from the NASA website (from 

http://antwrp.gsfc.nasa.gov/apod/ap990722.html). They are spinning in opposite directions in 

support of the predictions contained in my article "On Planetary Motion caused by Solar 

Space Vortex" [Journal of New Energy, Vol.3, No.2/3, Summer/Fall,1998]. 

[See http://antwrp.gsfc.nasa.gov/apod/colliding_galaxies.html for more pictures.] 

It was brought out in this article that the planets and the sun, due to their axial spin, will 

possess electrical charge, and will therefore be subjected to electrical repulsive forces between 

them. The stability of the planets in the solar system was analyzed taking this new electrical 

repulsive force into consideration.It was also generalized that all cosmic bodies, includig 

galaxies, possessing axial spin will have electrical charge. Cosmic bodies with similar 

direction of spin will repel; whereas, with opposite directions of their spin, will attract 

electrically. The formula for the quantitative determination of the electrical forces was also 

given in the article. 

It thus follows that the force of attraction between the pair of galaxies reported by NASA, if 

these are drawing closer and closer, is an electrical attractive force, and the galaxies must 

necessarily have opposite directions of their spin. 

It is added that the modern celestial mechanics takes no account of the electrical forces 

between the cosmic bodies. 

It would be of interest to know if the spins of these galaxies are indeed opposite; that will 

prove the existence of the new electrical force discussed in my above article. 

- - - - - 

[A presentation of the author can be found at the end of his previously published 

paper]

Strange Rapprochment 

Louis T. More: Prophet of the 20th Century 

(Theo Theocharis) 

"Belatedly ... a strange rapprochement is under way between the forces of religion and 

science." (Peter Stanford, "Science meets God half way", The Sunday Times News Review, p. 

3.9, 27 October 1996.) 

As I have been pointing out since 1977, and as I shall show below, this rapprochement is a 

debut-de-siècle [beginning-of-century] matter, not a fin-de-siècle [end-of-century] affair. 

(John Tusa, "They said God was dead - why won't he lie down?", Church Times 

(UK), 8 November 1996, pp. 12-13.) 

Prophet 

But at least one "social observer", Louis Trenchard More, who of course had to be 

knowledgeable in all the subjects that matter, came very close to making this prediction not 

much later than 1900 - specifically in 1912. The understanding shown in 1912 by L. T. More, 

("The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370-371, 1912) is so deep, 

the insight so visionary, and the prescience so profound, that the following relevant passage 

deserves to be quoted in full: 

 

(Louis Trenchard More, "The Theory of Relativity", The Nation (USA), Vol. XCIV, pp. 370- 

371, 1912.) 

Mysterianism 

In his regular column "Hard drive" in the London Daily Telegraph weekly supplement 

Connected, Peter Cochrane is described thus: "Peter Cochrane holds the Collier Chair for the 

Public Understanding of Science and Technology at the University of Bristol." In the opening 

paragraph of his "Bricks in an unreal city" (Hard drive, 10 February 2000), Peter Cochrane 

wrote with evident admiration:

244 

fundamental atomic understanding. One of my favourite Feynman key pronouncements is the 

shrewd: 

'I think we can safely assume that no one understands quantum mechanics.'>> 

In fact Richard Feynman was the best known living scientist in the world from the 1960s until 

he died in the 1980s. Moreover, the curious "no one understands quantum mechanics" 

viewpoint articulated in the very last year of the 20th century by a Professor for the Public 

Understanding of Science and Technology at a leading University has been the standard 

viewpoint of establishment science and philosophy throughout the 20th century. I recognised 

the stark and gross inconsistency pointed out here from the very beginning of my scientific 

studies in the 1970s when I also devised my standard rebuttal: 

"A theory that no one understands is not scientific but hopelessly mystic." (Theo Theocharis 

"Men of [Surreal] Ideas", The Listener, 4 May 1978.) 

Science Re-Enslaved by Religion 

"The 17th century is better remembered as the time that science liberated itself from 

theology." (Malcolm Povey, "In need of perspective", Financial Times, 20 June 1994, p. 26.) 

Prediction: The 20th century will be better remembered as the time that science 

re-enslaved itself to theology. 

- - - - - 


theotheocharis@ic4life.net

Ultimate Creative Ignorance 

(Theo Theocharis) 

I supply here independent support to the important argument involved in the title of Foster 

Lindley's (tfl0@msn.com) "Creative Ignorance" (Human and Ecological Risk Assessment, 

Vol. 7, No. 6, pp. 1593-1601, November 2001). It is useful to quote these passages that 

explicate the label "Creative Ignorance": 

"The probabilist converts cognitive uncertainty into physical uncertainty. … As the 

probabilist presents his failure to differentiate as a discovery about the nature of reality, it is 

a creative use of ignorance." 

It is not only the probabilist who "converts cognitive uncertainty into physical uncertainty". 

Every professor of physics everywhere does the same, and more (ie worse). The so-called 

Heisenberg's Uncertainty Principle was devised (in the 1920s) in order to codify a certain 

measumental inaccuracy. It was converted right away into physical uncertainty. Not much 

later, it was converted again - this time into some new convoluted combination of 

physical/cognitive certainty/uncertainty: the physicist knows (with certainty?) that the 

physical entities featuring in Heisenberg's inequality really fluctuate, but (at least for the time 

being) within the restricted bounds permitted by Heisenberg's inequality. 

This last conversion is best debunked as follows: 

Creation of the Universe: According to current cosmological thinking, a(n already existing) 

quantum of energy (obeying the again already existing law of Heisenberg's Uncertainty 

Principle) transformed itself into matter which somehow inflated itself to the presently known 

Universe. One is bound to ask: 

Which proposition is more believable?: 

(i) The Universe was created by an all-mighty God; 

(ii) The Universe was created by a tiny quantum fluctuation. 

On careful reflection, the latter does not give sufficient credit to Heisenberg, so it must be rephrased 

thus: 

(ii)' The Universe was created (some 15 billion years before Heisenberg's birth) by an 

uncertainty in Heisenberg's knowledge. 

There have been debates in physics and philosophy forums as to whether the act of observing 

creates the observed entity, but is there one professor of physics anywhere who has ever 

repudiated these other (now seventy year old) moronic abuses of elementary Aristotelian 

logic? 

- - - - - 


theotheocharis@ic4life.net 

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246 

What the Global Positioning System 

Tells Us about the Twin's Paradox 

(Tom Van Flandern) 

Abstract. In the GPS, all atomic clocks in all reference frames (in orbit and on the ground) are 

set once and stay synchronized. We can use this same trick to place a GPS-type clock aboard 

the spacecraft of a traveling twin. That clock will stay synchronized with Earth clocks, 

allowing a clear resolution of the twin's paradox in special relativity - why the traveler expects 

to come back younger, and why the stay-at-home twin is not entitled to the same expectation. 

Background 

In a previous article [ 1 ], I described how the Global Positioning System (GPS) is a marvelous 

laboratory for testing relativity because the orbiting and ground atomic clocks have differing 

gravitational potentials and high relative speeds. Their precision is such that the predicted 

relativistic clock corrections are confirmed to within a fraction of a percent. However, initial 

expectations based on special relativity were that clocks in different reference frames should 

have different readings and rates. Yet the Global Positioning System is designed in such a 

way that, after the individual clock rates are adjusted once pre-launch for the predicted 

relativity effects, all satellite clocks in all orbits remain in synchronization with one another 

and with all ground clocks without need for further consideration of relativity corrections, 

with the exception of one small correction needed for the slight non-circularity of the orbits. 

The previous article concluded with a discussion of what this means for Einstein's special 

relativity (SR), and for the competing Lorentzian relativity (LR) theory. The comparison 

favors LR as the simpler theory describing the relativity of motion. 

As history buffs may know, the Lorentz Ether Theory (LET) [ 2 ] appeared a year before 

Einstein's 1905 publication of SR. Of course, LET incorporated both the relativity principle 

(taken from Poincare, but it was first formulated about a generation earlier) and the Lorentz 

transformations that bear his name. The essential new element introduced by Einstein the 

following year was the equivalence of all inertial frames, thereby eliminating the need for the 

luminiferous ether. This first postulate of SR makes the Lorentz transformations reciprocal; 

i.e., they work equally well from any inertial frame to any other, then back again; so it has no 

meaning to ask which of two identical clocks in different frames is ticking slower in any 

absolute sense. The second postulate of SR makes the speed of light independent of not only 

the speed of the source (which is also true generally for waves in any medium, including 

luminiferous ether), but also independent of the speed of the observer (which is a feature 

unique to SR). 

Today, many physicists and students of physics have acquired the impression that 

these two postulates have been confirmed by observations. However, that is not the case. In 

fact, none of the eleven independent experiments verifying some aspect of SR [1] is able to 

verify either postulate. It is now widely believed that no experiment is capable of verifying 

these postulates even in principle [ 3 ], because they become automatically true by convention if 

one adopts the Einstein clock-synchronization method, and they become just as automatically 

false if one adopts a different synchronization convention such as the "universal time" 

postulate of Lorentz. Of interest here is the point that the GPS uses the latter synchronization 

convention for pragmatic reasons, as I will shortly explain.

So is the difference between SR and LET then purely cosmetic? No, it is not cosmetic 

at all. It is true that both SR and LET explain all existing electromagnetic-based experiments 

and, in that sense, would remain viable theories of the relativity of motion. But the difference 

between them is much more than aesthetic. In addition to a great difference in practicality for 

use in systems such as the GPS (in favor of LET), the two theories differ about whether or not 

material bodies can exceed the speed of light in forward time. In SR, that is proved impossible 

because time ceases to advance for any entity traveling at the speed of light. By contrast, in 

LR, no speed limit for material bodies exists. It is true that speed relative to the preferred 

frame causes electromagnetic-type clocks (which include all ordinary mechanical, biological, 

and atomic clocks) to slow, meter sticks to contract, and the momentum of bodies to be 

2 2 

increased by the relativistic factor γ = 1 1 − v c just as in SR. But in LR, time, space, 

and the matter content themselves are not affected. (Here, v is the speed of the body and c is 

the speed of light.) So the question of which theory better represents nature is of major 

importance to the future of physics, which is presently invested in the belief that speeds faster 

than light in forward time are not possible. 

Today, our concepts of the "luminiferous ether" are considerably different than they 

were in Lorentz's day. It is now widely recognized that the local gravity field serves as the 

"preferred frame" of LET. With this alteration from Lorentz's original concept but without 

any change in the math or structure of the theory, LET has now become known simply as 

"Lorentzian relativity" (LR). Although LR has no intrinsic speed limit, it recognizes the innate 

difficulty of material bodies composed in part of electrons, while propagating in luminiferous 

ether, being able to exceed the wave speed of that ether, the speed of light. LR treats this as 

analogous to a propeller-driven aircraft exceeding the speed of sound without any outside 

assists, such as from gravity. A force that cannot itself propagate faster than light cannot 

propel material bodies faster than light. 

Of critical importance to choosing the model that best represents nature, none of the 

eleven independent experiments testing SR verify frame reciprocity or distinguish SR from 

LR. In fact, historically, de Sitter, Sagnac, Michelson, and Ives concluded from their 

respective experiments that SR was falsified in favor of the Lorentz theory. 1 Indeed, the GPS 

itself is a practical realization of Lorentz's "universal time", wherein all clocks remain 

synchronized despite being in many different frames with high relative speeds. However, 

subsequent re-interpretation of SR allowed that theory to survive these objections. 

This "magic" is envisioned to happen by virtue of each clock in the system being 

synchronized to an imaginary clock in the Earth-centered inertial (ECI) frame, 

instantaneously co-located with the moving clock, and assumed to be in a gravitational 

potential equal to that at sea level at Earth's poles. (Note the "coincidence" that the magic 

makes use of the Lorentzian preferred frame, the local gravity field.) This trick makes the 

clock rates all the same as they would have been if they were at rest in the ECI frame and in a 

constant potential field. This is all very nice, but hardly what Einstein envisioned when 

speaking of two clocks in relative motion, one at a station and one on a passing train. How 

simple special relativity would have become all these years if physicists had realized that all 

they had to do was reset the clock rates so they all ticked at the same rate as the reference 

clock in the local gravity field! 

The converse is also true. Suppose we did not change the clock rates before launch, 

but instead let them tick at their design rates in accord with whatever speed and potential they 

experienced in orbit. Now, suppose we tried to Einstein-synchronize the system of clocks. 

Satellite and ground clocks would tick at different rates. And if we tried to work in any local, 

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instantaneously co-moving inertial frame, the corrections needed to synchronize with each 

orbiting clock would be unique to that observer's frame and different from moment to moment 

because both clocks are accelerating. The practical difficulties of operating the system would 

be virtually insurmountable. What we would gain by doing that is constancy of the measured 

speed of light in all inertial frames. But because all clocks are now re-synchronized to just the 

ECI frame in the GPS, the speed of light is constant in that one frame, and the invariance of 

the speed of light in other inertial frames is of no practical value. 

In a recent article, Ashby [ 4 ] claimed that the clock-epoch correction term (also called 

2 

"time slippage" term) in the Lorentz transformations, vX c (see Eq. below), can be dropped 

even when its value is large, but he is very vague about why. However, this particular term is 

the only difference of consequence between Einstein synchronization of clocks in different 

inertial frames and Lorentz synchronization of clocks to an underlying "universal time". And 

the GPS system has been designed to use Lorentz synchronization, for which one frame, the 

local gravity field or ECI, is special; not Einstein synchronization, wherein clocks tick at their 

natural rates and all inertial frames are equivalent. By itself, this does not prove LR "right" or 

SR "wrong". But the practical difficulties for GPS of not changing the natural rates of clocks 

pre-launch, or with the use of SR for any frame but the Lorentzian preferred frame, are very 

great. If a ring of satellites (A, B, C, …, Y, Z) circled the Earth in a common orbit, and each 

satellite tried to Einstein synchronize with the next in sequence, then when Z tried to complete 

the circuit by Einstein-synchronizing with A, the corrections required would lead to time 

readings for A different from the starting readings, making closure impossible. 

Introducing the twins 

The "twin's paradox" is an illustration of the complexity of SR's interpretations of nature. 

Suppose two identical twins start out at some common instant. One remains on Earth. The 

other (the "traveler") is on a spacecraft headed for Alpha Centauri (AC) four light-years away 

at 99% of the speed of light, for which speed the time dilation factor is γ ≈ 7 . (We choose a 

large value of γ so that the effects of the relativity of motion will be large and obvious, not 

subtle.) Upon arrival at AC, the traveler turns back to Earth at the same speed (or is replaced 

by a traveler already headed toward Earth of identical biological age at the moment they pass, 

to avoid need for an acceleration). The round trip requires slightly over 8 years Earth time; 

let's say 98 months to be specific. This is path 1 in Figure 1. When the twins are reunited, the 

Earth-bound twin is 98 months old, and the traveler is 14 months old (a factor of 7 less). 

Figure 2. 

The traveling twin's journey to Alpha Centauri (AC) begins at Earth (E). 

Upon arrival, the traveler can return to Earth by any path (1), 

continue on to Beta Centauri (2), or circle Alpha Centauri (3). 

That much is a clear prediction of SR. Note especially that no accelerations need 

actually occur at the beginning or end of the journey, nor even in the middle if we do the 

"twin replacement" trick. That is consistent with cyclotron experiments showing that

accelerations as such, even as great as 10 19 g (where g is the acceleration of gravity at sea 

level), have no effect on clocks [ 5 ]. At each stage of the journey where an event occurs, 

comparisons can be made without ambiguity between adjacent points, one in each of the 

inertial frames containing the clocks or twins to be compared. Despite the fact that many 

textbooks discussing the twin's paradox treat accelerations as essential, that is illusory. 

Accelerations are unbounded in size, and in principle can be done in an instant, allowing no 

local time to elapse in any relevant frame. Accelerations (as distinct from velocities) and 

forces (as distinct from potentials) do not change local clocks, clock rates, or biological aging. 

Now we come to the paradox part: Why isn't the traveler entitled to claim that the 

spacecraft remained at rest and the Earth traveled away at 99% of the speed of light, then 

turned around and came back? From that perspective, the original traveler would argue that 

the Earth-bound twin should be the younger one. We will examine the rather different 

answers to that question offered by SR and by LR. 

The traveler takes along a GPS clock 

Let's more closely follow what is happening to our two twins. Imagine that the inertial frame 

of reference containing Earth and AC is filled everywhere with synchronized clocks at rest, so 

that any traveler can always look out a window and read what time Earth-frame people think 

it is. See Figure 2. And let the traveler take a "GPS clock" along on his journey, along with an 

unadjusted "normal" clock. The GPS clock is preset in rate before the journey so that, once 

placed aboard the spacecraft, it will remain synchronized in epoch and rate with clocks on 

Earth, just as real GPS clocks do. Then the on-board GPS clock will always give readings 

identical to the nearest Earth-frame clock visible outside the spacecraft window. This instant 

ability to compare traveler's time in his own frame with time everywhere in the Earth-AC 

frame will prevent paradoxes from arising. 

Figure 2. 

From the Earth-frame, all stationary clocks are synchronized, and all clocks moving with the 

spacecraft are not. From the spacecraft, the situation is reciprocal. However, the on-board GPS clock 

always agrees with the Earth-frame clock immediately outside the spacecraft window. © 

Now let's examine the journey details. When the traveler's journey begins, the onboard 

native clock ticks slower than the GPS clock by a factor of seven. But isn't that already 

an asymmetry present at a stage where there is simply a relative motion, and no way to decide 

which twin should be aging slower? LR answers simply "yes" because the frame of the local 

gravity field is the preferred frame in which clocks tick fastest, and time in all other relatively 

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moving frames passes more slowly. But SR offers the opposite answer. And understanding 

that answer is the key to understanding SR. 

SR is a mathematical theory built around the Lorentz transformations. Let the time T 

be the reading on a clock fixed in the Earth frame; and let X be the relative location in the 

Earth frame of a clock fixed in the spacecraft frame moving at speed v relative to the Earth 

frame. Let t be the time reading on the natural clock in the traveling spacecraft, and x be the 

relative location of Earth in the spacecraft's frame. In that frame, Earth passes the spacecraft 

with a speed − v . As before, the Lorentz time dilation/length contraction parameter is γ , 

having a value of 7 when v = 0.99c 

. So in general, the relation between the Earth-frame 

clock and the spacecraft-frame clock is: 

2 

t = γ T − vX c 

( ) 

( ) 

x = γ X − vT 

Because the relationships are reciprocal (all inertial frames are equivalent in SR), the 

inverse relations (with v → − v ) must also hold: 

2 

( ) 

T = γ t − vx c 

( ) 

X = γ x − vt 

Now let's compare time in the two frames. First, let an observer at a clock fixed on 

Earth watch time on the spacecraft clock. Then the observer is looking at a point X = vT . 

Substituting that into eq. , we get the unsurprising result that x = 0 , meaning that the 

spacecraft clock remains fixed at the origin of its own coordinate system. And from the time 

transformation, using the definition of γ , we get t = T γ , which restates the well-known 

prediction of SR we cited above that the spacecraft clock will appear to the Earth observer to 

be ticking γ = 7 times slower than the Earth-fixed clock. 

That much is routine. But before we leave the Earth frame, let's do one more 

calculation. Suppose the spacecraft frame is likewise filled with clocks everywhere, Einsteinsynchronized 

with each other. Because all such clocks are at rest relative to one another, they 

can simply exchange light signals and assume that the light takes equal time for the uplink 

and downlink portions of its round trip. Then the average of the transmission and reception 

times on one clock must agree with the signal reflection time on the other clock by definition 

of "Einstein synchronization". Now, from the Earth frame, let's peer into the spacecraft frame 

at the point X = 0 , the fixed location of the Earth observer. From Eq. , we now have t = γ T . 

The meaning of this relation is that the Earth observer sees a succession of spacecraft-frame 

clocks parading by, and time on the succession of clocks goes by γ = 7 times faster than 

Earth time. 

You read that right. According to SR, at the same time that each and every clock in the 

spacecraft frame is seen by the Earth frame to tick γ = 7 times slower, time in the spacecraft 

frame on a succession of passing clocks is passing by γ = 7 times faster than Earth time. To 

repeat this essential point, in any inertial frame with a relative motion, all individual clocks 

tick slower but overall frame time moves forward at a faster rate. Such is the effect of the 

2 

vX c term in the transformation. The time difference between clocks in different frames is a 

function of the different rates they tick at and of the "time slippage" effect, whereby time is a 

function of location in any relatively moving frame. In SR, this would remain true even if we 

used the GPS trick and eliminated the rate differences between clocks. In general, the time 

slippage effect dominates the effect of a changed clock rate for any clock in a frame with

elative motion. (N.B. Time is everywhere the same when viewed from within an inertial 

frame. But it is everywhere different in that same frame from the perspective of any other 

frame with a relative motion because of time slippage.) 

It is worth studying the points in the preceding two paragraphs because, while 

mathematically permissible, they defy our intuitions and are what makes relativity such an 

unintuitive theory. 

The traveler looks back at the Earth twin 

Now let's switch to the spacecraft frame and look back at the Earth-frame clock at x = vt 

using Eq. . Then we get X = 0 and T = t γ . So the spacecraft clock sees the Earth clock 

ticking γ = 7 times slower than itself. Substituting x = 0 , we get T = γ t : the spacecraft twin 

sees Earth-frame clocks streaming by outside his window with time elapsing on a succession 

of them at γ = 7 time faster. So both effects, relative clock rates and frame time from time 

slippage, are reciprocal and symmetric between the two frames. 

And that is SR's answer to the symmetry challenge we posed at the outset of the 

spacecraft's journey. Both LR and SR predict that the spacecraft's clocks will appear to tick 

slower than all Earth-frame clocks as viewed by Earth-frame observers. But SR (only) 

predicts that the situation looks reciprocal and symmetric for observers in the spacecraft frame 

looking at clocks in the Earth frame. The traveler is therefore not surprised by the behavior of 

the GPS clock on board, which correctly records a combination slower clock rate plus a fast 

time slippage for the Earth frame, and stays in agreement with the Earth-frame clocks passing 

by just outside the spacecraft window. 

Now consider the traveler's arrival at AC, when the spacecraft turns around or is 

replaced by a spacecraft heading Earthward at the same speed. Neither the natural clock nor 

the on-board GPS clock changes rate or reading significantly during the turn-around. 

However, before the turn-around, the Earth-frame clocks say four years (actually, 49 months) 

of Earth time have elapsed since the journey began, and the spacecraft natural clock says 

seven months of spacecraft time have elapsed. But the spacecraft infers that only a single 

month has elapsed back on Earth because a single clock in another frame is affected only by 

clock slowing, not time slippage; whereas the spacecraft agrees that 49 total months have 

elapsed at AC because the journey began with a 48-month time slippage for AC and added 

one more month during the journey. As usual, time slippage corrections (where applicable) 

dominate clock readings in other frames. 

We now come to the crux of the resolution of the paradox, which seems paradoxical 

only in SR. The traveler has inferred that only one month has elapsed back on Earth since his 

journey began, so by spacecraft-frame reckoning, Earth time is just one month later than the 

actual departure time. For example, if the journey commenced in 2000 January, when the 

traveler arrives at AC, the on-board GPS clock reads 2004 February; but the traveler infers 

that Earth clocks still read 2000 February. Because of the finite speed of light, the traveler can 

see Earth only as it was, not as it is now, and therefore cannot check this inference by direct 

observation. According to SR, all these clock-reading inferences are not just illusions, but 

reflect the real, physical time for each frame involved. So at the same time and place that an 

AC resident infers that Earth time is 2004 February, the spacecraft traveler infers it is 2000 

February - a four-year difference; and both are correct for their respective frames. 

Then the spacecraft turns around. Nothing changes locally. But inferences about 

remote time change greatly because of time slippage, which now has the opposite sign. Now 

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the traveler infers that Earth time is 2008 February - four years into the future instead of the 

past. As a consequence, the traveler will again infer that only one month of Earth time will 

elapse during the return journey, and all participants agree that Earth time upon the traveler's 

return will be 2008 March. The traveler arrives back younger (14 months old) than the stayat-home 

twin (98 months - over 8 years old). According to LR, this is because the traveler had 

a high speed relative to the preferred frame, the local gravity field; and there never was any 

symmetry between the two frames. But according to SR, the elapsed time is a combination of 

slowed aging and time slippage effects, the latter changing discontinuously when the direction 

of the traveler changes. 2 

The Earth twin thinks the traveler should naturally age slower because his clocks run 

slower. And the traveler thinks the Earth twin should naturally age faster because the time 

slippage effect dominated the slowed aging effect when that twin turned around. Note that the 

traveler could have taken any path whatever as long as the spacecraft speed relative to the 

Earth frame remained 0.99 c . Then at every instant along the journey, the traveler's 

biological age will be a factor γ = 7 less than the elapsed time on the on-board GPS clock, 

which will agree with the Earth clocks upon return. 

Indeed, the spacecraft could have simply continued in a straight line past AC and on to 

Beta Centauri (BC), say (for purposes of this example only), 8 light-years from Earth. Then 

there was no turn-around event, but the traveler is still just 14 months old on arrival, and 

twins born on BC at the same time the Earth twin was born (according to Earth-frame clocks) 

will still be 98 months old. And the traveler will infer that the BC twins started out 96 months 

old at the journey's beginning, and aged just two months during the journey. So clearly, 

neither the turn-around event nor any acceleration is essential to the result; and the SR 

resolution of the paradox retains its symmetry and the equivalence of all frames. 

Hence, from the traveler's perspective, wherever the spacecraft goes in any direction 

without changing speed relative to the Earth frame, it will encounter Earth frame clocks with 

more elapsed time than on the natural clock aboard the spacecraft (but with the same elapsed 

time as for the on-board GPS clock). But the traveler will infer that all clocks in the Earth 

frame are always ticking slower than the natural spacecraft clock, and beings in the Earth 

frame are always aging more slowly than the traveler. Everything encountered can be 

explained by a combination of clock rate changes and time slippage. The traveler cannot infer 

that the Earth-bound twin will be the younger one upon the spacecraft's return because Earth 

experienced a time slippage event (whether sudden or gradual), rapidly aging everyone on 

Earth during the traveler's journey. That time slippage event is no different in character than 

the one that a hypothetical twin on Beta Centauri would experience if the traveler continued 

on past AC without a turn-around event. 

The traveler takes different paths 

What we have just described are careful and correct inferences of SR as applied to the twin's 

paradox. This also shows the essentially mathematical nature of the theory, because it does 

violence to what we fondly call "common sense". The most important point to note carefully 

is that the theory is internally consistent, and no mathematical contradictions can be found no 

matter how the transformation equations are manipulated, or how many frames or twins are 

introduced. The next important point to note is that SR makes demands on our credulity that 

LR does not. Let's examine why. 

At the point of turn-around on the original journey from Earth to AC, the traveler's 

inferences about time on Earth changed suddenly. Instead of the physically unrealistic instant

turn-around, let's assume the spacecraft "orbits" around AC to perform the turn-around. (To 

stay at a safe distance from the star at the same speed, this would require propulsion, not just 

gravity.) This can still take a time short enough to be neglected, especially at such a high 

relative speed. So the traveler's spacecraft changes from headed away from Earth and 

inferring the Earth year is 2000, to traveling toward Earth and inferring the Earth year is 2008. 

Again, SR says this is real, physical time, and not an illusion. 

So before commencing a journey back to Earth, let's suppose the traveler orbits AC 

several times. Then each time the traveler heads away from Earth in that orbit, Earth time 

drops back to 2000; and each time the traveler heads toward Earth, inferred Earth time 

becomes 2008. The Earth-year is intermediate for intermediate orbital positions. Now the 

significance of repeating this situation several times is that, as Earth time goes to 2008, many 

people will have died and others will be born. And on each occasion that Earth time reverts to 

2000, some of the dead will be resurrected and some living young children in 2008 will cease 

to exist in 2000. Note that while all this is happening according to SR, the on-board GPS 

clock representing LR's "universal time" continues to insist that Earth time is the same as 

spacecraft time and AC time: 2004 everywhere. In SR, effects of this type are never 

observable because they "lie outside the observer's light cone", hidden from direct view by the 

finite speed of light. Nonetheless, SR insists that such changes affect real, physical time and 

are not mere illusions, because the viewpoint of each inertial frame is just as valid as that 

from any other frame. 

Conclusions 

In LR, one reference frame (the local gravity field) is preferred; and speed cannot affect time, 

but only the rate of ticking of mechanical, electromagnetic, or biological clocks. However, 

just as we do not assume that time has been affected when the temperature rises and causes a 

pendulum clock to slow down, LR says that changes in clock rates are changes in the rates of 

physical processes, and do not affect space or time. So by carrying an on-board GPS clock on 

the spacecraft, we are offered a clear choice between models: Earth time can be what SR 

infers it is, or it can be what the GPS clock says it is. In the former case, SR works, but leads 

to heavy-duty complexities and fantastic inferences about the nature of time at remote 

locations. Moreover, the proof that nothing can travel faster than light in forward time stands 

intact. In the latter case, LR works with great simplicity and in full accord with our intuitions 

about the universality of the instant "now". And the speed of light is no longer a universal 

speed limit because time itself is never affected either by motion or by gravity. 

Aside from these practical difficulties with the use of SR in the GPS, Einstein's special 

relativity is also under challenge in a more serious way from the "speed of gravity" issue, 

because the proven existence of anything propagating faster than light in forward time (as all 

experiments indicate is the case for gravity) would falsify SR outright [ 6 , 7 ]. So it is entirely 

possible that reality is Lorentzian, not Einsteinian, with respect to the relativity of motion. In 

that case, physics may have no speed limit when the driving forces are gravitational or 

electrodynamic rather than electromagnetic in nature. And that may be the most important 

thing that the GPS has helped us to appreciate. 

Notes 

[1] T. Van Flandern, "What the Global Positioning System tells us about relativity", in Open 

Questions in Relativistic Physics, F. Selleri, ed., Apeiron, Montreal, 81-90 (1998). Also available online 

at , "cosmology" tab, "gravity" sub-tab. 

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254 

[2] H.A. Lorentz, Lectures on Theoretical Physics, Vol. III, "The principle of relativity for uniform 

translations", Macmillan & Co., London, 208-211 (1931). Contains summary of and citation to 

original 1904 paper. 

[3] H. Erlichson, "The rod contraction-clock retardation ether theory and the special theory of 

relativity", AJP 41, 1068-1077 (1973). 

[4] N. Ashby, "Relativity and the Global Positioning System", Phys.Today May, 41-47 (2002). 

[5] Bailey, J., Borer, K., Combley, F., et al., "Measurements of relativistic time dilation for positive 

and negative muons in a circular orbit", Nature 268, 301-305 (1997). 

[6] T. Van Flandern, "The speed of gravity - What the experiments say", Phys.Lett. A 250, 1-11 

(1998). 

[7] T. Van Flandern and J.P. Vigier, "Experimental repeal of the speed limit for gravitational, 

electrodynamic, and quantum field interactions", Found.Phys. 32(#7), 1031-1068 (2002). 

1 De Sitter argued that the forward displacement of starlight (aberration) depended on absolute, not 

relative, speeds because both components of a double star, each with some unique velocity, had the 

same aberration. Sagnac argued that the fringe shifts expected but not seen in the Michelson-Morley 

experiment are seen if the experiment is done on a rotating platform. Michelson argued in the 1925 

Michelson-Gale experiment that the Earth was just such a rotating platform. Ives argued that ions 

radiated at frequencies determined by absolute, not relative, motion because they had to pick a specific 

frequency to radiate at. In each case, a complex-but-now-familiar SR explanation could account for 

the same observed results. 

2 We note in passing that the effect that SR expects accelerations or frame changes to have on remote 

clocks would constitute an instantaneous action at a distance, a violation of the causality principle. 

Acknowledgments 

The author thanks the Meta Research Board and members for financial support, with a special 

thanks to Tim Seward. The artwork in Figure 2 is Copyright (2002) by Boris Starosta, 

. 

- - - - - 

Tom Van Flandern received his Ph.D. degree in Astronomy, specializing in 

celestial mechanics, from Yale University in 1969. He spent 20 years at the U.S. 

Naval Observatory, where he became the Chief of the Celestial Mechanics 

Branch. In 1991, Tom formed a Washington, DC-based organization, Meta 

Research, to foster research into ideas not otherwise supported solely because 

they conflict with mainstream theories in Astronomy. Tom is editor of the Meta 

Research Bulletin, which specializes in reporting anomalies and evidence that 

does not fit with standard theories in the field. During the past few years, he has 

also been a Research Associate at the University of Maryland Physics 

Department in College Park, MD, and a consultant to the Army Research 

Laboratory in Adelphi, MD, working on improving the accuracy of the Global 

Positioning System (GPS). North Atlantic Books is the publisher of Tom's 1993 

book, Dark Matter, Missing Planets and New Comets. A second edition was 

published in 1999. As with his research papers, the book is critical of many

standard models in astronomy, such as the Oort Cloud, the Dirty Snowball, and 

the Big Bang theory. Tom also organizes the Eclipse Edge Expeditions to 

optimal solar eclipse viewing sites. During his career as a professional research 

astronomer, Tom has been honored by a prize from the Gravity Research 

Foundation; served on the Council of American Astronomical Society's Division 

on Dynamical Astronomy; taught astronomy at the University of South Florida 

and to Navy Department employees; been a consultant to NASA's Jet Propulsion 

Lab; and done several spots for the "Project Universe" series that continues to 

air occasionally on public TV. 

Meta Research 

http://metaresearch.org/ 

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256 

REPRINTS

Sulle attrazioni newtoniane di origine idrodinamica 

(Emilio Almansi) 

1. In un liquido omogeneo, indefinito (praticamente abbastanza esteso in tutte le direzioni), si 

abbia un numero qualunque di corpi C , C' , C'' , ... , i quali subiscano rapide variazioni di 

forma, od anche solo di posizione, tali che il fenomeno presenti, nel suo insieme, un periodo 

θ piccolissimo. 

Quando siano verificate certe condizioni che accenno più avanti, avviene che, per ogni 

corpo, la forza risultante delle pressioni che il liquido esercita sugli elementi della sua 

superficie ha, in un intervallo di tempo multiplo di θ , un valor medio corrispondente 

all'attrazione che su quel corpo eserciterebbero gli altri, se i corpi del sistema possedessero 

certe masse m , m' , m'', le quali si attraessero secondo la legge di Newton. 

Questo interessante fenomeno, ed altri analoghi, furono per la prima volta studiati, in casi 

particolari, sia dal lato matematico, sia sperimentalmente, dal prof. C.A. Bjerknes. 

L'argomento è stato poi ripreso, ed ampiamente svolto in un suo corso di lezioni, dal figlio 

prof. V. Bjerknes(1). 

I procedimenti analitici da me seguiti in altra Nota(2), permettono di arrivare al risultato nel 

modo più semplice e generale. 

2. Supporremo che nel movimento indotto nel liquido la velocità sia ovunque continua, derivi 

da un potenziale ϕ , e si annulli all' infinito; che i pesi delle particelle liquide siano 

trascurabili; che la densità sia uguale ad 1 . 

Denotiamo con (F) la forza che al tempo t agisce sopra un corpo C del sistema. Essa può 

decomporsi (Nota preced.) in due forze (F0) ed (F) . Le proiezioni X0 , Y0 , Z0 sopra gli assi 

coordinati della forza (F0) sono derivate esatte rispetto al tempo di funzioni periodiche col 

periodo θ : onde il valore medio (in un intervallo multiplo di θ ) della forza stessa - vale a 

dire la forza che ha per proiezioni i valori medii di X0 , Y0 , Z0 - è nullo. Noi trascureremo 

questa forza (F0) . 

Le proiezioni della forza (F) sono 

X = ∫ ⎥ ⎥ 

⎡ 

2 

2 

2 

1 

∂ ⎤ 

⎢ 

⎛ ∂ ϕ ⎞ ⎛ ∂ ϕ ⎞ ⎛ ∂ ϕ ⎞ 

∂ ϕ ∂ ϕ ∂ ϕ ϕ 

σ ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ α − + + dσ 

⎢ 2 

∂ ∂ ∂ ∂ 

⎣ 

⎝ ∂ x ⎠ ⎝ ∂ y ⎠ ⎝ ∂ z ⎠ x y z x 

⎦ 

ecc., rappresentando σ la superficie del corpo, ed α , β , γ i coseni della normale esterna(3). 

Il potenziale di velocità ϕ presenta, in ogni istante, tutti i caratteri del potenziale 

newtoniano di masse μ , μ' , μ'' , ... distribuite negli spazi S , S' , S'' , ... occupati dai corpi. 

Infinite distribuzioni dànno luogo, nello spazio esterno, allo stesso potenziale ϕ : noi 

supporremo di fissarne una. Verremo così a definire la funzione ϕ anche negli spaz! S , S', 

S'' , ... Supporremo che essa risulti, in ciascuno di questi spazi, finita e continua insieme alle 

sue derivate prime e seconde. Attraversando le superficie dei corpi, la funzione ϕ e le sue 

derivate prime non dovranno subire discontinuità. La densità ρ relativa a questa 

distribuzione di masse ideali sarà: 

2 2 2 

− 1 ⎡ ∂ ϕ ∂ ϕ ∂ ϕ ⎤ 

ρ = ⎢ + + 

2 2 2 ⎥ 

4π 

⎣ ∂ x ∂ y ∂ z ⎦ 

. 

, 

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258 

Ciò posto, trasformiamo, nella espressione di X , l'integrale esteso a σ in un integrale 

esteso allo spazio S limitato da σ . Otterremo: 

2 2 2 

⎡ ∂ ϕ ∂ ϕ ∂ ϕ ⎤ ∂ ϕ 

X = - ∫ S ⎢ + + ⎥ dS 

2 2 2 

⎣ ∂ x ∂ y ∂ z ⎦ ∂ x 

Poniamo 

X1 = 

∂ x 

∂ ϕ ∂ ϕ 

, Y1 = , Z1 = 

∂ y 

. 

∂ ϕ 

, 

∂ z 

e teniamo conto della espressione di ρ . Avremo: 

X = 4 ∫ X ρ dS 

π S 1 

e, analogamente, 

Y = 4 ∫ Y ρ dS , Z = 4 ∫ Z ρ dS . 

π S 1 

π S 1 

Queste formule possiamo interpretarle dicendo che la forza (F) relativa al corpo C è, in 

ogni istante, quella stessa che si avrebbe se le masse ρdS si attraessero secondo la legge di 

Newton, e la costante dell'attrazione fosse uguale a 4π . 

Parimente si potrebbe dimostrare che i momenti rispetto agli assi coordinati delle pressioni 

esercitate dal liquido sugli elementi di σ sono uguali ai momenti delle forze 4πX1ρdS , ecc. 

3. Supponiamo, ora, che le mutue distanze fra i corpi C , C' , C'' , ... siano grandissime 

rispetto alle loro dimensioni lineari. Denoti P un punto fisso, che si trovi costantemente nello 

spazio S occupato da C . Così per gli altri corpi C' , C'' , ... , consideriamo i punti fissi P' , 

P'' , ... 

Nelle formule precedenti noi possiamo ritenere che X1 , Y1 , Z1 siano le derivate del 

potenziale ϕ , dovuto alle sole masse esterne μ' , μ'' , ... (la resultante delle mutue azioni che 

si esercitano tra le masse elementari ρdS di uno stesso corpo essendo identicamente nulla). 

Invece di X1 , Y1 , Z1 scriviamo X1 + δX1 , Y1 + δY1 , Z1 + δZ1 , intendendo ora che X1 , Y1 , 

Z1 siano le derivate, nel punto P , del potenziale ϕ , calcolato come se le masse μ' , μ'' , ... 

fossero concentrate nei punti P', P'' , ... Ponendo 

δX = 4 ∫ δ X ρ dS , ecc., 

π S 1 

avremo: X = 4πX1μ + δX , ecc. Ammettiamo che la forza di componenti δX , δY , δZ sia 

trascurabile rispetto alla forza di componenti 4πX1μ , 4πY1μ , 4πZ1μ (ciò che potrà non 

avvenire; per es., se μ= 0). Potremo allora ritenere X = 4πX1μ , ecc. Onde, detta r la 

distanza costante PP' , e posto 

μ μ ' 

f = 4π 2 

r 

la forza (F) risu1terà, in ogni istante, dall'attrazione (f) dovuta al corpo C' , e delle altre 

analoghe dovute agli altri corpi.

Le masse μ , μ' , ... si possono esprimere molto semplicemente mediante i volumi S , S' , ... 

dei corpi corrispondenti. Si ha infatti: 

μ = 

− 1 ∂ ϕ 

σ dσ 

4π 

∫ ∂ n 

. 

∂ ϕ 

E poichè è uguale alla componente, secondo la normale esterna, della velocità di un 

∂ n 

punto di σ , se diciamo ora dS l'incremento che subisce, nel tempo dt , il volume S , sarà 

∂ ϕ 

ds = dt ∫ σ dσ 

∂ n 

e, perciò, 

μ = 

− 1 dS 

4π 

dt 

. 

Analogamente sarà μ' = 

q = 

avremo 

1 

4π 

q 

f = 2 : 

r 

dS dS' 

dt dt 

, 

, 

− 1 

4π 

dS' 

dt 

. Onde, ponendo 

dalle quali formule vediamo che se in un certo istante i volumi S , S' sono ambedue crescenti 

od ambedue decrescenti, e quindi q > 0 , la forza (f) è realmente un'attrazione; altrimenti, è 

una ripulsione. 

4. Il valor medio (F') della forza (F) , quindi ancora della forza (F) , in un intervallo 

multiplo di θ , o uguale a θ , sarà la risultante della forza (f') di grandezza 

q ' 

f' = 2 , 

r 

ove q' è il valore medio di q , e delle analoghe relative agli altri corpi. Avremo dunque: 

θ 

1 1 dS dS' 

dt 

q' = ∫ qdt = 

4 ∫ dt dt θ 

θ 0 

θ 

π 0 

. 

Facciamo ora un'ipotesi più particolare intorno al modo di variare dei volumi S , S' , ecc.: 

supponiamo cioè che si abbia 

S = S0(1+hε) , ecc., 

259

260 

ove S0 ed h rappresentano due quantità costanti per il corpo C , ε una funzione del tempo, 

periodica con periodo θ , uguale per tutti i corpi. Se poniamo 

dS dε dS' dε 

m = hS0 , m' = hS' , sarà: = m , = m' . E, perciò, 

dt dt dt dt 

q' = ∫ θ 

mm' 

dε 

2 dt 

( ) 

4 dt θ 

quindi 

π 0 

mm ' 

f' = k 2 , 

r 

essendo 

k = ∫ θ 

1 dε 

2 dt 

( ) 

4 dt θ 

π 0 

. 

; 

In questo caso, dunque, attribuito alla costante dell'attrazione il valore dato dall'ultima 

formula, si ha una perfetta analogia tra la forza (F') e le attrazioni newtoniane delle masse 

ideali (costanti) m , m' , ... 

5. Nella formula S = S0(1+hε) , noi possiamo sostituire ad ε una funzione lineare di ε , con 

che verranno solo a variare le costanti S0 ed h . Potremo allora fare in modo che il massimo 

e il minimo valore della funzione periodica ε siano +1 e -1 . Diciamo S1 ed S2 i valori 

corrispondenti di S (notando che, se la costante h è negativa, S 1 rappresenterà il valor 

minimo di S ). Si avrà S1 - S2 = 2hS0 = 2m ; quindi 

1 

m = (S1 - S2) . 

2 

Le masse m vengono così ad essere le semi-differenze fra i valori estremi dei volumi dei 

corpi. 

t 

Quanto alla costante k , osserviamo che, se s'introduce la variabile τ = , si ha 

θ 

dt dε 1 

dτ = , = 

θ dt θ 

1 

k = 2 

θ 

1 

4 

∫ θ 

π 0 

dε 

2 

( ) dτ 

dτ 

d ε 

, 

dτ 

. 

Di qui vediamo che per una determinata funzione ε(τ) (per esempio, se 

t 

ε = sen 2πτ = sen 2π ) la costante dell'attrazione è inversamente proporzionale al 

θ 

quadrato del periodo.

(1) Fields of force, Columbia University Press. New-York, 1906. Vedasi anche la Memoria di 

W. Voigt, Beiträge zur Hydrodynamik, Gött. Nachr., a. 1891. 

[NdR - A proposito della relazione tra i Bjerknes qui citati, e il C.J. Bjerknes autore sia di due 

articoli in questa sezione di Episteme, sia del libro presentato nell'apposita rubrica della I 

Parte, si veda appunto la detta recensione.] 

(2) Sopra le azioni le quali si esercitano fra corpi che si muovono o si deformano entro una 

massa liquida, Rendiconti della R. Accad. dei Lincei, dicembre 1913. [Riporteremo tra breve 

qui di seguito il paragrafo introduttivo di questo lavoro.] 

(3) Nella Nota preced. le X ed X0 di questa Nota sono chiamate X1 ed X2 ; la quantità 

sotto il segno d'integrazione nella espressione di X ( X1 ) è denotata con -H . La espressione 

di H è data a pag. 537. 

- - - - - - 

Questo lavoro è stato pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1914, Vol. 

XXIII, 1° Sem., pp. 287-291. 

* * * * * 

Riteniamo al solito di fare cosa utile ai lettori offrendo loro il paragrafo introduttivo 

dell'articolo di cui alla precedente Nota 2, che apparve sempre sui Rendiconti della Reale 

Accademia dei Lincei, 1913, Vol. XXII, 2° Sem., pp. 533-544. 

Meccanica. - Sopra le azioni le quali si esercitano fra corpi che si muovono o si 

deformano entro una massa liquida. Nota del Corrisp. E. ALMANSI. 

1. È noto che due sfere immerse in una massa liquida sufficientemente estesa in tutte le 

direzioni, aventi i loro centri in due punti fissi dello spazio, e raggi periodicamente variabili 

intorno ad un valor medio, al quale si conservino sempre vicinissimi, esercitano una su l'altra 

un'azione attrattiva o repulsiva, secondochè le loro pulsazioni hanno la medesima fase, o fase 

opposta. 

Parimente, se, restando costanti i raggi delle sfere, i centri si spostano sopra una retta, 

oscillando intorno a due punti fissi, le due sfere si attraggono o si respingono a seconda che i 

loro centri hanno, in ogni istante, velocità rivolte in senso contrario, o nello stesso senso. 

La trattazione analitica dei problemi di questo tipo, pur supponendo, come io supporrò, 

irrotazionale il movimento del liquido, e trascurabili le forze di massa, incontra difficoltà le 

quali, fatta eccezione per un numero limitatissimo di casi (tra cui quelli accennati), sono da 

ritersi insormontabili. 

Se però ci si contenta di determinare i caratteri generali del fenomeno, di stabilire, per 

esempio, se fra due corpi, in date condizioni di movimento, si esercitano azioni attrattive o 

repulsive, rinunziando alla loro valutazione quantitativa, si arriva con facilità, in tutti quei casi 

che più interessano, allo scopo prefisso. 

È appunto la trattazione del problema così ridotto quella che io qui mi propongo(1). [...] 

(1) Sul problema delle sfere pulsanti o oscillanti, ved. W. Voigt, Beiträge zur Hydrodynamik, 

Gött. Nachr., a. 1891. 

261

262 

Unforgettable, unforgivable, Stefan... 

(Si veda anche la foto con cui si apre il Reprint di Omero Speri e Piero Zorzi nella I Parte di questo 

stesso numero/See also the photograph which appears in the Reprint by Omero Speri and Piero Zorzi 

in the first Part of this same number) 

Marinov: Annus Horribilis 

(The Story of) A Payed Advertisement Published by Nature 

(Stefan Marinov) 

The year l996 will be an earthquake year for conventional physics: many formulas in the 

textbooks will be changed, many century-old dogmas will be renounced and many saints will 

be de-sainted. This radical change had to begin tens of years ago but the lack of glasnost in 

physics all over the world has delayed it and instead to have evolutional step-by-step 

reformations and several lighter earthquakes, now there will be a tremendous one. Vous l'avez 

voulu, Georges Dandins! 

By my half-a-century experimental and theoretical work I showed the following (see 

references in my 16 books, 60 refereed papers, 8 paid advertisements and numerous papers 

and editor's comments in the journal DEUTSCHE PHYSIK edited by me): 

1. The principle of relativity is wrong. Indeed, I rneasured three times optico-mechanically 

and once electromagnetically the Earth's absolute velocity. Its magnitude is 350 km sec -1 wlth 

equatorial coordinates of its apex δ = -20° , α = 12 h (approx.). 

2. The principle of equivalence is wrong. Indeed, my interferometric "coupled mirrors" 

experiment which was carried out during a year showed that when the laboratory's 

acceleration was kinematic (acceleration with respect to distant stars), the laboratory's 

velocity changed, while when it was dynamic (gravitational attraction by the Earth) there was 

no change. 

3. The energy conservation law is wrong. My machines MAMIN COLIU and VENETIN 

COLIU which work with zero, or near to zero, Lenz effect, and SIBERIAN COLIU which

works with anti-Lenz effect violated this law. Only because of lack of money I could not 

close the energetic cycle in the first two, but the third one was not expensive and I could run it 

as a perpetuum mobile. The day when I shall present this machine at a press-conference will 

be the start-day for the earthquake. 

4. The Lorentz equation is wrong. If there are two electric charges q , q' moving with 

velocities v , v' and the vector-distance from q' to q is r , according to the Lorentz 

equation the force with which q'v' acts on qv is given by the following Grassmann formula 

fG = (μ0qq'/4πr 3 ){(v.r)v' - (v.v')r}. (1) 

Numerous experiments done by other authors (Hering's experiments are from the beginning 

of the century!) and by me showed that the force acting on qv can be not only transverse to 

its velocity, as required by (1), but also longitudinal. Any rational man when seeing at least 

one falsifying experiment rejects the respective formula (Popper), however for thousands and 

thousands of Betonköpfe [heads made with ferro-concrete!] even hundred experiments were 

not enough. In the photograph [not included in the original] there is one such falsifying 

experiment which (as well as the other) can be carried out by children: A cylindrical magnet 

is cut along one of its axial planes and the one half is turned up-down (the magnetic forces 

themselves do the rotation). Around this magnet, there is à trough filled with mercury in 

which the copper ring which can be seen at right swims (the children take salt solution and 

suspend the ring on threads). After sending current of some tens of amperes from the battery 

at left, which is regulated by the rheostat, the ring begins to rotate. That's all! 

5. The Lorentz-Marinov equation is the right one. As according to (1) f'G is not equal and 

oppositely directed to fG , I obtained Marinov formula by the most simple and natural 

symmetrization of (1) (take into account that r = -r') 

fM = (fG - f'G)/2 = (μ0qq'/8πr 3 ){(v'.r)v + (v.r)v' - 2(v.v')r} . (2) 

Proceeding from (2), and assuming Φ ≠ 0 , ∂A/∂t ≠ 0 , I obtained by the most simple 

calculations that the force with which an electric system acts on a test charge q moving with 

velocity v is 

f/q = -gradΦ - ∂A/∂t + v×B + vS = Elor + v×B + vS , (3) 

where Φ, A are the electric and magnetic potentials generated by the system at the point of 

the charges location, Blor = rotA is the Lorentz magnetic intensity, Swhit = -divA/2 is the 

Whittaker magnetic intensity and 

Bmar = -(μ0/8π) ∫ q'(v×v')(r.v)/v 2 r 3 , 

Smar = -(μ0/8π) ∫ q'(v.v')(r.v)/v 2 r 3 , (4) 

are the Marinov vector and scalar magnetic intensities. B = Blor + Bmar is called vector 

magnetic intensity and S = Swhitt + Smar is called scalar magnetic intensity. (3) is called the 

Lorentz-Marinov equation. If neglecting the last term and under B we understand Blor we 

obtain the Lorentz equation which I call the Lorentz-Grassmann equation. That's the whole 

theory! 

263

264 

6. The angular momentum conservation law is wrong. My Bul-Cub machine with interrupted 

current and rotating Ampere bridge with interrupted current rotated under the action of 

internal forces only. Marinov's formula allows violation of the angular momentum 

conservation law as the magnetic forces with which two charges interact are equal and 

oppositely directed but may not lie on the line connecting them. 

7. It is impossible to violate the momentum conservation law in electromagnetism. Obvious 

conclusion from Marinov's formula. 

8. Displacement current does not exist. For closed circuits both Grassmann and Marinov 

formulas do not allow violation of the momentum and angular momentum conservation laws 

as the first terms in (1) and (2) contain total differentials. As conventional physics believes in 

the displacement current of Maxwell, it accepts that all currents always are closed. I showed 

by numerous experiments that there is no displacement current (neither in vacuum nor in 

dielectrics) and one can interrupt the circuits by the help of condensers. At the age of 15 I 

understood that displacement current is a phantasmagoria and presented to my teacher in 

Sofia the following objection: "If the displacement current between the plates of a condenser 

acts with magnetic forces on other currents, then according to Newton's third law the other 

currents must act with magnetic forces on the displacement current and set it in motion. But 

how, comrade teacher, can vacuum be set in motion?" Teacher's answer was: "Shut up, 

child!" 

9. The gauge transformations are illegitimate. According to conventional physics not the 

potentials but the intensities determine the motion of the test charge (exactly the opposite is 

true), and thus any change of the potentials which leaves the intensities the same is allowable, 

i.e. one can calibrate the potentials. It is easy to see that the calibration divA = 0 is allowable. 

Thus conventional physics believes that a really existing force, the Whittaker force fw = 

-qvdivA/2 = qvSwhitt can be put equal to zero. Monstrosity! To see the action of fw take two 

metal spheres the one charged positively and the other negatively. Put around one of the 

spheres a circular wire along which current flows, so that it is perpendicular to the line 

connecting the spheres. When connecting the spheres by a wire and current begins to flow, the 

circular wire begins to rotate. The only force which acts on the circular wire is fw . 

10. There is no propagation of interaction. As only mass can move from one point to another, 

"interaction" can be only a ghost. But a rational man does not believe in ghosts. on the other 

hand, the mathematical expressions of Bmar and Smar show that the "fields" cannot propagate 

in space with a certain velocity, as Bmar and Smar depend on the direction of motion of the 

test charge. To these people who may object that one is not sure whether the Lorentz-Marinov 

equation is the right one, my answer is: Until the day when some falsifying experiment should 

be presented (ths day will never come!) the world is impelled to accept it as true. 

11. Potential, radiation and radiation reaction electric intensities. These three kinds of 

intensities can be obtained if putting in the expression for the Lorentz electric intensity Elor 

(see (3)) the observation electric and magnetic potentials 

Φ= q/4πε0r , A = μ0qv/4πr 

with r = r' - v'.r'/c , v = v' + u'r'/c, (5) 

where r , v , u are distance, velocity and acceleration at the observation moment t and r' , 

v' , u' at the advanced mornent t' = t - r/c (conventional physics wrongly calls t' "retarded 

moment"). Conventional physics, following Liénard and Wiechert, wrongly writes A with

v' . For this reason conventional physics obtains only the potential and radiation intensities, 

Epot , Erad , and artificially introduces the radiation reaction intensity Erea coming to 

phantasmagoric "self-accelerations". Proceeding from (5) I (and any child who can 

differentiate!) obtained also the radiation reaction intensity Erea = -μ0qw/6πc , where w = w' 

is the charge's super-acceleration. Erad = μ0qr'×{(r' - v'r'/c)×u'}/4π(r' - v'.r'/c) is due to 

moving mass (radiated energy), as charges moving with acceleration lose energy, while Erea 

acts on the radiating charge itself. To obtain all radiation effects one has simply to integrate 

the obtained formulas for a single charge. That's nearly all about radiation of electromagnetic 

waves! 

12. There are no "fields". According to the "field-marshals" the "fields" exist physically. One 

can move them and a moving magnetic field produces electric field, etc. When I hear all these 

stupidities, I get diarrhea. After repeating the Rowland experiment (a magnetic needle near a 

charged disk deviates when the disk is set in rotation), I carried out the inverse one (the disk 

at rest, the needle rotates) and the co-moving one (disk and needle rotate), taking instead of a 

needle a Hall detector. According te the "field-marshals" the inverse experiment must give the 

same effect as the direct one (I observed no effect), while the co-moving experiment must 

give null result (I observed the same effect as the direct experiment). The inertial experiments 

can be done charging a conveyer belt. 

13. Current conducting wires become charged positively. Conventional physics asserts that 

they remain neutral (Clausius postulate). Meanwhile always after measurements, the rheostat 

in the photograph [included in the original but not here, due to its poor quality] remained 

charged and touching it by hand there was a spark. The positive sign was established by the 

method known to ancient Greeks. Every child explains the effect taking into account that the 

positive electrode of the battery "sucks" electrons from the wire while the negative electrode 

"spits" electrons and the former effect is primary. 

14. B-machines and S-machines. The electromagnetic machines working on B are called Bmachines 

and these ones working on S are called S-machines. By the help of the first three 

fingers of his right hand any child older than 15 can show when looking at the third term in 

(3) that the B-generators brake. Meanwhile by the help of only one finger any child younger 

than 15 can show when looking at the fourth term in (3) that the S-generators accelerate. 

15. The perpetuum mobile SIBERIAN COLIU. Swhitt produced by the first term in (2) and for 

a complete circuit is null. For this reason can be observed only at interrupted circuits (see item 

9). However Smar can be different from zero also for a complete circuit. Why then has 

nobody observed it? - Because all people have worked with cylindrical or quasi-cylindrical 

magnets for which Smar = 0 . Who has cut a cylindrical rnagnet in two pieces rotating the one 

half up-down? - NOBODY!!! The first man who has done this is called Gennadi Nicolaev and 

lives in Tomsk [... - Russian words follow]. For this reason I called this magnet the 

SIBERIAN COLIU magnet and the perpetuum mobile which I constructed with it is the 

SIBERIAN COLIU machine. The machine shown in the photograph [once again not included 

in the original] is a SIBERIAN COLIU machine. It will work as a perpetuum mobile if the 

driving torque produced by the current induced in the ring when it will be set in rotation with 

a certain velocity will be larger than the friction torque. I constructed this machine in the 

photograph in 1993 and the last three years I did nothing else than to try to increase its driving 

torque and decrease its friction torque. The driving torque was produced only by the S (i.e., 

Smar ) currents. Smar is very strong near the cutting plane, from the one side positive, from the 

other negative. The dozens of my SIBERIAN COLIU machines are presented with 

photographs in DEUTSCHE PHYSIK. 

265

266 

16. All conventional theories for the origin of Earth's magnetization are wrong. If rotating a 

cylindrical piece of any metal by a boring machine, one sees that it becomes magnetized. 

Conventional physics believes first that only ferromagnetics become magnetized and second 

that the magnetization is proportional to the angular rotational velocity, as this was 

promulgated by Barnett. My friend C. Monstein demonstrated that the magnetization is 

proportional to the linear rotational velocity and I called this the Monstein-Barnett effect. 

Proceeding from the Monstein-Barnett effect I calculated the magnetization of the Earth, the 

Sun and the planets, obtaining excellent coincidences with the measured values. As Venus is 

the only planet whose nucleus is liquid, it is not magnetized. The most cherished conventional 

theory for Earth's magnetization is the "unipolar dynamo theory" of Elsasser. It is ridiculous, 

as a unipolar machine can work only at the existence of sliding contacts and moving with 

respect to each other parts. 

17. Magretic energy does exist. By the most elementary speculations and calculations I 

showed that: a) the gravitational energy of two masses is not a negative quantitiy, as accepted 

by conventional physics, but a positive quantity, b) the gravitational potential generated by all 

masses of the universe is equal to c 2 , c) electricity and gravity are two completely analogical 

sciences from a mathematical point of view. The only difference is that the gravitational 

"charges" are the proper masses m0 = m/(1 - v 2 /c 2 ) 1/2 and that negative masses do not exist. 

There are no other differences. Thus a magretic energy, i.e., a "magnetic kind" of energy in 

gravity must exist and gravity is to be called gravimagretism (this is the title of part IV of my 

encyclopaedic work CLASSICAL PHYSICS). I proposed a very simple experiment which can 

reveal the existence of magretic energy. This experiment, moreover, can serve for 

measurement of the Earth's absolute velocity. 

18. The recession hypothesis for the galaxies is wrong. I call stellar "red shift" this one which 

is caused by the gravitational action of the star on the emitted by it light, galactic "red shift" 

this one which is caused by the gravitational action of the respective gaIaxy and cosmic - by 

all cosmic matter. Conventional physic believes that the big "red shifts" of Iight coming from 

remote galaxies are due to their recession velocities. This is a phantasmagoria. The most 

simple calculation, which can be carried out by any child, shows that they are due to the 

gravitational action of all cosmic matter and that they are proportional not to the distance of 

the emitting galaxy (or quasar) but to the square of this distance. I showed that the 

experimental data fit much better to a square plot. Respectively, instead of a Hubble constant, 

a Hubble-Marinov constant is te be introduced, for which the children obtain the strictly 

defined value HM 2 = 2πγμ/3c 2 , where γ is the gravitationa constant and μ is the average 

mass density in the Universe. 

NOTE. On the 5 March 1996 I submitted to NATURE my paper AFTER 500 YEARS 

COLUMBUS-EGG-PROBLEM HAS FINALLY BEEN SOLVED, in which I show how a body 

can be maintained in a state of UNSTABLE equilibrium (problem which, contrary to the 

general opinion, Columbus has NOT solved). My "Marinov egg" is supported by magnetic 

forces. If it has SPHERICAL form, it has three degrees of freedom (the Euler angles) free and 

represents moreover a PERPETUUM MOBILE. If before the 1 May the paper will not appear 

in the scientific columns of NATURE, I shall publish it as a paid advertisement. In the first (or 

second) case 15 days after the publication I shall present my SIBERIAN COLIU perpetuun 

mobile at a press conference. 

Stefan Marinov 

Morellenfeldgasse 16, A-8010 Graz 

- - - - -

[The previous pages are reproduced from pp. 34-35 of Marinov's Deutsche Physik 

(International Glasnost Journal on Fundamental Physics), Vol. 5, N. 19, July-September 1996, 

and appeared in Nature, Vol. 380, N. 6572, 28 March 1996, p. xiv, as a payed Advertisement, 

with the attached NOTE as reported. Marinov extensively explains later on in his journal (pp. 

40-45) how he tried to publish instead the following text, but that he was told that: "we are 

enable to publish the advertisement unless [this note] is deleted [...] we would naturally 

refund your money" (letter from Nature, 15th March 1996), so that he had to accept at last the 

publication of an "amended" version.] 

> In my advertisement (whose text is published on p. 34 of this issue) the following NOTE 

was attached: 

NOTE. In 1986 Dr. Maddox, the then-editor of NATURE, accepted for publication my big 

paper "Experimental violations of the principles of relativity, equivalence, and conservation 

of energy and angular momentum". During my visit in March 1987 he personaily began to 

compose this paper on his computer and I stayed in his office and corrected any sheet which 

he gave me. He could not compose the whole paper and I left London. However during a year 

the composition of the paper remained, as Schubert's symphony, unvollendet. Thus in June 

1988 I flew to London and composed the paper myself in NATURE's composition office. The 

paper had to appear on the 18 August 1988 but because of the Benveniste's case ìts 

publìcatiori was postponed for the 13 October. "I do not have the stomach for a second battle 

in such a short tirme" wrote to me Dr. Maddox on the 29 July. This paper is still not 

published. If the paper will not appear in the scientifìc columns of NATURE until the 1 May 

1996, I shall publish it as a paid advertisement. In the first (or second) case 15 days after the 

publicatìon of the paper I shall present my perpetuum mobile SIBERIAN COLIU at a press 

conference. 

As in a week or so after my 13-February-letter no answer came from Mrs. Smith, I asked her 

on the phone which is the matter. She told me that there are problems with the NOTE and that 

she has to consult Dr. Campbell and Dr. Maddox. Until the 26 February no answer came and I 

phoned again. [...] [The conclusion of this story has already been mentioned: after Nature's 

refusal of 15th March, Marinov proposed a different shortened version, which was found 

acceptable: "I can confirm that your amended paragraph of today is acceptable for 

publication" [loc. cit., p. 45]. 

- - - - - 

[The following one is Nature's letter of 26th January 1996 (see the quoted issue of Deutsche 

Physik, p. 38) which refused a paper proposed by Marinov only a few days before, namely on 

22nd January 1996. It was this circumstance which forced him to ask for the publication of 

the payed advertisement above.] 

267

268 

MARINOV'S NOTE. 

First I would like to note that if an editor has pricks of conscience when rejecting a paper, he 

never mentions in bis rejecting letter (if he decides such a letter to write!) the title of the paper 

and the date of submission. The same does Dr. Campbell in his above letter. Thus the title of 

my rejected article was 

EXPERIMENTAL VIOLATIONS OF THE PRINCIPLES OF RELATIVITY, 

EQUIVALENCE, AND CONSERVATION OF ENERGY AND ANGULAR MOMENTUM, 

and it was submitted on the 22 January 1996 by post. 

This paper, as a matter of fact, was accepted for publication by Dr. Maddox in April 1986 

and in final form in June 1988 but it never appeared in NATURE (see the story in detail in the 

following pages). The paper, as composed by me in June in London was published in THE 

THORNY WAY OF TRUTH, Part III (1988), p. 146. 

But Dr. Campbell allowed to me to publish an advertisenìent in NATURE and in her fax of 

the 9 February Mrs. Smith wrote me that the price for two pages will be 5290 £. 

- - - - - 

[Furthermore, on April 1996, after a new correspondence's exchange, Dr. Campbell wrote to 

Marinov the following final letter, which is published at p. 50 of the quoted issue of Deutsche 

Physik, together with a comment of our poor friend Stefan*.]

Only in religion and similar AUTHORITATIVE spiritual and ideological domains are there 

"orthodox" and "unorthodox" views. In physics there are views confirmed or rejected by 

experiments. Of course, there are views for whose verification there are no experiments, or 

contradictory views which predict the same experiments. However a FORMULA can be 

either right or wrong, a formula cannot be "orthodox" or "unorthodox". In my writings I 

present FORMULAS. And I present EXPERIMENTS which can be calculated by these 

formulas and which cannot be calculated by the formulas of "orthodox" physics. 

- - - - - 

[* On the morning of July 15th 1997, Stefan Marinov committed suicide in Graz, the Austrian 

town where he lived very poorly since many years as an exile. As far as his scientific activity 

is concerned, since the times of the previous Advertisement, he had the resources to edit three 

more numbers of Deutsche Physik, namely NN. 20, 21 and 22: the very last one is dated 

April-June 1997... 

More information about this singular figure of dissident XXth Century physicist can be found 

in the article N. 13 ("In Stefan Marinov memoriam") published at the web page: 

http://www.dipmat.unipg.it/~bartocci/listast.htm .] 

269

270 

Intorno alla legge di resistenza al moto 

dei corpi in un mezzo pulviscolare 

(N. Moisseiev) 

INTRODUZIONE. 

Ci proponiamo nel presente articolo di esporre la deduzione della legge di resistenza al moto 

dei corpi in un mezzo pulviscolare, basandoci sugli stessi schemi che furono già posti a 

fondamento di. talune sezioni di un nostro precedente lavoro (1) . 

Questioni relative alla teoria del moto in un mezzo resistente cominciano nuovamente a 

suscitare interesse fra gli studiosi che lavorano nel campo della cosmogonia ed in campi 

affini. Indichiamo ad esempio la serie dei lavori pubblicati dal prof. T. Levi-Civita (2) , i quali 

mirano tanto a dedurre la legge razionale di resistenza al moto, quanto a stabilire le equazioni 

differenziali del moto stesso, ed altresì la serie di studi di G.N. Duboscin (Russ. Astronomical 

Journal), dedicati principalmente all'analisi generale delle forme e delle proprietà del moto di 

un punto in un mezzo resistente ed in campi di forze centrali. 

Il problema stesso può essere trattato da due punti di vista diversi: come problema di 

resistenza di un fluido compressibile o no al moto in seno di esso, oppure come problema di 

resistenza al moto di un mezzo composto di punti discreti, di molecole, l'azione reciproca. 

delle quali ha importanza e va presa in considerazione solamente per definire la struttura del 

mezzo nel suo insieme, mentre nell'interrelazione loro col corpo che subisce resistenza al suo 

moto, dette particelle reagiscono su di esso in modo affatto indipendente l'una dall'altra. 

La prima questione, che rappresenta in sostanza un problema di idro od aerodinamica, può 

presentare interesse per l'astronomia solamente in relazione al moto in mezzi di densità 

sufficientemente grande, come per es. il passaggio di una meteora attraverso l'atmosfera di un 

pianeta ecc. 

Il secondo problema per altro presenta per la cosmogonia un interesse considerevolmente 

maggiore, avendo esso da fare con mezzi molto rarefatti. Ed è per l'appunto questo secondo 

aspetto del problema che prendiamo di mira nel presente lavoro. 

§ I. - Espressioni generali per la resistenza nel caso di flusso semplice. 

Rappresentiamoci un corpo sferico S , di raggio D intorno al cui centro è descritta una sfera 

di raggio ρ , che divide il campo - in cui si può trascurare l'attrazione di questo corpo S - dal 

campo, interno per rapporto a questa "sfera d'azione", in cui il moto di un punto isolato viene 

retto unicamente dall'attrazione del corpo S . Rappresentiamo con x0 il quoziente D/ρ . 

Ammettiamo poi che lo spazio esterno alla sfera d'azione sia, con densità uguale, riempito 

di particelle materiali tanto piccole per dimensioni e per massa che si possa non tener conto 

della loro azione reciproca. Sia n il numero di particelle per unità di volume e μ la massa di 

una particella isolata. Supponiamo, che tutte le particelle abbiano masse eguali. 

Supponiamo poi che il corpo S si muova rispetto al "centro di moto" (3) del complesso di 

particelle con una velocità r . Esaminiamo, nel paragrafo presente, il caso in cui le particelle 

non abbiano velocità proprie per rapporto al loro "centro di moto". Questo caso per l'appunto 

noi chiameremo caso di flusso semplice. Chiameremo asse del flusso la direzione della 

velocità del corpo per rapporto allo sciame di particelle. 

La resistenza che le particelle offriranno al moto del corpo S consterà di due contributi 

diversi:

1. Resistenza delle particelle che passano attraverso la sfera d'azione senza urtare il corpo S ; 

2. Resistenza di particelle urtanti il corpo. L'uno si considererà come assolutamente 

anelastico. 

Applichiamoci a dedurre la formola che corrisponde alle particelle della prima specie. 

Indichiamo, come si usa (4) , con α l'angolo fra la velocità di una particella e il raggio vettore 

nel momento d'entrata nella sfera d'azione; esso sarà anche eguale all'angolo del raggio 

vettore del punto d'entrata coll'asse del flusso. Siano poi R e N le coordinate polari, per le 

quali l'asse del flusso serve di asse polare, e finalmente N(ρ) l'angolo N corrispondente al 

punto d'uscita dalla sfera d'azione. 

Allora, la proiezione della velocità d'entrata sull'asse del flusso sarà 

- r , 

e la proiezione della velocità d'uscita dello stesso punto: 

r cos(N(ρ) + α) . 

Perciò l'aumento di quantità di moto per il corpo S in direzione dell'asse del flusso in 

conseguenza dell'incontro con una particella sarà eguale a: 

(1) - μ r cos 2 [(N(ρ) + α)/2] . 

D'altra parte l'equazione della traiettoria di una particella entro la sfera d'azione può essere 

assunta sotto la forma: 

(2) r2 R R R 

2 ρ sin2(α) + (1 - r ρ)sin(α)sin(N) + cos(α)cos(N) - = 0 , 

ρ 

ρ 

ρ 

donde ricaviamo: 

(3) [(N(ρ) + α)/2] = arctg[(1 - r 2 ρ)tg(α)] . 

Così l'espressione (1) si trascrive nel modo seguente: 

(1.1) - 2 μ r 

1 + 

( 1 

1 

2 2 2 

− r ρ ) tg ( α ) 

. 

Perciò il completo aumento di quantità di moto del corpo in direzione dell'asse del flusso 

nell'intervallo di tempo δt provocato dall'incontro con particelle che non vengano ad urtare il 

corpo stesso sarà: 

(4) M δt = - μ n 4πρ2 π 

2 

δt ∫ 

α = α ( D) 

sin( 

α ) cos( α ) dα 

1 + ( 1 − 2 2 2 

r ρ ) tg ( α ) 

dove α(D) rappresenta il valore limite di α , che corrisponde al. caso in cui la particella 

viene a contatto col corpo S, cioè: 

271

272 

2 

D 2D 

D 1 

α(D) = arcsin + ( 1 − ) 

2 2 

2 , 

ρ ρ ρ r 

e M la massa del corpo S. 

E così, finalmente, per la reazione cercata abbiamo l'espressione 

dr 

(5) R1 = M ( )1 = 

dt 

2 2 

2 2 

μ n2π 

ρ ( 1 − r ρ ) 

( 1 − r ρ ) 

= 

2 [ 

ln 

2 2 

2 2 

2 - 1 + sin 

( 2 − r ρ ) r ρ ( r ρ − 2) 

1 + r ρ ( r ρ − 2) 

sin ( α ( D)) 

2 (α(D))] . 

Occupiamoci ora della deduzione della seconda parte della reazione, dovuta all'urto con le 

particelle per le quali 

α < α(D) . 

E' facile vedere che se ωR è l'angolo del raggio vettore con la velocità, alla distanza R, e rR 

la velocità alla stessa distanza, la componente della quantità di moto di una particella urtante 

il corpo S nel punto (N,D) lungo l'asse del flusso sarà: 

(6) -μ rD cos(N - ωD ) . 

Approfittando dell'equazione della traiettoria e della legge delle aree otteniamo: 

(6.1) cos(N - ωD ) = 

= 

cos( α ) 

2 2 

x ( r ρ − 

2) 

[ 1 

2 2 

2 

2 2 

2 

+ 2x 

− r ρ sin ( α ) − r ρ ( 1 − r ρ )[ x( 

r ρ − 2) 

+ 1] 

sin ( α ) 

. 

2 2 

2 

2 2 

+ r ρ ( r ρ − 2) 

sin ( α )] x ( r ρ − 2) 

+ 2x 

Per trovare l'espressione spettante alla variazione di velocità del corpo S nel piccolo 

intervallo di tempo δt , in conseguenza dell'urto colle particelle del nostro sciame, possiamo 

procedere nel modo seguente: 

Immaginiamoci un certo corpo P* , la cui massa μ* sia eguale alla somma delle masse di 

tutte le particelle, che verranno ad urtarsi col corpo S durante l'intervallo di tempo δt , 

mentre la componente della quantità di moto rispetto al corpo S sia eguale alla somma delle 

componenti delle quantità di moto delle particelle medesime, cioè alla somma delle quantità 

(6). Essendo δt abbastanza piccolo, l'effetto dell'urto con questo corpo fittizio P* e l'effetto 

dell'urto con lo sciame delle particelle coincideranno fra loro. Così, l'aumento di velocità del 

corpo S si esprimerà con la formola seguente, derivante dalle legge di urto di corpi 

assolutamente anelastici: 

(7) δr = 

( μ r) 

* 

M + μ * 

dove M e μ* sono rispettivamente le masse dei corpi S e P* e (μr)* la componente delle 

quantità di moto del corpo P* rispetto a S . La formola (7) rimane naturalmente valida 

indipendentemente dalle velocità assolute dei corpi in questione, poiché in essa intervengono 

solo velocità relative. 

Abbiamo poi:

(8) (μr)* = -μ n 2πρ 2 

e 

α ( D) 

(9) μ* = μ n 2πρ2 ∫ 

α = 0 

α ( D) 

∫ rrD 

α = 0 

cos( N − ω ) sin( 


. δt 

rsin( 


. δt . 

Perciò la reazione cercata sarà in questo caso semplicemente eguale a: 

(10) R2 = M ( dt 

dr 

)2 = - μ n 2πρ2 r rD ∫ 

α = 0 

D 

α ( D) 

cos( N − ω 

dove a cos(N - ωD) va sostituita la sua espressione (6.1). 

Per rD abbiamo la formola seguente: 

(6.2) rD = 

1 

ρ x 

2 

2 − x + r ρ x . 

D 

) sin( 


Riassumendo ciò che precede, perveniamo alla conclusione che la forza di resistenza offerta 

dal nostro mezzo al moto del corpo S sarà rappresentata dalla formola: 

(11) R = R1 + R2 . 

Quest'espressione - particolarmente per il secondo addendo - riesce abbastanza complicata. 

Non staremo perciò a trascrivere le espressioni complete per il caso generale, ma ci 

limiteremo all'analisi della legge trovata nelle sue caratteristiche essenziali. E per questo 

esamineremo in una prossima Nota i casi particolari più importanti. 

(1) N. Moisseiev, Ueber einige Grundfragen der lheorie des Ursprungs der Kometen, 

Meteore und des kosmischen Staubes, I., II., III. Teil, "Publications de l'Institut 

Astrophysique", vol. V, fasc. I. 

(2) T. Levi-Civita, Corpuscoli cosmici e distribuzione Maxwelliana, "Atti Acc. Pontificia", 

Anno LXXXIII (1930), pp. 176-189; Ancora sul moto di un corpo di massa variabile, questi 

"Rendiconti", vol. XI, 1930, pp. 626-632; ecc. 

(3) Vedi Ueber einige Grundfragen ecc., I. Teil, $ 1. 

(4) V. loc. cit. 

- - - - - 

Questo lavoro, presentato dal Socio Tullio Levi-Civita nella seduta del 3 gennaio 1932, è stato 

pubblicato nei Rendiconti della Reale Accademia dei Lincei, 1932, Vol. XV, pp. 135-139. 

273

274 

Exodus of Einstein's Special Theory in Seven Simple Steps 

Introduction. 

(Carl A. Zapffe) 

For those who admire the orderliness of epistemology in theoretical physics, and are 

committed to the requirements of logic in experimental physics, the following should be of 

interest, and particularly because it knifes through the confusion of a century's wrangling over 

c ± v values for the velocity of light. 

The Seven Steps. 

Seven steps of factual information come under present consideration, the first two of which 

serve to shake loose the long-standing and generally unquestioning fixation upon Einstein's 

special theory of relativity (STR) so that it can be re-examined without bias: 

I. The mass-energy relationship E = mc 2 does not depend upon the STR, whereupon the 

fate of the two are not inseparable. 

As Lewis [1] demonstrated in 1908, and Einstein himself admitted in 1950 [2], the 

fact of mass-energy equivalence has been inherent within the charge-momentum relationships 

of Maxwell's field equations since long before Einstein was born. 

II. Elementary-particle phenomena in nuclear physics, which do exhibit the (1 - v 2 /c 2 ) -1/2 

relationship of an asymptotic c for both decay life τ and mass increase in terms of e/m , do 

not necessarily confirm the Lorentz transfomation for t and x . 

This traditional identity is pure surmise, following from the convenience of the 

(1 - v 2 /c 2 ) -1/2 term already appearing in the Lorentz transformation, and the heuristic appeal of 

an argument that, since even the complex structure of the human being is composed of 

elementary particles, that which measures time τ for the one measures time t for the other. 

But on the one hand, these velocity-dependent changes - and specifically if velocity be proved 

absolute - submit as well to the same treatment as the rate equations of chemistry and 

thermodynamics, which of course support neither one transformation nor another; while on 

the other hand heuristics is scarcely the dependable tool for bridging such a gap as that 

between pions and hemoglobin. Metallurgists use similar τ measurements for the decay 

behaviour of the positron [3,4], which is about as elementary as a particle can get; and the 

changes in this case have no relationship whatever with velocity, the velocity being v = 0 . 

Next we encounter these two massive criticisms of the STR epistemology, 

one pinpointing the long debate over the chronometric paradoxes, the other using the steps of 

logic to return the physical model from Einstein back to Lorentz: 

III. An impossible contradiction stands in the prediction of the Einstein equations that two 

clocks, in motion relative to one another, can each be found running slow. 

This classical controversy was spearheaded by the late Herbert J. Dingle, whose 

book Science at the Crossroads [5] should be read. Despite the widely ranging imagination 

of STR apologists, the only acceptable answer next follows. 

IV. Only if the velocity is absolute can this contradiction be resolved; and if velocity is 

absolute so is space.

This was the monumental work of Ives [6], and the classical papers of Builder [7,8], 

recently confirrned experimentally by studies of isotropy and anisotropy of the 3°K 

background radiation [9]. 

V. But if both velocity and space are absolute, then so is time. 

This follows simply from v = x/t ; and the time t is presumably that d 2 s/dt 2 of the 

cosmically unfolding "Big Bang", or its competing models. Therefore any velocity-dependent 

features, and specifically those of elementary particles, are referable on the one hand to the 

chronometry of this cosmic unfolding, and on the other hand to the isotropy of its radiative 

framework. 

There only remains to resolve certain problems with the seemingly 

electromagnetic or Maxwellian substructuring of this space. 

Return to Galilean-type Transformation. 

VI. An elementary principle of geophysics is that light from the aurora borealis or 

australis, and indeed every other electromagnetic disturbance within the domain of the 

terrestrial magnetosphere, arrives upon the surface at velocity c relative to geocentric rest 

coordinates. Similarly, it is presumed in astrophysics that all radiation traversing a stellar 

magnetosphere does so at velocity c relative to the coordinates of the repective 

magnetosphere. 

VII. Since experimental physics has similarly proved, from the time of Arago's starlit 

prisms in 1810 [10], to such recent tests as those of Brillet and Hall [11], that light from 

either terrestrial or extraterrestrial sorces similarly traverses the local magnetosphere at 

velocity c , .simple principles of geometry and trigonometry then require that c ± v light 

velocities do obtain, though the differential is only discoverable along the magnetosheath 

which separates the Maxwellian domain of one magnetosphere from that of another. 

This is the main thrust of the Magnetospheric Ether-Drag Theory [12, 13], which 

merely calls attention of relativists to principles already welI established in geophysics. 

Conclusion. 

From this progression of seven observations, one can only arrive at the following seven 

conclusions: 

1. Einstein's physical model for his special theory of relativity must be abandoned in 

favour of that of Lorentz. 

2. Lorentz's physical model must similarly be abandoned because of its outmoded field 

features from standpoints of magnetospheric physics. 

3. The Einstein-Lorentz transformation must then be abandoned also because of these 

errors in points of physical model. 

4. With abandonment of the Lorentz transformation, velocity-dependent phenomena 

such as those in elementary-particle physics enter the province of mere rate equations: 

dϕ/dv , d 2 ϕ/dt 2 , dτ = f(v) = τ0 (1 - v 2 /c 2 ) -1/2 , ... etc. 

5. All (1 - v 2 /c 2 ) -1/2 relationships in general become interpreted merely as asymptotic 

cosine or sec θ functions, identical with the linear equations for subsonic aerodynamics and 

hydrodynamics, and unrelated except fortuitously to this same factor in the Lorentz-Einstein 

transformation. 

6. No alteration at all attends the mass-energy equivalence E = mc 2 . 

275

276 

7. A physical model is new at hand, long known to geophysics but completely novel to 

relativistic physics, in which space is structured in terms of the phenomenology of 

electrodynamics, and which not only permits experimental confirmation, but promises an 

entirely new navigational approach to astronautic odometry - measuring of one's position in 

celestial reaches of so-called "empty" space. 

Bibliography 

[1] Lewis, G.N.: A Revision ol the Fundamental Laws of Matter and Energy, Phil. Mag. 16, 70517 

(1908). 

[2] Einstein, A.: Out of My Later Years, Philosoph. Lib., New York, viii + 282 (1950). 

[3] Lynn, K. G. and Byrne, J. G.: Positron Lifetime Studies Made in Fatigue-Damaged AISA 4340 

Samples, Metall. Trans. (A) 7, 604-6 (Apr. 1976). 

[4] Hadnagy, T. D.; Byrne, J. G.; and Miller, G. R.: Effect of Porosity on the Mean Lifetime of 

Positrons in Scintered and Hot-Pressed Alpha-Alumina, J. Am. Ceramics Soc. 60, 461-3 (Sept.- 

Oct. 1977). 

[5] Dingle, H.: Science at the Crossroads, Martin Brian and O'Keefe, London, 256 pp. (1972). 

[6] Hazelett, R. and Turner, D. (ed. by): The Einstein Myth and the Ives Papers, The Devin-Adair 

Co., Old Greenwich, CO. ix + 313 (1979). 

[7] Builder, G.: Ether and Relativity, Australian J. of Phystcs 2, 279-97 (1958). 

[8] Builder, G.: The Constancy of the Velocity of Light, Australian J. Phystcs 2, 457-80 (1958). 

[9] Smoot, G. F.; Gorenstein, M. V.; and Muller, R. A.: Detection of Anisotropy in the Cosmic 

Blackbody Radiation, Phys. Rev. Letts. 39, No. 14, 898-901 (3 Oct. 1977). 

[10] Arago, F.: (Fr.) The Velocity of Light, Abs. Procès-verbaux des Séances de 1'Académie des 

Sciences, Paris, p. 399 (l0 Dec. 1810). 

[11] Brillet, A.; and Hall, J. L.: Improved Laser Test of the Isotropy of Space, Phys. Rev. Lett. 42, 

549-52 (1979). 

[12] Zapffe, C. A.: A Magnetospheric Ether-Drag Theory and the Reference Frames of 

Relativistic Physics, SST. 2 No. 4, 439-54; disc. 455-9 (1979); 3, No. 4, 483-5 (1980). 

[13] Zapffe, C. A.: The Magnetosphere in Relativistic Physics, Ind. J. Theoret. Phys. 30, No. 1 

(1982). 

* * * * * 

This essay first appeared in The Toth-Maatian Review, Volume 3, Number 4, 

January 1985, pp. 1531-1535. By: CARL A. ZAPFFE, 6410 Murray Hill Rd., Baltimore, 

MD 21212.

RECENSIONI/ 

REVIEWS 

277

278 

Albert Einstein, The Incorrigible Plagiarist 


(XTX Inc., DownersGorve, Illinois, USA, 2002) 

"The secret to creativity is knowing how to hide your sources" 

(Albert Einstein) 

Proposing again the remark which we made some time ago in the presentation of Kostro's 

Einstein and the Ether (Episteme, N. 3, 21 April 2001, pp. 306-310), "common people", and 

even "common scientists", will be surprised by the facts they discover in Bjerknes' book 

(about 400 pages), which is quite useful, in that it establishes a realistic - and more 

reasonable! - picture of one of the most propagandized scientific myths of all time, namely 

Einstein's myth (see for instance: Alan J. Friedman & Carol C. Donley, Einstein as Myth and 

Muse, Cambridge University Press, 1985). 

As a matter of fact, reading this text should be a must for all people professionally interested 

in the "history" of Physics or of Science (for these readers the book, its "polemical" thesis 

notwithstanding, could become an indispensable tool, packed as it is with information, 

quotations, meticulous references, etc.), but it is highly recommended even to teachers, 

scientists of all kind, philosophers, epistemologists, in general to every person interested in 

the evolution of human civilization and knowledge. Indeed, it would be difficult to deny that 

the emergence of modern science is one of the most relevant events of all times, and that 

Relativity in particular is the "theory" which had the greatest impact and influence on XXth 

Century Western thought - though, in our opinion, and clearly in Bjerknes' as well, a negative 

one). 

The book is a successful attempt to break down some of the many commonplaces and 

misconceptions which fill the typically apologetic History of Science, and the author does not

seem at all afraid to take on such a "giant". As a consequence, the result of his efforts is a 

genuinely "rare find" and an interesting one. 

In addition, we must emphasize that Christopher Jon Bjerknes is the great great grandson of 

Carl Anton Bjerknes, who created the Pulsating Sphere Theory of Gravity and of 

Electromagnetism, and who played an important rôle in the creation of the concept of charged 

particle mass. 

Vilhelm, Carl's son, also became famous for his work in Meteorology (Polar Front Theory; 

see for instance Appropriating the Weather: Vilhelm Bjerknes and Construction of a Modern 

Meteorology, by Robert Marc Friedman, Cornell University Press, 1993; Vilhelm Bjerknes, 

MEM Volume of the American Meteorological Society, 1962), but his primary focus was 

always on Physics and Hydrodynamics of Aether Models, and he was the scientist who gave 

the Columbia lectures which are quoted in Almansi's paper (Fields of force, Columbia 

University Press, New-York, 1906; see the section entitled Reprints in this same volume of 

Episteme). 

Continuing a truly fine family tradition, Vilhelm's son, Jacob, is also quite famous for his 

work in Meteorology (Theory of Cyclones - El Niño), and now we can say that Christopher 

Jon is carrying on following the footsteps of "aether theorists", who disliked (as we do) 

Einstein's theory, and the consequent disappearance of the concept of aether from mainstream 

Physics. 

We must emphasize that this choice of "party" does not influence the usefulness of Bjerknes' 

essay even for those not willing to admit this criticism of Relativity. As a matter of fact, the 

book could even be construed to be rather more in favor of Relativity than the contrary, since 

the proof that Einstein "borrowed" many ideas from others famous scientists, renders them 

responsible for the dangerous nichilistic and irrational drift of modern scientific thought, 

which Episteme has always aimed to fight... 

We proceed with the presentation of the book presenting first its Table of Contents, and 

further a few excerpts. Afterwards, we publish some additional commentary, mainly Phipps' 

review (another scientist well known for his rather critical attitude against Relativity; we 

thank Dr. Eugene F. Mallove, the Editor-in-Chief of Infinite Energy Magazine, for his consent 

to publish it in parallel). We end this "chapter" with an Appendix written by Bjerknes himself 

for the next edition of his research, honored to be able to present it to our readers in exclusive 

preview. 

TABLE OF CONTENTS: 

1. THE PRI0RITY MYTH 

2. SPACE-TIME, OR IS IT "TIME-SPACE"? 

3. "THEORY OF RELATIVITY" OR "PSEUDORELATIVISM"? 

4. HERO WORSHIP 

5. E = mc 2 

6. EINSTEIN'S MODUS OPERANDI 

7. HISTORY 

8. MILEVA EINSTEIN-MARITY 

9. P0LITICS AND ANECDOTES 

NOTES 

INDEX 

279

280 

info@xtxinc.com 

http://www.xtxinc.com 

- - - - - 

[Two articles of the author, together with information about his life and work, 

are published in this same volume of Episteme] 

- - - - - 

Excerpts (Reprinted by permission. All rights reserved) 

It is easily proven that Albert Einstein did not originate the special theory of relativity in its 

entirety, or even in its majority. The historic record is readily available. Ludwig Gustav 

Lange, Woldemar Voigt, George Francis FitzGerald, Joseph Larmor, Hendrik Antoon 

Lorentz, Jules Henri Poincaré, Paul Drude, Paul Langevin, and many others, slowly 

developed the theory, step by step, and based it on thousands of years of recorded thought and 

research. Einstein may have made a few contributions to the theory, such as the relativistic 

equations for aberration and the Doppler-Fizeau Effect, though he may also have rendered an 

incorrect equation for the transverse mass of an electron, which, when corrected, becomes 

Lorentz' equation. 

Albert Einstein's first work on the theory of relativity did not appear until 1905. There is 

substantial evidence that Albert Einstein did not write this 1905 paper on the "principle of 

relativity" alone. His wife, Mileva Einstein-Marity, may have been co-author, or the sole 

author, of the work. 

If Albert Einstein did not originate the major concepts of the special theory of relativity, how 

could such a historically significant fact have escaped the attention of the world for nearly a 

century? The simple answer is that it did not. 

- - - - - 

Book Description 

(from an auto-review appeared in Canberra Times, an Australian newspaper, Thursday, 19 

September 2002) 

The name ''Einstein'' evokes images of a good-humoured genius, who revolutionised our 

concepts of space, time, energy, mass and motion. Time named Albert Einstein "person of the 

century". The language itself has incorporated "Einstein" into our common vocabulary as a 

synonym for extraordinary brilliance. Many consider Einstein to have been the finest mind in 

recorded human history. 

That is the popular image, fostered by textbooks, the media, and hero worshiping physicists 

and historians. However, when one reads the scientific literature written by Einstein's 

contemporaries, a quite different picture emerges: one of an irrational plagiarist, who 

manipulated credit for their work.

Einstein is perhaps most famous for the special theory of relativity, published in 1905 in the 

German physics journal, Annalen der Physik. The paper was devoid of references, a fact that 

Einstein's friend and Nobel prize winner for physics, Max Born, found troubling. 

''The striking point is that it contains not a single reference to previous literature,'' Born stated 

in 1955, before the International Relativity Conference in Bern. ''It gives you the impression 

of quite a new venture. But that is, of course, as I have tried to explain, not true.'' 

Though Einstein's 1905 article contained no references, it was so strikingly similar to a paper 

written by Hendrik Lorentz the previous year, that Walter Kaufmann and Max Planck felt a 

need to publicly point out that Einstein had merely provided a metaphysical reinterpretation 

and generalisation of Lorentz' scientific theory, a metaphysical reinterpretation and 

generalisation Henri Poincare had already published. 

As Charles Nordmann, astronomer to the Paris Observatory, pointed out: ''It is really to Henri 

Poincare, the great Frenchman whose death has left a void that will never be filled, that we 

must accord the merit of having first proved, with the greatest lucidity and the most prudent 

audacity, that time and space, as we know them, can only be relative. A few quotations from 

his works will not be out of place. They will show that the credit for most of the things which 

are currently attributed to Einstein is, in reality, due to Poincare.'' 

Einstein acknowledged the fact, but justified his plagiarism in a cavalier fashion in Annalen 

der Physik in 1907. "It appears to me that it is the nature of the business that what follows has 

already been partly solved by other authors. Despite that fact, since the issues of concern are 

here addressed from a new point of view, I believe I am entitled to leave out a thoroughly 

pedantic survey of the literature, all the more so because it is hoped that these gaps will yet be 

filled by other authors, as has already happened with my first work on the principle of 

relativity through the commendable efforts of Mr. Planck and Mr. Kaufmann." 

The completed field equations of the general theory of relativity were first deduced by David 

Hilbert, a fact Einstein was forced to acknowledge in 1916, after he had plagiarised them 

from Hilbert in late 1915. Paul Gerber solved the problem of the perihelion of Mercury in 

1898. Physicist Ernst Gehrcke gave a lecture on the theory of relativity in the Berlin 

Philharmonic on August 24, 1920, and publicly confronted Einstein, who was in attendance, 

with Einstein's plagiarism of Lorentz' mathematical formalisms of the special theory of 

relativity, Palagyi's space-time concepts, Varicak's non-Euclidean geometry and of the 

plagiarism of the mathematical solution of the problem of the perihelion of Mercury first 

arrived at by Gerber. Gehrcke addressed Einstein to his face and told the crowd that the 

emperor had no clothes. 

This was Einstein's response published in the Berliner Tageblatt und Handels-Zeitung on 

August 27, 1920, translated into English in the book Albert Einstein's Theory of General 

Relativity edited by Gerald E. Tauber: ". . . Gerber, who has given the correct formula for the 

perihelion motion of Mercury before I did. The experts are not only in agreement that 

Gerber's derivation is wrong through and through, but the formula cannot be obtained as a 

consequence of the main assumption made by Gerber. Mr Gerber's work is therefore 

completely useless, an unsuccessful and erroneous theoretical attempt. 

"I maintain that the theory of general relativity has provided the first real explanation of the 

perihelion motion of mercury. I have not mentioned the work by Gerber originally, because I 

did not know it when I wrote my work on the perihelion motion of Mercury; even if I had 

been aware of it, I would not have had any reason to mention it." 

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The fact that Einstein was a plagiarist is common knowledge in the physics community. What 

isn't so well-known is that the sources Einstein parroted were also largely unoriginal. In 1919, 

writing in the Philosophical Magazine Harry Bateman, a British mathematician and physicist 

who had emigrated to the United States, unsuccessfully sought acknowledgment of his work. 

"I am perhaps entitled to do this as my work on the subject of general relativity was published 

before that of Einstein and Kottler, and appears to have been overlooked by recent writers." 

My book is a documentation of Einstein's plagiarism of the theory of relativity. It discloses his 

method for manipulating credit for the work of his contemporaries, reprints the prior works he 

parroted, and demonstrates that he could not have drawn his conclusions without prior 

knowledge of the works he copied but failed to reference. 

Numerous republished quotations from Einstein's contemporaries prove that they were aware 

of his plagiarism. Side-by-side comparisons of Einstein's words juxtaposed to those of his 

predecessors prove the almost verbatim repetition. There is even substantial evidence 

presented in the book that Einstein plagiarised the work of his first wife, Mileva Maric, who 

had plagiarised others. 

"Although generally associated with the names of Einstein and Minkowski, the really essentia physical 

considerations underlying the theories are due to Larmor and Lorentz." -- Alfred Arthur Robb 

"Einstein published a paper which set forth the relativity theory of Poincaré and Lorentz with some 

amplifications, and which attracted much attention." -- Sir Edmund Whittaker 

"The appearance of Dr. Silberstein's recent article on 'General Relativity without the Equivalence 

Hypothesis' encourages me to restate my own views on the subject. I am perhaps entitled to do this as 

my work on the subject of General Relativity was published before that of Einstein and Kottler, and 

appears to have been overlooked by recent writers." -- Harry Bateman 

"All this was maintained by Poincare and others long before the time of Einstein, and one does 

injustice to truth in ascribing the discovery to him." -- Charles Nordmann 

"Many of you have looked upon [Einstein's] paper 'Zur Elektrodynamik bewegter Koerper' in Annalen 

der Physik ... and you will have noticed some peculiarities. The striking point is that it contains not a 

single reference to previous literature. It gives you the impression of quite a new venture. But that is, 

of course, as I have tried to explain, not true." -- Max Born 

"In point of fact, therefore, Poincaré was not only the first to enunciate the principle, but he also 

discovered in Lorentz's work the necessary mathematical formulation of the principle. All this 

happened before Einstein's paper appeared." -- G. H. Keswani 

"Einstein's explanation is a dimensional disguise for Lorentz's. ... Thus Einstein's theory is not a denial 

of, nor an alternative for, that of Lorentz. It is only a duplicate and disguise for it. ... Einstein 

continually maintains that the theory of Lorentz is right, only he disagrees with his 'interpretation.' Is it 

not clear, therefore, that in this, as in other cases, Einstein's theory is merely a disguise for Lorentz's, 

the apparent disagreement about 'interpretation' being a matter of words only?" -- James Mackaye

- - - - - 

Mr Bjerknes, an American historian of science, has authored six books on 

Einstein and the theory of relativity. Albert Einstein: The Incorrigible Plagiarist 

(ISBN 0971962987) is available at www.amazon.com. 

A reviewer, a physicist, July 18, 2002 

- - - - - 

ALBERT EINSTEIN WAS INDEED A PLAGIARIST 

This book is very well documented, and, therefore, very convincing. I read the Dover reprint 

of 'The Principle of Relativity' years ago, and realized then that Einstein just copied Lorentz, 

because Lorentz' article appeared a before Einstein's and says essentially the same things. But 

this book goes far beyond that and really shows a pattern by Einstein of plagiarism. I was 

surprised to discover that Einstein's wife may have written the journal articles for him. The 

number of citations and quotations in this book is really impressive and together form a 

compelling argument stated in a very logical progression of facts. My only regret is that there 

isn't more on the general theory of relativity, but the author hinted that more is to come, and 

that this book is part of a series. I look forward to the future releases. I'm pleased with it and 

would recommend it. It will change your view of Einstein and of the theory of relativity. If 

you are doing research, I can tell you that I have never seen a book which provides more 

information on the complete history of the theories than this book, including Whittaker's. 

* * * * * 

Review of Albert Einstein The Incorrigible Plagiarist 

(Thomas E. Phipps, Jr.) 

(From Infinite Energy Magazine, N. 47, 6 October, 2002) 

(http://www.infinite-energy.com) 

Hagiophobia is defined as "a morbid dread of holy things." There is no question that the 

author of this book, Christopher Jon Bjerknes, is an exemplary sufferer from this too-rare 

complaint. For in our time Albert Einstein has been sanctified … perhaps even above Albert 

Schweitzer, who certified the holiness of all living things, himself included. Einstein's life 

having been told and retold by numerous hagiographers, Bjerknes has made it his aim to 

provide the market with equally numerous anti-hagiographies - this being apparently the sixth 

he has written. The publishers have burdened the latest with a disclaimer, "This book is 

intended solely for entertainment purposes." However, we all know that nothing entertains 

better than a good character assassination. 

For this purpose the book employs the Socratic method, the asking of loaded questions - in 

the style of, "Was this man ever known to stop beating his wife?" Physicists, who lead the 

pack of Einstein idolaters, will dismiss Bjerknes's questions with contempt. But I think others 

will be impressed, if nothing else, by the sheer doggedness of the scholarship that has gone 

into the bibliography. This fills almost half the book and comprises 567 numbered endnotes, 

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some of which stretch for more than a page and include extensive references to the literature. 

Among these notes will be found almost anything that has been written by or about Einstein 

or his ideas, to the present date. My own limited scholarly resources noted only one omission: 

Karl Popper, the philosopher who first (?) linked the names of Einstein and Parmenides, is 

absent. But Parmenides is here, as he amply deserves to be. 

From the start we note a deep schism: the author would like to side with feminists who see 

Einstein's work as actually done by his much smarter first wife Mileva; but, since Bjerknes 

also wants to paint that same work as stolen from earlier investigators, he faces an abiding 

problem of whose character to assassinate. Here the Socratic method proves a life-saver: 

Rather than offering a definitive choice, he provides weaponry for assassinating both Albert 

and Mileva, and leaves it to the reader's political preference, an open question, which 

candidate to take as the priority target. 

Given all this smoke, how much fire is present? Einstein (or Einstein-Marity, the first wife) 

stands accused primarily of "plagiarism" in respect to the basic ideas of the special relativity 

theory. Narrowly construed, plagiarism refers to the copying of an earlier author's published 

words. No such charge can be laid against Einstein. The author exhibits not a single instance 

of word-copying or what the litigious would term copyright infringement. But that is not what 

Bjerknes means. He is referring to the theft of ideas without acknowledgment. Here the case 

is much stronger and also much fuzzier. Einstein's 1905 paper (which - amazingly - was 

originally submitted to Annalen der Physik under the name Einstein-Marity, according to the 

first-hand account, cited here, of Abram Joffe) contained not a single reference to earlier 

work. This is frowned on in modern science, and should have been challenged by the editor 

even then. For Einstein would have been a poor scholar, indeed, if he had failed to read 

Poincare's prior work on relativity, which explicitly enunciated the Principle of Relativity. 

One can understand omission of any reference to the much earlier work of Wilhelm Weber, 

who developed the first and last relativistic formulation of electrodynamics in terms of 

relative coordinates, velocities, and accelerations - since such would have directed attention to 

the persistence of absolutist elements within "special relativity" theory. (The "observer" or 

"frame" is such an element - a tertium quid extraneous to the intrinsic elements to be 

described in nature, and wholly absent from Weber's theory. Minkowski's covariant 

symmetrizing of the quid among all its quiddities alleviates, but does not eradicate, this echo 

of absolutism.) 

Another dilemma of the author in respect to special relativity is whether to concentrate his 

attack on the theory itself or on its creator. If the theory is no good and was in fact stolen by 

Einstein (or by Mileva) from predecessors, then it would seem the blame for this no-goodness 

should fall most heavily on the latter. Error plagiarized is not error sanitized. Its provenance 

aside, Bjerknes clearly distrusts the special theory (as does the present reviewer); but the book 

makes little serious contribution to the comparatively vast (though little known and little 

regarded) literature of its logical criticism. 

Einstein's (or Einstein-Marity's) originality consisted in adjoining the Poincare relativity 

principle to the Maxwell equations (which contain only one field propagation velocity 

parameter c and thus necessitate what we now call "Einstein's second postulate") and in 

showing that these stark logical ingredients suffice to imply a kinematics based on the 

mathematical coordinate transformations that Lorentz had already spelled out. Clearly the 

ideas pre-existed. But, as all inventors know, it is not permissible to patent ideas. If the 

combining of pre-existing ideas in new patterns is to be called "plagiarism," then it would not 

be an over-statement to say that all scientific progress and all invention depend on just this 

kind of plagiarism … for what did Newton do but plagiarize from the giants on whose 

shoulders he acknowledged standing? He neglected only to attach names to the giants. So did 

Einstein. In both cases the behavior was perhaps a trifle magisterial … and also perhaps more 

than a trifle forgivable. Still, unpleasant doubts persist in the Einstein case: Bjerknes shows 

that Einstein's scientific publications reveal a lifetime pattern of similar magisterial behavior.

The absence of attributions in the 1905 paper was not a one-off occurrence. For example, I 

quote from page 231 of the book: "David Hilbert, on whom Einstein went calling for help, 

published the general theory of relativity before Einstein. Why after many years of failure, did 

Einstein suddenly realize, within a few days after David Hilbert's work was public, the 

equations which Hilbert published before him, and then submit his, Einstein's, identical 

formulations?" 

As you can see, this last (stripped of its Socratic question mark) constitutes a genuine charge 

of plagiarism … but it is not backed by chapter and verse citation, equation number by 

corresponding equation number, word by word. Lacking such substantiation, the charge 

cannot stand in court. In law, equations, like ideas, cannot be copyrighted or patented. Still, 

here is more smoke. It is doubtful if all such can be permanently cleared away. But one would 

like to see scholarship comparable to that of Bjerknes applied to the task. Otherwise, a 

polluted atmosphere and a bad odor linger. 

In conclusion, I recommend the book to Einstein scholars and to sociologists of science as a 

genuinely valuable bibliographical resource for further research on the man and his times - 

and as a target for the Einstein hagiographers to shoot down if they can. Other readers, in 

search of more than entertainment, must proceed with caution. 

Thomas E. Phipps, Jr. 

908 South Busey Avenue 

Urbana, IL 61801, USA 

(XTX, Inc., Downers Grove, IL 60515, 2002, Paperback $19.95, ISBN 0-9719629-8-7) 

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A Short History of the Concept of Relative Simultaneity 

in the Special Theory of Relativity 


Abstract. There is a common misconception enunciated in numerous histories, that Albert Einstein 

was the first person to propose the relativity of simultaneity. It is often alleged that the paper, "Zur 

Elektrodynamik bewegter Körper", Annalen der Physik, Series 4, Volume 17, (1905), pp. 891-921, at 

892-895, contained the first proposal of a clock synchronization method employing observers and light 

signals. Given the absence of references in Einstein's work, it has been further assumed by some that 

the revised thought-experiment regarding a midpoint and relative simultaneity, which appeared in 

Einstein's 1916 work, "Die Relativität der Gleichzeitigkeit", Über die spezielle und die allgemeine 

Relativitätstheorie, Chapter 9, Friedr. Vieweg & Sohn, Braunschweig, (1917), pp. 16-19, was also an 

original idea. The historic record proves otherwise. 

Piecing together the Missing References in Einstein's Plagiarized Works 

In 1887, Woldemar Voigt published the following relativistic transformation of space-time 

coordinates [1]: 

x' = x - vt , y' = y / γ , z' = z / γ , t' = t - vx / c 2 , where γ = 1 / ( 1 - v 2 / c 2 ) 1/2 . 

Poincaré asserted that simultaneity is relative, in 1898: 

"XII. But let us pass to examples less artificial; to understand the definition implicitly supposed by the 

savants, let us watch them at work and look for the rules by which they investigate simultaneity. 

I will take two simple examples, the measurement of the velocity of light and the determination of 

longitude. 

When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this 

moment, happened nevertheless fifty years ago, I seek his meaning, and to that end I shall ask him first 

how he knows it, that is, how he has measured the velocity of light. 

He has begun by supposing that light has a constant velocity, and in particular that its velocity is the 

same in all directions. That is a postulate without which no measurement of this velocity could be 

attempted. This postulate could never be verified directly by experiment; it might be contradicted by it 

if the results of different measurements were not concordant. We should think ourselves fortunate that 

this contradiction has not happened and that the slight discordances which may happen can be readily 

explained. 

The postulate, at all events, resembling the principle of sufficient reason, has been accepted by 

everybody; what I wish to emphasize is that it furnishes us with a new rule for the investigation of 

simultaneity, entirely different from that which we have enunciated above. 

This postulate assumed, let us see how the velocity of light has been measured. You know that 

Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its 

prediction. But how is this prediction made? It is by the aid of astronomic laws, for instance Newton's 

law. 

Could not the observed facts be just as well explained if we attributed to the velocity of light a little 

different value from that adopted, and supposed Newton's law only approximate? Only this would lead 

to replacing Newton's law by another more complicated. So for the velocity of light a value is adopted, 

such that the astronomic laws compatible with this value may be as simple as possible. When 

navigators or geographers determine a longitude, they have to solve just the problem we are 

discussing; they must, without being at Paris, calculate Paris time. How do they accomplish it? They 

carry a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the

quantitative problem of the measurement of time. I need not take up the difficulties relative to this 

latter problem, since above I have emphasized them at length. 

Or else they observe an astronomic phenomenon, such as an eclipse of the moon, and they suppose 

that this phenomenon is perceived simultaneously from all points of the earth. That is not altogether 

true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there 

would be a correction to make according to a complicated rule. 

Or else finally they use the telegraph. It is clear first that the reception of the signal at Berlin, for 

instance, is after the sending of this same signal from Paris. This is the rule of cause and effect 

analyzed above. But how much after? In general, the duration of the transmission is neglected and the 

two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be 

made by a complicated calculation; in practise it is not made, because it would be well within the 

errors of observation; its theoretic necessity is none the less from our point of view, which is that of a 

rigorous definition. From this discussion, I wish to emphasize two things: (1) The rules applied are 

exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the 

quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether 

account must be taken of a velocity of transmission, as that of light, because such a velocity could not 

be measured without measuring a time. 

XIII 

To conclude: We have not a direct intuition of simultaneity, nor of the equality of two durations. If we 

think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply 

almost always without taking count of them.[2]" 

Circa 1899, Poincaré clarified the fact that he saw no distinction between "time" and "local 

time": 

"Allow me a couple of remarks regarding the new variable t': it is what Lorentz calls the local time. At 

a given point t and t' will not defer but by a constant, t' will, therefore, always represent the time, but 

the origin of the times being different for the different points serves as justification for his 

designation." 

"Disons deux mots sur la nouvelle variable t': c'est ce que Lorentz appelle le temps locale. En un point 

donné t et t' ne différeront que par une constante, t' représentera donc toujours le temps mais l'origine 

des temps étant différente aux différents points: cela justifie sa dénomination.[3]" 

In 1900, Poincaré stated: 

"In order for the compensation to occur, the phenomena must correspond, not to the true time t, but to 

some determined local time t' defined in the following way. 

I suppose that observers located at different points synchronize their watches with the aid of light 

signals; which they attempt to adjust to the time of the transmission of these signals, but these 

observers are unaware of their movement of translation and they consequently believe that the signals 

travel at the same speed in both directions, they restrict themselves to crossing the observations, 

sending a signal from A to B, then another from B to A. The local time t' is the time determined by 

watches synchronized in this manner. 

If in such a case 

V = 1 / K0 ½ 

is the speed of light, and v the translation of the Earth, that I imagine to be parallel to the positive x 

axis, one will have: 

t' = t - vx / V 2 ." 

"Pour que la compensation se fasse, il faut rapporter les phénomènes, non pas au temps vrai t, mais à 

un certain temps local 'N défini de la façon suivante. 

Je suppose que des observateurs placés en différents points, règlent leurs montres à l'aide de signaux 

lumineux; qu'ils cherchent à corriger ces signaux du temps de la transmission, mais qu'ignorant le 

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mouvement de translation dont ils sont animès et croyant par conséquent que les signaux se 

transmettent également vite dans les deux sens, ils se bornent à croiser les observations, en envoyant 

un signal de A en B, puis un autre de B en A. Le temps local tNest le temps marqué par les montres 

ainsi réglées. 

Si alors 

V = 1 / K0 ½ 

est la vitesse de la lumière, et v la translation de la Terre que je suppose parallèle à l'axe des x positifs, 

on aura: 

t' = t - vx / V 2 . [4]" 

We know that Einstein had read Poincaré's paper.[5] 

In 1902, Poincaré asserted, and we know, from Solovine's accounts [6], that Einstein had read 

this work of Poincaré's: 

"There is no absolute time. When we say that two periods are equal, the statement has no meaning, 

and can only acquire a meaning by convention. Not only have we no direct intuition of the equality of 

two periods, but we have not even direct intuition of the simultaneity of two events occurring in two 

different places. I have explained this in an article entitled 'Mesure du Temps.' [7]" 

Again, in 1904, Poincaré asserted that simultaneity is relative, and elaborated on the light 

synchronization method that Mileva Einstein-Marity and Albert Einstein copied, in 1905, 

without citation to Poincaré. Poincaré stated in 1904, 

"We come to the principle of relativity: this not only is confirmed by daily experience, not only is it a 

necessary consequence of the hypothesis of central forces, but it is imposed in an irresistible way upon 

our good sense, and yet it also is battered. 

Consider two electrified bodies; though they seem to us at rest, they are both carried along by the 

motion of the earth; an electric charge in motion, Rowland has taught us, is equivalent to a current; 

these two charged bodies are, therefore, equivalent to two parallel currents of the same sense and these 

two currents should attract each other. In measuring this attraction, we measure the velocity of the 

earth; not its velocity in relation to the sun or the fixed stars, but its absolute velocity. 

I well know what one will say, it is not its absolute velocity that is measured, it is its velocity in 

relation to the ether. How unsatisfactory that is! Is it not evident that from the principle so understood 

we could no longer get anything? It could no longer tell us anything just because it would no longer 

fear any contradiction. 

If we succeed in measuring anything, we would always be free to say that this is not the absolute 

velocity in relation to the ether, it might always be the velocity in relation to some new unknown fluid 

with which we might fill space. 

Indeed, experience has taken on itself to ruin this interpretation of the principle of relativity; all 

attempts to measure the velocity of the earth in relation to the ether have led to negative results. This 

time experimental physics has been more faithful to the principle than mathematical physics; the 

theorists, to put in accord their other general views, would not have spared it; but experiment has been 

stubborn in confirming it. 

The means have been varied in a thousand ways and finally Michelson has pushed precision to its last 

limits; nothing has come of it. It is precisely to explain this obstinacy that the mathematicians are 

forced today to employ all their ingenuity. 

Their task was not easy, and if Lorentz has gotten through it, it is only by accumulating hypotheses. 

The most ingenious idea has been that of local time. 

Imagine two observers who wish to adjust their watches by optical signals; they exchange signals, but 

as they know that the transmission of light is not instantaneous, they take care to cross them. 

When the station B perceives the signal from the station A, its clock should not mark the same hour as 

that of the station A at the moment of sending the signal, but this hour augmented by a constant 

representing the duration of the transmission. Suppose, for example, that the station A sends its signal

when its clock marks the hour o, and that the station B perceives it when its clock marks the hour t. 

The clocks are adjusted if the slowness equal to t represents the duration of the transmission, and to 

verify it, the station B sends in its turn a signal when its clock marks o; then the station A should 

perceive it when its clock marks t. The timepieces are then adjusted. And in fact, they mark the same 

hour at the same physical instant, but on one condition, which is that the two stations are fixed. In the 

contrary case the duration of the transmission will not be the same in the two senses, since the station 

A, for example, moves forward to meet the optical perturbation emanating from B, while the station B 

flies away before the perturbation emanating from A. The watches adjusted in that manner do not 

mark, therefore, the true time, they mark what one may call the local time, so that one of them goes 

slow on the other. It matters little since we have no means of perceiving it. All the phenomena which 

happen at A, for example, will be late, but all will be equally so, and the observer who ascertains them 

will not perceive it since his watch is slow; so as the principle of relativity would have it, he will have 

no means of knowing whether he is at rest or in absolute motion.[8]" 

Mileva Einstein-Marity and Albert Einstein parroted Poincaré's clock synchronization 

procedures, without acknowledging that Poincaré had stated them first. From the Einsteins' 

1905 paper: 

"I. KINEMATICAL PART 

§ 1. Definition of Simultaneity 

[Consider a system of coordinates, in which the Newtonian mechanical equations are valid. In order to 

put the contradistinction from the [moving] systems of coordinates to be introduced later into words, 

and for the exact definition of the conceptualization, we call this system of coordinates the 'resting 

system'.] 

If a material point is at rest relatively to this system of co-ordinates, its position can be defined 

relatively thereto by the employment of rigid standards of measurement and the methods of Euclidean 

geometry, and can be expressed in Cartesian co-ordinates. 

If we wish to describe the motion of a material point, we give the values of its co-ordinates as 

functions of the time. Now we must bear carefully in mind that a mathematical description of this kind 

has no physical meaning unless we are quite clear as to what we understand by 'time.' We have to take 

into account that all our judgments in which time plays a part are always judgments of simultaneous 

events. If, for instance, I say, 'That train arrives here at 7 o'clock,' I mean something like this: 'The 

pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.' 

It might appear possible to overcome all the difficulties attending the definition of 'time' by 

substituting 'the position of the small hand of my watch' for 'time.' And in fact such a definition is 

satisfactory when we are concerned with defining a time exclusively for the place where the watch is 

located; but it is no longer satisfactory when we have to connect in time series of events occurring at 

different places, or - what comes to the same thing - to evaluate the times of events occurring at places 

remote from the watch. 

We might, of course, content ourselves with time values determined by an observer stationed together 

with the watch at the origin of the co-ordinates, and co-ordinating the corresponding positions of the 

hands with light signals, given out by every event to be timed, and reaching him through empty space. 

But this co-ordination has the disadvantage that it is not independent of the standpoint of the observer 

with the watch or clock, as we know from experience. We arrive at a much more practical 

determination along the following line of thought. 

If at the point A of space there is a clock, an observer at A can determine the time values of events in 

the immediate proximity of A by finding the positions of the hands which are simultaneous with these 

events. If there is at the point B of space another clock in all respects resembling the one at A, it is 

possible for an observer at B to determine the time values of events in the immediate neighbourhood 

of B. But it is not possible without further assumption to compare, in respect of time, an event at A 

with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a 

common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that 

the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A. Let 

a ray of light start at the 'A time' from A towards B, let it at the 'B time' be reflected at B in the 

direction of A, and arrive again at A at the 'A time'. 

In accordance with definition the two clocks synchronize if 

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tB - tA = t'A - tB. 

We assume that this definition of synchronism is free from contradictions, and possible for any 

number of points; and that the following relations are universally valid: - 

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B. 

2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C 

also synchronize with each other. 

Thus with the help of certain imaginary physical experiments we have settled what is to be understood 

by synchronous resting clocks located at different places, and have evidently obtained a definition of 

'simultaneous,' or 'synchronous,' and of 'time.' The 'time' of an event is that which is given 

simultaneously with the event by a resting clock located at the place of the event, this clock being 

synchronous, and indeed synchronous for all time determinations, with a specified stationary clock. 

[We set forth, according to present experience, that the magnitude 

( 2 A B ) / ( t'A - tA ) = c 

is a universal constant (the velocity of light in empty space).] 

It is essential to have time defined by means of resting clocks in the resting system, and the time now 

defined being appropriate to the resting system we call it 'the time of the resting system.'[9]" 

Albert Einstein believed he had a right to plagiarize, if he could put a new spin on an old idea. 

He asserted this "privilege" in 1907: 

"It appears to me that it is the nature of the business that what follows has already been partly solved 

by other authors. Despite that fact, since the issues of concern are here addressed from a new point of 

view, I believe I am entitled to leave out a thoroughly pedantic survey of the literature, all the more so 

because it is hoped that these gaps will yet be filled by other authors, as has already happened with my 

first work on the principle of relativity through the commendable efforts of Mr. Planck and Mr. 

Kaufmann.[10]" 

D. F. Comstock wrote, in 1910, in his popular exposition on the theory of relativity: 

"The whole principle of relativity may be based on an answer to the question: When are two events 

which happen at some distance from each other to be considered simultaneous? The answer, 'When 

they happen at the same time,' only shifts the problem. The question is, how can we make two events 

happen at the same time when there is a considerable distance between them. 

Most people will, I think, agree that one of the very best practical and simple ways would be to send a 

signal to each point from a point halfway between them. The velocity with which signals travel 

through space is of course the characteristic 'space velocity,' the velocity of light. 

Two clocks, one at A and the other at B, can therefore be set running in unison by means of a light 

signal sent to each from a place midway between them. 

Now suppose both clock A and clock B are on a kind of sidewalk or platform moving uniformly past 

us with velocity v. In Fig. 1 (2) is the moving platform and (1) is the fixed one, on which we consider 

ourselves placed. Since the observer on platform (2) is moving uniformly he can have no reason to 

consider himself moving at all, and he will use just the method we have indicated to set his two clocks 

A and B in unison. He will, that is, 

send a light flash from C, the point midway between A and B, and when this flash reaches the two 

clocks he will start them with the same reading.

To us on the fixed platform, however, it will of course be evident that the clock B is really a little 

behind clock A, for, since the whole system is moving in the direction of the arrow, light will take 

longer to go from C to B than from C to A. Thus the clock on the moving platform which leads the 

other will be behind in time. 

Now it is very important to see that the two clocks are in unison for the observer moving with them (in 

the only sense in which the word 'unison' has any meaning for him), for if we adopt the first postulate 

of relativity, there is no way in which he can know that he is moving. In other words, he has just as 

much fundamental right to consider himself stationary as we have to consider ourselves stationary, 

and therefore just as much right to apply the midway signal method to set his clocks in unison as we 

have in the setting of our 'stationary clocks.' 'Stationary' is, therefore, a relative term and anything 

which we can say about the moving system dependent on its motion, can with absolutely equal right 

be said by the moving observer about our system. 

We are, therefore, forced to the conclusion that, unless we discard one of the two relativity postulates, 

the simultaneity of two distant events means a different thing to two different observers if they are 

moving with respect to each other. 

The fact that the moving observer disagrees with us as to the reading of his two clocks as well as to the 

reading of two similar clocks on our 'stationary' platform, gives us a complete basis for all other 

differences due to point of view. 

A very simple calculation will show that the difference in time between the two moving clocks is 

[The time it takes light to go from C to B is ½ / (V - v) and the time to go from C to A is ½ / (V + v). 

The difference in these two times is the amount by which the clocks disagree and this difference 

becomes, on simplification, the expression given above. - Notation found in the original.] 

1/V β / (1 - β 2 ) 

where 

l = distance between clocks A and B; 

v = velocity of moving system; 

V = velocity of light; 

β = v / V. 

The way in which this difference of opinion with regard to time between the moving observer and 

ourselves leads to a difference of opinion with regard to length also may very easily be indicated as 

follows: 

Suppose the moving observer desires to let us know the distance between his clocks and says he will 

have an assistant stationed at each clock and each of these, at a given instant, is to make a black line 

on our platform. He will, therefore, he says, be able to leave marked on our platform an exact measure 

of the length between his clocks and we can then compare it at leisure withy any standard we choose 

to apply. 

We, however, object to this measure left with us, on the ground that the two assistants did not make 

their marks simultaneously and hence the marks left on our platform do not, we say, represent truly the 

distance between his clocks. The difference is readily shown in Fig. 2, where M represents the black 

mark made on our platform at a certain time by the assistant at A, and N that made by the assistant at B 

at a later time. The latter assistant waited, we say, until his clock read the same as clock A, waited, that 

is, until B was at B'; and then made the mark N. The moving observer declares, therefore, that the 

distance MN is equal to the distance AB, while we say that MN is greater than AB. 

Again it must be emphasized that, because of the first fundamental postulate, there is no universal 

standard to be applied in settling such a difference of opinion. Neither the standpoint of the 'moving' 

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observer nor our standpoint is wrong. The two merely represent two different sides of reality. Any one 

could ask: What is the 'true' length of a metal rod? Two observers working at different temperatures 

come to different conclusions as to the 'true length.' Both are right. It depends on what is meant by 

'true.' Again, asking a question which might have been asked centuries ago, is a man walking toward 

the stern of an east bound ship really moving west? We must answer 'that depends' and we must have 

knowledge of the questioner's view-point before we can answer yes or no. 

A similar distinction emerges from the principle of relativity. What is the distance between the two 

clocks? Answer: that depends. Are we to consider ourselves with the clock system when we answer, or 

passing the clocks with a hundredth the velocity of light or passing the clocks with a tenth the velocity 

of light? The answer in each case must be different, but in each case may be true. 

It must be remembered that the results of the principle of relativity are as true and no truer than its 

postulates. If future experience bears out these postulates then the length of the body, even of a 

geometrical line, in fact the very meaning of 'length,' depends on the point of view, that is, on the 

relative motion of the observer and the object measured. The reason this conclusion seems at first 

contrary to common sense is doubtless because we, as a race, have never had occasion to observe 

directly velocities high enough to make such effects sensible. The velocities which occur in some of 

the newly investigated domains of physics are just as new and outside our former experience as the 

fifth dimension.[11]" 

Citing Comstock's above quoted work, Robert Daniel Carmichael wrote, in 1912: 

"§ 9. Simultaneity of Events Happening at Different Places. - Let us now assume two systems of 

reference S and S' moving with a uniform relative velocity v. Let an observer on S' undertake to adjust 

two clocks at different places so that they shall simultaneously indicate the same time. We will 

suppose that he does this in the following very natural manner: 

[Compare Comstock, Science, N. S., 31 (1900) [sic]: 767-772. - Notation found in the original.] 

Two stations A and B are chosen in the line of relative motion of S and S' and at a distance d apart. The 

point C midway between these two stations is found by measurement. 

The observer is himself stationed at C and has assistants at A and B. A single light signal is flashed 

from C to A and to B, and as soon as the light ray reaches each station the clock there is set at an hour 

agreed upon beforehand. The observer on S' now concludes that his two clocks, the one at A and the 

other at B, are simultaneously marking the same hour; for, in his opinion (since he supposes his system 

to be at rest), the light has taken exactly the same time to travel from C to A as to travel from C to B. 

Now let us suppose that an observer on the system S has watched the work of regulating these clocks 

on S'. The distances CA and CB appear to him to be 

½ d (1 - β 2 ) 1/2 

instead of ½ d. Moreover, since the velocity of light is independent of the velocity of the source, it 

appears to him that the light ray proceeding from C to A has approached A at the velocity c + v, where 

c is the velocity of light, while the light ray going from C to B has approached B at the velocity c - v. 

Thus to him it appears that the light has taken longer to go from C to B than from C to A by the 

amount 

½ d (1 - β 2 ) 1/2 / ( c - v ) - ½ d (1 - β 2 ) 1/2 / ( c + v ) 

= vd (1 - β 2 ) 1/2 / ( c 2 - v 2 ) . 

But since β = v / c the last expression is readily found to be equal to

( v / c 2 ) [ d / (1 - β 2 ) 1/2 ] . 

Therefore, to an observer on S the clocks on S' appear to mark different times; and the difference is 

that given by the last expression above. 

Thus we have the following conclusion: 

THEOREM VII. Let two systems of reference S and S' have a uniform relative velocity v. Let an observer 

on S' place two clocks at a distance d apart in the line of relative motion of S and S' and adjust them 

so that they appear to him to mark simultaneously the same time. Then to an observer on S the clock 

on S' which is forward in point of motion appears to be behind in point of time by the amount 

( v / c 2 ) [ d / (1 - β 2 ) 1/2 ] , 

where c is the velocity of light and β = v / c (MVLR). 

It should be emphasized that the clocks on S' are in agreement in the only sense in which they can be 

in agreement for an observer on that system who supposes (as he naturally will) that his own system is 

at rest-notwithstanding the fact that to an observer on the other system there appears to be an 

irreconcilable disagreement depending for its amount directly on the distance apart of the two clocks. 

According to the result of the last theorem the notion of simultaneity of events happening at different 

places is indefinite in meaning until some convention is adopted as to how simultaneity is to be 

determined. In other words, there is no such thing as the absolute simultaneity of events happening at 

different places.[12]" 

Albert Einstein, who sought a "new point of view" from plagiarizing Poincaré's 1900 clock 

synchronization method, plagiarized Comstock (1910) and Carmichael (1912), in Einstein's 

book of 1916: 

"THE RELATIVITY OF SIMULTANEITY 

UP to now our considerations have been referred to a particular body of reference, which we have 

styled a 'railway embankment.' We suppose a very long train travelling along the rails with the 

constant velocity v and in the direction indicated in Fig. I. People travelling in this train will with 

advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in 

reference to the train. 

Then every event which takes place along the line also takes place at a particular point of the train. 

Also the definition of simultaneity can be given relative to the train in exactly the same way as with 

respect to the embankment. As a natural consequence, however, the following question arises: 

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to 

the railway embankment also simultaneous relatively to the train? We shall show directly that the 

answer must be in the negative. 

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we 

mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at 

the mid-point M of the length AB of the embankment. But the events A and B also correspond to 

positions A and B on the train. Let M' be the mid-point of the distance AB on the traveling train. Just 

when the flashes 

[As judged from the embankment. - Notation found in the original.] 

of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in 

the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not 

possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes 

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of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. 

Now in reality (considered with reference to the railway embankment) he is hastening towards the 

beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence 

the observer will see the beam of light emitted from B earlier than he will see that emitted from A. 

Observers who take the railway train as their reference-body must therefore come to the conclusion 

that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important 

result: 

Events which are simultaneous with reference to the embankment are not simultaneous with respect to 

the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its 

own particular time; unless we are told the reference-body to which the statement of time refers, there 

is no meaning in a statement of the time of an event. 

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the 

statement of time had an absolute significance, i.e. that it is independent of the state of motion of the 

body of reference. But we have just seen that this assumption is incompatible with the most natural 

definition of simultaneity; if we discard this assumption, then the conflict between the law of the 

propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears. 

We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In 

that section we concluded that the man in the carriage, who traverses the distance w per second 

relative to the carriage, traverses the same distance also with respect to the embankment in each 

second of time. But, according to the foregoing considerations, the time required by a particular 

occurrence with respect to the carriage must not be considered equal to the duration of the same 

occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the 

man in walking travels the distance w relative to the railway line in a time which is equal to one 

second as judged from the embankment. 

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light 

of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the 

introduction of the theory of relativity.[13]" 

This chapter "by Einstein" has often been criticized as being "absolutist" and "Lorentzian". 

One understands why it was written in the fashion that it was, when one reads the source 

material, which Einstein plagiarized to produce it. 

References and Notes 

1. W. Voigt, "Ueber das Doppler'sche Princip", Nachrichten von der Königlichen Gesellschaft der 

Wissenschaften und der Georg-Augusts-Universität zu Göttingen, (1887), pp. 41-51; republished 

Physikalische Zeitschrift, Volume 16, Number 20, (October15, 1915), pp. 381-386; English 

translation, as well as very useful commentary, are found in A. Ernst and Jong-Ping Hsu (W. Kern is 

credited with assisting in the translation), "First Proposal of the Universal Speed of Light by Voigt in 

1887", Chinese Journal of Physics (The Physical Society of the Republic of China), Volume 39, 

Number 3, (June, 2001), pp. 211-230; URL: http://psroc.phys.ntu.edu.tw/cjp/v39/211.pdf . Lorentz 

acknowledged Voigt's priority, and suggested that the "Lorentz Transformation" be called the 

"Transformations of Relativity": See: H. A. Lorentz, Theory of Electrons, B. G. Teubner, Leipzig, 

(1909), p. 198 footnote; and H. A. Lorentz, "Deux memoirs de Henri Poincaré", Acta Mathematica, 

Volume 38, (1921), p. 295; reprinted in Œuvres de Henri Poincaré, Volume XI, Gautier-Villars, 

(1956), pp. 247-261. Minkowski also acknowledged Voigt's priority: See: The Principle of Relativity, 

Dover, New York, (1952), p. 81; and Physikalische Zeitschrift, Volume 9, Number 22, (November 1, 

1908), p. 762. For further discussion of Voigt's relativistic transformation, see: R. Dugas, A History of 

Mechanics, Dover, New York, (1988), pp. 468, 484, 494; A. Pais, Subtle is the Lord, Oxford 

University Press, Oxford, New York, Toronto, Melbourne, (1982), pp. 121-122. 

2. H. Poincaré, "La Mesure du Temps", Revue de Métaphysique et de Morale, Volume 6, (January, 

1898) pp. 1-13; The Value of Science, The Science Press, New York, (1907), pp. 26-36. 

3. H. Poincaré, Electrité et Optique, Gauthier-Villars, Paris, (1901), p. 530.

4. H. Poincaré, "La Théorie de Lorentz et le Principe de la Réaction", Archives Néerlandaises des 

Sciences Exactes et Naturelles, Series 2, Volume 5, (1900), pp. 252-278, at 272-273. 

5. A. Einstein, "Das Prinzip von der Erhaltung der Schwerpunktsbewegung und die Trägheit der 

Energie", Annalen der Physik, Volume 20, (1906), pp. 627-633, at 627. 

6. J. Stachel, Ed., The Collected Papers of Albert Einstein, Volume 2, Princeton University Press, 

(1989), pp. xxiv-xxv. 

7. H. Poincaré, Science and Hypothesis, Dover, New York, (1952), p. 90. 

8. H. Poincaré's St. Louis lecture from September of 1904, La Revue des Idées, 80, (November 15, 

1905); "L'État Actuel et l'Avenir de la Physique Mathématique", Bulletin des Sciences Mathématique, 

Series 2, Volume 28, (1904), p. 302-324; English translation, "The Principles of Mathematical 

Physics", The Monist, Volume 15, Number 1, (January, 1905), pp. 1-24. 

9. The Principle of Relativity, Dover, New York, (1952), pp. 38-40. In order to maintain conformity 

with the original German text, necessary corrections have been made, as indicated by bracketed text. 

"Resting" has been substituted for "stationary", in conformity with the original German text. 

10. A. Einstein, "Ueber die vom Relativitaetsprinzip gefordterte Traegheit der Energie", Annalen der 

Physik, Series 4, Volume 23, (1907), pp. 371-384, at 373. 

11. D. F. Comstock, "The Principle of Relativity", Science, New Series, Volume 31, Number 803, (20 

May 1910), pp. 767-772, at 768-770. 

12. R. D. Carmichael, "On the Theory of Relativity", The Physical Review, Volume 35, Number 3, 

(September 1912), pp. 153-176, at 170-171; republished in "The Theory of Relativity", Mathematical 

Monographs No. 12, John Wiley & Sons, New York, (1914/1920), pp. 40-41. 

13. A. Einstein, "The Relativity of Simultaneity", Relativity: The Special and the General Theory, 

Chapter 9, Methuen, London, (1920), pp. 30-33. 

- - - - - 

[A presentation of the author is given at the end of the first of his previous two 

papers published in this same issue of Episteme] 


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[Spettacolare immagine della grande galassia a spirale NGC 1232 della costellazione Eridano. 

La galassia è grande circa il doppio della nostra Via Lattea e dista 100 milioni di anni luce. 

La regione centrale contiene stelle vecchie rossastre mentre i bracci a spirale sono popolati di giovani 

stelle blu e di regioni in cui nascono nuove stelle. 

Sulla sinistra c'è anche una piccola galassia compagna. L'immagine è basata su tre fotografie in 

ultravioletto, blu e rosso ed è stata realizzata nel 1998 con il VLT (Very Large Telescope) dell'ESO 

(Osservatorio Europeo del Sud). Dell'ESO fanno parte dieci paesi fra cui l'Italia.] 

La natura del tempo 

(Propagazioni super-luminali - Paradosso dei gemelli - Teletrasporto) 

(a cura di Franco Selleri) 

(Edizioni Dedalo, Bari, 2002) 

"I fisici di Copenhagen e di Göttingen non si limitarono ad enunciare 

le loro tesi anticausali ed antirealistiche, ma crearono una 

sequela impressionante di veri e propri " 

(Franco Selleri) 

Attenendosi a una formula ormai consueta, Episteme ritiene di fare cosa utile ai suoi lettori di 

lingua italiana con il presentare un'opera che esce nelle librerie più o meno nello stesso 

periodo di questo numero "speciale" della rivista, e che al pari di esso è testimone di quel 

"discomfort towards the actual establishment's philosophy of Nature and of Science", di cui si 

diceva nelle righe di introduzione al capitolo dedicato alla "fisica alternativa" on line. 

Le "analogie" naturalmente non finiscono qui, e vanno dagli argomenti trattati al fatto che tra 

gli autori ve ne sono di già ben noti ed apprezzati a chi frequenta la nostra pubblicazione, 

senza tacere la circostanza (già lamentata nella "Lettera dell'editore..." con cui si apre il 

presente volume) che talora le argomentazioni critiche contro la "relatività", e "derivazioni"

(siffatti sono da ritenersi invero, sia pure in maniera indiretta, taluni sviluppi della fisica 

teorica del XX secolo), non appaiono interamente "cristalline" - ciò che, come si è affermato 

nella citata "Lettera", nulla toglie peraltro al generale interesse, e soprattutto alle finalità, del 

complesso dell'opera. Per esempio, alcune considerazioni sul paradosso dei gemelli, 

sull'effetto Sagnac, etc., che "confondono" trattamento delle accelerazioni in relatività 

speciale (in assenza cioè di gravitazione, vale a dire di curvatura dello spazio-tempo) e 

relatività generale (il collegamento viene effettuato - secondo una procedura del resto assai 

comune in simili casi - attraverso il "principio di equivalenza", che è in realtà assai più 

"delicato" delle sue enunciazioni-utilizzazioni "ingenue"), oppure discutono in maniera 

implicita, sebbene in un contesto relativistico, "oggetti fisici" mediante le "categorie 

ordinarie" di spazio e di tempo, il che non può naturalmente non ingenerare equivociapparenti 

"contraddizioni interne" (tra i responsabili della poco brillante situazione descritta 

bisogna annoverare per la verità gli stessi fisici "ortodossi", Einstein in primis, del quale non 

sarebbe un totale autentico "paradosso" sostenere che non avesse "compreso" appieno le 

"esigenze" della sua propria teoria...). 

Ma lasciamo che sia direttamente il libro in oggetto a presentarsi, riportando alla fine, 

secondo il nostro solito modo, l'intero suo sommario. 

- - - - - 

La comprensibilità del tempo nei processi naturali è stata messa fortemente in dubbio dalla 

fisica del Novecento, soprattutto a causa delle relazioni di indeterminazione di Heisenberg e 

del relativismo filosofico che ha accompagnato l'affermarsi delle teorie di Einstein. Gli 

sviluppi recenti presentati in questo libro, permettono il recupero di una descrizione 

soddisfacente del tempo e del cambiamento. 

In base a quanto sosteneva Popper, la realtà del tempo e del cambiamento è il punto cruciale 

della scienza. Gli autori dei saggi qui raccolti concordano con lui e ognuno di essi discute un 

diverso problema riguardante la natura del tempo in modo semplice e chiaro. Numerosi sono 

gli argomenti trattati: la relazione di indeterminazione energia-tempo e lo scontro Einstein- 

Bohr; il tempo medio di vita delle particelle instabili; il teletrasporto in tempo zero da Star 

Trek alla meccanica quantistica; la trattazione relativistica del tempo e la questione della 

simultaneità; il misterioso effetto Sagnac e le sue implicazioni sul tempo; il paradosso dei 

gemelli secondo la relatività del tempo e secondo una teoria alternativa basata sulla 

simultaneità assoluta; i segnali "super-luminali". Gli autori offrono inoltre risposte a tanti 

interrogativi come ad esempio: un orologio su un aereo in volo segna il tempo più 

lentamente? Il campo gravitazionale terrestre influenza il tempo segnato dagli orologi atomici 

sui satelliti in orbita? Il tempo futuro è predeterminato come sostiene l'interpretazione 

ortodossa della teoria della relatività? Se lo è, come è possibile la nostra evidente libertà di 

scelta? È possibile sfruttare i segnali super-luminali per inviare messaggi verso il tempo 

passato? L'opera si rivolge ad un pubblico ampio con un interesse scientifico, ma anche a 

studenti e studiosi. 

Introduzione, Franco Selleri 

- - - - - 

La relazione di indeterminazione energia-tempo, Augusto Garuccio 

Introduzione - Che cos'è l'azione? - Quanto è piccolo il quanto d'azione - Le relazioni di 

indeterminazione e il dibattito sulla meccanica quantistica - Uno scontro tra giganti - Come 

interpretare la relazione energia-tempo - Regole di indeterminazione, causalità, descrizione 

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spazio-temporale degli eventi quantistici 

Il teletrasporto?, Milena D'Angelo 

Reversibilità e irreversibilità del tempo in Meccanica Statistica, Giuseppe Gonnella 

Il principio dell'aumento dell'entropia - Il punto di vista molecolare e la meccanica statistica - 

Il teorema H - Le obiezioni di Loschmidt e Zermelo - L'entropia di Boltzmann - Il tempo e 

l'universo 

As time goes by... - Le antiparticelle e la freccia del tempo, Vincenzo Berardi 

Viaggiare nel tempo - Le antiparticelle - La scoperta del positrone - L'interpretazione di 

Feynman - Indietro nel tempo? - Epilogo 

Ritardo degli orologi in moto, Michele Barone 

Effetti al secondo ordine di v/c - Convenzione o Proprietà della Natura? - Violazioni 

dell'invarianza delle trasformazioni di Lorentz 

Il paradosso dei gemelli, Romano Manaresi 

Il viaggio - Il paradosso - Il senso comune - TRR, Il principio di relatività - Realtà e 

apparenza - La (non) soluzione di TRR - Inversione di marcia - TRG, Il principio di 

equivalenza - Il potenziale gravitazionale - La soluzione di TRG - Velocità o accelerazione? - 

Spiegazione causale e spiegazione strutturale - Effetto gemelli senza accelerazioni - La 

previsione di TRR - Lo spazio-tempo di Minkowski - Nessun conflitto - Le Trasformazioni 

Inerziali - L'effetto gemelli - Impossibilità di individuare lo spazio assoluto - 

Conclusioni 

Il futuro è predeterminato?, Nicola Russo 

La teoria della relatività e il tempo - Einstein-Parmenide e il libero arbitrio - Le teorie 

equivalenti alla relatività - Le trasformazioni inerziali - La realtà ritrovata 

Gli orologi della teoria relativistica, Ludwik Kostro 

La parola "orologio" nel linguaggio ordinario e in quello scientifico - La dilatazione del 

tempo nei sistemi di riferimento in moto e nei campi gravitazionali - Esempi di processi 

periodici che anticipano anziché ritardare - Processi naturali la cui esistenza dipende 

interamente dal campo gravitazionale - Processi fisici la cui esistenza non dipende dal campo 

gravitazionale - Processi fisici parzialmente influenzati dal campo gravitazionale - Gli orologi 

e la teoria della gravitazione di Newton - Relatività generale e orologi a sorgente di energia 

gravitazionale - Quali orologi considerava Einstein nella sua teoria? - Conclusioni 

Il tempo sui satelliti del GPS e l'effetto Sagnac, Francesca Intini 

La misura del tempo - Il Sistema di Posizionamcnto Globale - Il tempo del GPS - Come 

funziona - Fattori di correzione - Le correzioni relativistiche - La correzione di Sagnac - 

L'effetto Sagnac - Conclusioni 

Simultaneità relativistica, Massimo Brighi 

Cosa accade, adesso, su Marte? - Simultaneità classica - Sistemi di riferimento ed eventi - Lo 

spazio-tempo di Minkowski - Simultaneità relativistica (la soluzione di Einstein) - 

Simultaneità, sincronizzazione e velocità di sola andata - La velocità della luce - Trasporto di 

orologi - Simultaneità non standard - Proprietà della relazione di simultaneità - Simultaneità 

assoluta - Il teorema di Malament - Simultaneità in sistemi di riferimento accelerati e 

relatività generale - Conclusioni

I FLOP nella trattazione relativistica del tempo, Rocco Vittorio Macrì 

Il concetto di Falsificatore Logico Potenziale (FLOP) - La metafisica operativoverificazionista 

e i FLOP del Gedankenexperiment - La e i FLOP nei 

fondamenti relativistici - Considerazioni conclusive sui razzi vettori della TRS 

Esperimenti : una panoramica, Erasmo Recami 

Introduzione - Relatività Speciale ed Estesa - La situazione sperimentale 

E' possibile inviare messaggi verso il passato?, Franco Selleri 

Segnali superluminali e paradosso causale - La regola reinterpretativa di Recami - Il tempo 

non può essere capovolto - Trasformazioni fra sistemi inerziali - Le trasformazioni equivalenti 

- La relatività della simultaneità resta esclusa - Solo la simultaneità assoluta è possibile 

- - - - - 

[Franco Selleri insegna fisica teorica all¹Università di Bari. È autore di alcuni 

libri pubblicati in una decina di lingue e di numerosi articoli scientifici che 

trattano di fisica delle particelle e di fondamenti della teoria dei quanti e della 

relatività.] 

ordini@edizionidedalo.it 

http://www.edizionidedalo.it/ 

299

EPISTEME - Giano Bifronte

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