ISBN 9788393310500  viXra
ISBN 9788393310500
Copyright © 2012 by Sylwester Kornowski
All rights reserved
ISBN 9788393310500
1
The Everlasting Theory and Special Number Theory
Sylwester Kornowski
Acknowledgments
I am enormously grateful to Paul Walewski for comments on part of the manuscript and
meticulous care with the copyediting.
Contents
Abstract 2
1 Experimental Data and Program of Ultimate Theory
2 Phase Transitions of Newtonian Spacetime, Neutrinos,
4
Nucleons, Electrons, Pions and Muons 11
3 Interactions 27
4 Structure of Particles (continuation) 44
5 Liquidlike Plasma 54
6 New Cosmology 56
7 Fourshell Model of Atomic Nucleus 73
8 Mathematical Constants 79
9 Fractal Field 83
10 New Big Bang Theory 87
11 Reformulated Quantum Chromodynamics 90
12 Proton and Loops as Foundations of Theory of Chaos 99
13 Theoretical Curve for the KaontoPion Ratio 104
14 The Cross Section for Production of the W Boson 106
15 Neutrino Speed 108
16 Mtheory 114
17 Perihelion Precession of Mercury and Venus 116
18 Foundations of Quantum Physics 117
19 Foundations of General Theory of Relativity
20 The Combination of Quantum Physics
119
and General Theory of Relativity
21 General Relativity in Reformulated QCD
121
and New Cosmology
22 Electroweak Interactions, NonAbelian Gauge Theories
122
and Origin of E = mc 2
125
Recapitulation and Ultimate Equation 128
Definitions 138
2
Abstract: The Everlasting Theory is the lacking part of the ultimate theory and is free from
singularities and infinities. There are the two longdistance interactions. This suggests that
there are two parallel spacetimes. Density of the most fundamental spacetime, which I call
Newtonian spacetime or modified Higgs field, leads to the gravitational constant whereas
density of the second spacetime, which I refer to as the Einstein spacetime, leads to the finestructure
constant. The nature on its lowest levels once again behaves classically. The
components of the two parallel spacetimes are today the classical objects. This causes that the
complete set of the initial conditions, which describe properties of the two spacetimes, is not
numerous and very simple. The fundamental conditions lead to the initial conditions applied
in the mainstream theories i.e. the General Theory of Relativity and the Quantum Theory of
Fields but also to the masses of leptons and quarks applied in the Standard Model. Since I
start from the fundamental initial conditions, I proved that the initial conditions applied in the
mainstream theories are incomplete and there appear many incorrect interpretations. The main
reason that the mainstream theories must be reformulated is the fact that they neglect the
classical internal structure of the bare fermions. In reality, there is torus and ball in its centre.
The surfaces of the tori inside the bare fermions look as the Ketterle surface for strongly
interacting gas. It is very difficult to describe mathematically such structure to add it to
Lagrangian. We must apply new methods. In the last section titled “Definitions”, I widely
described the relations between presented here the Everlasting Theory and the mainstream
theories. I described origin of Higgs mechanism and hierarchy problem, Planck critical
quantities, confinement and mass gaps, hadronization and limitations in the Quantum
Chromodynamics. Presented here the confinement breaks symmetry between gravity and
weak interactions.
Contrary to the mainstream theories, the Everlasting Theory acts correctly at whole
spectrum of sizes. To explain the inflation, longdistance entanglement, cohesion of wave
function and constancy of the speed of light, we need the fundamental spacetime composed of
tachyons. The tachyons have inertial mass only i.e. they are the gravitationally massless
particles. Moreover, their mean spin is in approximation 10 67 times smaller than the reduced
Planck constant. This means that in approximation we can assume that the fundamental
spacetime is the gravitationally massless scalar field. There are the two basic phenomena. The
saturation of interactions of the tachyons leads to the phase transitions of the
fundamental/Newtonian spacetime. The first phase transition leads to the closed strings the
neutrinos consist of, the second leads to the Einstein spacetime, third to the core of baryons
whereas the fourth to the cosmic object, the Protoworld, after the era of inflation (there
appears the new cosmology). In Einstein’s spacetime the quantum effects and fractal objects
appear. The second phenomenon, i.e. the symmetrical decays of the bosons in very high
temperatures, leads to the TitiusBode law for the strong interactions and to the Titiusbode
law for the gravitational interactions acting nearly the black holes. Due to the TitiusBode law
for the strong interactions, there appears the atomlike structure of baryons. The core of
baryons is the black hole in respect of the strong interactions whereas the ball in its centre is
the black hole in respect of the weak interactions. Their masses are quantized so they emit the
surplus energy. The same concerns the gravitational black holes. On base of these two
phenomena and the 7 parameters only, I calculated several hundred basic theoretical results
consistent or very close to experimental data. I calculated the basic physical constants as well
and mass of electron. Due to the fact that the nature on its lowest levels once again behaves
classically, the lacking part of the ultimate theory, i.e. the Everlasting Theory, is
mathematically very simple, even simpler than the Newtonian mechanics. But there appear
the Uncertainty Principle and the relativistic formulae as well.
The E. Kasner solution for the flat anisotropic model (1921) in the General Theory of
Relativity leads to the numbers characteristic for the bare fermions, especially for the tori. On
3
the other hand, the internal structure of the bare fermions leads to the known interactions and
the quantum behaviour of the electron. Electron consists of the Einstein spacetime
components and due to the fundamental/Newtonian spacetime, it can disappear in one place
and appear in another and so on. Such behaviour leads to wave function. We can see that
quantum behaviour follows from existence of the two parallel spacetimes. Value of the
gravitational constant depends on the internal structure of the neutrinos and inertial mass
density of the Newtonian spacetime. This means that Quantum Gravity is associated with the
quantum behaviour of the neutrinos. Neutrinos consist of the binary systems of the closed
strings so neutrinos can be the quantum particles only in spacetime composed of the binary
systems of the closed strings. Such spacetime was in existence only in the era of inflation. In
this era, this spacetime decayed into small regions and today the binary systems of the closed
strings are inside the neutrinos. The Quantum Gravity was valid in the era of inflation only.
Today the gravity is classical because due to the lack of spacetime composed of the closed
strings there cannot be created the neutrinoantineutrino pairs similarly as the electronpositron
pairs from the Einstein spacetime components. The Kasner solution and the scales
for the charges (weak, electric and strong) in the generalized Kasner solution and the BKL
oscillatory model, lead to the phase transitions of the fundamental spacetime and to the
Protoworldneutrino transition that caused the exit of the early Universe from the blackhole
state. The phase transitions are the foundations of the modified/useful string/M theory. There
is also the ultimate equation that combines the masses of sources of all types of interactions.
The Kasner solution leads to the new cosmology as well. We can say also that the Kasner
solution is the foundations of the Quantum Theory of Gravity and Quantum Theory of Fields
without singularities and infinities.
The Everlasting Theory based on the phase transitions of the fundamental/Newtonian
spacetime shows where the nonAbelian gauge theories become useless. Due to the phase
transitions and entanglement, the new fields have the toruslike shapes. They behave in
different way than the gauge fields then we must apply new methods. The symmetry group
SU(3)×SU(2)×U(1) is incomplete in lowenergy regime. There is lack of the stable structures
that appear due to the phase transitions of the Newtonian spacetime. The incompleteness
causes that the Standard Model does not lead to the superluminal neutrinos which appeared in
the supernova SN 1987A explosion and does not lead to the masses of nucleons. The
Everlasting Theory shows that the liquidlike plasma obtained in the highenergy collisions of
nucleons consists of the cores of baryons. Within reformulated Quantum Chromodynamics, I
described the electronpositron and nucleonnucleon collisions. The new structure of proton
and loops is the foundations of the theory of chaos. The structure of proton leads to the
Feigenbaum scaling whereas the loops to the Mandelbrotlike set. I wrote the generalized
Schrödinger equation that contains gravity and showed how we can obtain the generalized
Dirac equation. I described also the perihelion precession of Mercury and Venus and solved
the 4/3factor problem for massenergy relation for classical electron. The origin of DNA
follows from the reformulated QCD.
The ultimate theory must contain nonperturbative and perturbative theories. The ground state
of the Einstein spacetime consists of the nonrotatingspin neutrinoantineutrino pairs. The
total helicity of this state is zero and it consists of particles which spin is unitary. In such
spacetime cannot appear loops which have helicity so mass as well. In reality, a unitaryspin
loop (the loop state) is the binary system of two entangled halfintegralspin loops with
opposite helicities i.e. the resultant helicity is zero. In such spacetime do not appear
turbulences. Such loop can easily transform into a fermionantifermion pair (the fermion
state). Perturbation theories concern the loop states whereas the nonperturbative theories the
fermion states so we cannot neglect the structure of bare fermions.
4
Experimental Data and Program of Ultimate Theory
The direct and indirect evidences that there are in existence the superluminal particles are as
follows. There are the superluminal neutrinos. Entangled photons show that they can
communicate with speeds higher than the c. The wave functions fill the whole our Universe.
The wave function describing our Universe can be the coherent mathematical object if the
very distant points of the wave function can communicate with speeds much higher than the c.
We can say that coherent quantum physics needs the tachyons. Also the MichelsonMorley
experiment leads to conclusion that masses emit the tachyons because then the speed of light
in relation to the field composed of the tachyons and ‘attached’ to a mass does not depend on
rotation of the mass and its other motions.
In the Einstein General Theory of Relativity we apply formula for the total energy E of
particles in the Einstein spacetime in which the mass M is for inertial mass equal to
gravitational mass.
Assume that the word ‘imaginary’ concerns physical quantities characteristic for objects
that have broken contact with the wave function that describes state of the Universe. This
means that such objects cannot emit some particles. Assume that the tachyons are the
internally structureless objects, i.e. they are the pieces of space, so they cannot emit some
objects. From this follows that the tachyons have only the inertial mass m. Substitute ic
instead c, iv instead v and im instead M, where i = sqrt(–1). Then the formula for the total
energy N of a gas composed of tachyons is:
N = – imc 2 /sqrt(1 – v 2 /c 2 ) = mc 2 /sqrt(v 2 /c 2 – 1).
We can see that the Theory of Relativity leads to the imaginary Newtonian spacetime
composed of the tachyons i.e. to the fundamental spacetime. The Theory of Relativity is the
more fundamental theory than the Quantum Physics. The Quantum Physics appears on higher
level of nature and is associated with the excited states of the Einstein spacetime. There are in
existence two spacetimes i.e. the Einstein spacetime and the imaginary Newtonian spacetime.
I will show that the phase transitions of the imaginary Newtonian spacetime lead to the
Einstein spacetime. My theory shows that tachyons are moving with speeds about 8·10 88 times
higher than the c. The total energy T of the two spacetimes we can define as the sum of the
energy E that appears in the Theory of Relativity and the imaginary energy N associated with
the Newtonian spacetime:
T = E + iN.
The m is in proportion to volume of tachyon i.e. m = aV so N = aVc 2 /sqrt(v 2 /c 2 – 1). We can
see that when speed of a tachyon increases then its energy decreases. It is possible only due to
the higher grinding of tachyons when they move with higher speed. For infinite speed of a
tachyon, its volume is equal to zero i.e. in the ‘gas’ there is infinite number of mathematical
points moving with infinite speeds. But such state of the gas composed of tachyons cannot be
realized because the total volume of the increasing number of tachyons still must be the same
and positive.
The Everlasting Theory starts with three assumptions:
1.
That there exists the Newtonian spacetime that is composed of structureless tachyons that
have a positive mass;
2.
That there are possible phase transitions of the Newtonian spacetime; and
3.
That among other stable objects arising due to the phase transitions of the Newtonian
spacetime, the massive core of baryons arises. Due to the symmetrical decaying of virtual
5
bosons, outside the massive core, the use of the TitiusBode law for the strong interactions
is obligatory. This will lead to an atomlike structure of baryons.
The Newtonian spacetime maintains a classical approach i.e. the behaviour of tachyons
cannot be described by a wave function due to the lack of more fundamental spacetime.
Nature begins from classical objects whereas the quantum physics approach on the higher
levels of nature.
The diagram entitled ‘Main ideas’, shows the main structure of the everlasting theory. In
general, the Einstein theories of relativity describe the motions of particles in smooth
gravitational field. By and large, quantum physics describes the interactions of particles with
fields via quantum fields (i.e. via unsmooth fields where quantum particles appear). The
quantum particles disappear in one place of a field or spacetime and appear in another and so
on. Unification of the smoothness and the ‘roughness’ of fields within one mathematical
description is, however, still not realized. The diagram shows that to understand the
differences between general relativity and the quantum physics, we must be familiar with the
internal structure of Einstein spacetime and bare particles.
The Everlasting Theory is the lacking part of the ultimate theory. The Everlasting Theory is
the theory of internal structures and interactions of the stable objects and the two spacetimes.
Even the quantum particles for the periods of spinning are the stable objects. The stable
objects arise due to the phase transitions of the imaginary Newtonian spacetime. The key
components of the Everlasting Theory are the properties of the imaginary Newtonian
spacetime, its phase transitions leading to the stable objects and the TitiusBode law for the
strong interactions that leads to the atomlike structure of baryons.
The ground state of the Einstein spacetime consists of nonrotatingspin binary systems of
neutrinos. To detect the nonrotatingspin binary systems of neutrinos we must measure mass
with accuracy about 10 67 kg. No one has identified the products of neutrinoantineutrino
annihilations. This suggests that in the today Universe the neutrinos are the nonquantum
particles i.e. their state does not describe a wave function due to a too low energy density of
Newtonian and Einstein spacetimes. In the Einstein’s spacetime, the virtual particleantiparticle
pairs can arise. Photons are the rotational energies of the entangled Einstein
spacetime components. The c=299,792,458 m/s is the natural speed of the entangled binary
systems of neutrinos in the gradients of gravity ‘attached’ to the masses. Due to the
Newtonian spacetime, the photons can also behave as quantum particles i.e. their energy can
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disappear in one place of Einstein’s spacetime and appear in another and so on. The nonrotatingspin
binary systems of binary systems of neutrinos (the neutrino bidipoles) with
parallel spins carry the gravitational energy. Due to the internal structure of the rotating
neutrino bidipoles, they behave as two entangled photons. Gravitons are not in existence.
Gradients produced in Newtonian spacetime by neutrinos are impressed on the Einstein
spacetime as well. The gravitational constant depends on the internal structure of neutrinos
and properties of the Newtonian spacetime. The phase transitions of the Newtonian spacetime
show that cosmology should begin from different initial conditions than the Cosmological
Standard Model.
Conclusions from experimental data
1.
Pions appear in the main channels of the decay of the Lambda and Sigma+ hyperons.
During the decay of the hyperon Lambda, negatively charged and neutral pions appear.
On the basis of this experimental data [1] we can assume that a neutron with a probability
of x about 0.63 is composed of a positively charged core and a negative pion.
Furthermore, the probability (1x) is composed of a neutral core and a neutral pion.
During the decay of the hyperon Sigma+, neutral and positively charged pions appear. On
the basis of this experimental data [1] we can assume that the proton with a probability y
about 0.51 is composed of a positively charged core and a neutral pion and the probability
(1y) is composed of a neutral core and a positive pion.
2.
We know that the nucleonnuclear magnetic moment ratios are about +2.79 for a proton
[1] and 1.91 for a neutron [1]. On the basis of these experimental results, we can assume
that the mass of the charged core is about H(charged)~727 MeV and the relativistic
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charged pion is W(charged)~216 MeV. Such values of the probabilities and masses lead
to the experimental data for magnetic moments.
3.
During the extreme energetic collisions of ions, a liquidlike substance appears [2]. This
also suggests that there is a massive core inside a nucleon.
4.
The triplet np scattering length is approximately 5.4 fm. The singlet np effective range is
approximately 2.7 fm whereas the triplet np effective range is approximately 1.7 fm.
Assume that outside of the core of nucleons the TitiusBode law for strong interactions
r(d)=A+dB where A~0.7 fm, B~0.5 fm, and d=0, 1, 2, 4 is obligatory. The diameter of the
last ‘orbit’ is, therefore, 2r(d=4)=2(A+4B)=5.4 fm, the radius of last orbit is
r(d=4)=A+4B=2.7 fm, whereas the radius of the last but one orbit is r(d=2)=A+2B=1.7
fm.
5.
Observed entangled particles separated spatially need superluminal particles.
6.
We know that gravitational constant has the same value for all mass. This and the Planck
length suggest that whole matter should be composed of inflexible particles having size
close to the Planck length – they are the neutrinos.
7.
Very dense cosmic objects, for example the NGC 4261 galaxy (there is ‘point’ mass in
centre of ring/torus), and some stable particles having a high internal energy density
should appear similar because the macrocosm and microcosm describes the same set of
physical laws.
8.
The creation of one additional baryon for approximately a billion baryonantibaryon
annihilations leads to the temperature of the Universe today being a few hundred billion
times higher than the measured. This suggests that baryonantibaryon symmetry was
broken before the ‘soft’ big bang after the period of inflation.
9.
We are unable to see the biproducts of neutrinoantineutrino annihilation. This suggests
that neutrinos are very stable particles and this suggests that the oscillation of neutrinos is
impossible as well. The observed ‘oscillations’ of neutrinos are due to the fact that the
Einstein spacetime consists of the binary systems of neutrinos. In fact, we observe the
exchanges of free neutrinos for the neutrinos in the binary systems of neutrinos.
Why we must change the physical vision of nature
Have the bare particles an internal structure? Why are theories associated with particle
physics extremely complicated? Authors of these theories assume that bare particles are point
particles or closed strings and have a size of about 10 35 m. This, in fact, is not true. The phase
transitions of the Newtonian spacetime show that the bare particles have a very rich internal
structure. Interactions of the bare particles with fields depend on their internal structures.
Various theories show that these internal structures are neglected or are difficult to
understand. As a result, there appear strange properties of the fields and postulated particles to
obtain theoretical results consistent with experimental data. We can for example remove
almost all of the diagrams in the QED when we take into account the weak interactions of the
bare electrons. The new electroweak theory is equivalent to the QED because the Einstein
spacetime composed of the binary systems of neutrinos can carry the electromagnetic and
weak interactions. Moreover, the electromagnetic mass of an electronpositron pair is equal to
the bare mass of electron calculated within this theory. This is the Feynman ‘hocuspocus’
8
which causes that the QED and the theory of electrons and photons presented within the
Everlasting Theory are the equivalent theories. The new electroweak theory is nonperturbative.
The higher dimensions and flexible strings in the string/M theory are
consequently not necessary. We can replace the higher dimensions enlarging phase spaces. In
understanding the internal structure of bare particles, we can very easy calculate the total
cross sections, lengths of scattering and effective radii without applying the theory of
scattering. Due to the stable objects, the nonperturbative everlasting theory is very simple in
comparison to the Standard Model or string/M theory or Cosmological Standard Model and as
a result the number of parameters is reduced to seven.
Can one formula describe all interactions? In the formula couplingconstant=G(i)Mm/(ch),
the M defines the total mass of the source(s) of interactions being in touch plus the mass of
the simplest component of the field responsible for the interactions (for example, for strong
interactions they are the gluons for mesons and gluon loops for baryons). Whereas the m is
the mass of the carrier of the interaction (for example, for the strong interactions they are the
gluon loops for mesons and pions for baryons). The constants of interactions G(i) are directly
proportional to the mass densities of fields, for example the ratio of the G(i) for
electromagnetic interactions to the gravitational constant (i.e. for the longdistance fields) is
equal to approximately 4.2·10 42 . Such a definition leads to the correct values for coupling
constants for low and high energies. The above formula shows that for particles without mass
the coupling constant is equal to zero. It is obvious that for strong and electromagnetic
interactions we cannot apply massless particles. We can see that the massless particles can be
responsible for the interactions after their transformation into particles carrying mass. The
entangled photons can transform into the electronpositron pairs whereas the entangled gluons
into loops or balls carrying mass or into pions. Scientists do not fully understand Einstein’s
formula E=mc 2 and that the origin of energy and mass is different. This formula follows from
the law of conservation of spin and constancy of the natural speed of the entangled binary
systems of neutrinos in the gradients of gravity ‘attached’ to mass. Energy is associated with
the motions of mass. In electromagnetism, we can separate pure energy (i.e. the photons) from
an field carrying photons, i.e. from Einstein spacetime having mass density. Photons cannot
exist without the Einstein spacetime. Without the Einstein spacetime, the photons cannot
transform into the electronpositron pairs i.e. they cannot carry the electromagnetic
interactions. The carriers of the gravitational force must have mass as well.
How should we define mass? Mass is directly proportional to the total volume of the
structureless tachyons that a particle consists of, whereas energy is defined by motions of this
mass. When in the Einstein’s spacetime there appears a loop or a particle accelerates, then
there decreases local pressure in this spacetime that increases the local mass density of the
Einstein spacetime. We can say that mass (or volume of tachyons) and energy (or motions of
tachyons) are the two everlasting attributes of nature and the inertial and gravitational masses
have the same origin. The volume of the structureless tachyons defines all masses i.e. inertial,
gravitational, and relativistic.
Can the baryons have an atomlike structure? The definition of the Planck length
l=(Gh/(2πc 3 )) 1/2 =1.6·10 35 m suggests that the similarity of structures can be broken at most
for sizes smaller than about 10 35 m. We see that galaxies, the solar system and atoms all have
an atomlike structure. Since the baryons have sizes much greater than the Planck length, so
they should also take the form of an atomlike structure. My theory is that there is a massive
core and outside there is the TitiusBode law that is obligatory for strong interactions. On
orbits are pions. In strong fields, pions behave in a similar way to electronelectron pairs in
the ground state of atoms, which leads to the selection rules inside baryons.
Has the supersymmetry different interpretation? Since the total internal helicity of the fields
must be equal to zero all fermions (all fermions have internal helicities not equal to zero) arise
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as fermionantifermion pairs i.e. bosons. Such pairs behave like bosons. For example,
electrons arise as electronpositron pairs, closed strings arise as closed stringantistring pairs,
and so on. Such phenomena that cause the quantum effects in the Einstein and Newtonian
spacetimes are ‘softened’ because the internal helicity of the fields is still equal to zero. This
is the reason why fields carrying forces are composed of bosons. There is also the fermionboson
supersymmetry that follows from the phase transitions of the imaginary Newtonian
spacetime. Inside the stable objects (fermions) appear the loops (bosons). The ratio of the
masses of a stable object to the associated loop is 10.77. The postulated exotic particles are
not in existence.
Summary
Theory starting from the gas composed of the tachyons is more fundamental than the
Theory of Relativity and the Quantum Physics.
In the QCD, there is the procedure error for the lowenergy regime. At first there should be
defined the exact masses of the up and down quarks and next, from these parameters, we
should derive the properties of the resting nucleons i.e., among other things, we should
calculate the masses of the nucleons and their magnetic moments. The big problems to
calculate these physical quantities from the initial parameters follow from the procedure error
for the lowenergy regime. The Everlasting Theory shows that it is not true that almost whole
mass of resting nucleons (it is the lowenergy regime also) is the relativistic mass of the up
and down quarks. We can say that due to the procedure error the QCD is incorrect for the
lowenergy regime.
In the theory of the weak interactions, there is the masshierarchy error for the lowenergy
regime. The W and Z bosons are responsible for the weak interactions for energies higher
than about 125 GeV, not for lower. This causes that the calculated values of the coupling
constants for the weak interactions in the lowenergy regime are incorrect. This causes that
there appears the hocuspocus in the QED and causes that there is no proof that QCD
‘confines’ for low energies. The new theory of the weak interactions shows also that the
YangMills theory has a mass gap i.e. the weak interactions in the ground state of the Einstein
spacetime cause that the massless fields acquire mass.
Due to the internal structure of the core of baryons described within the Everlasting Theory,
we can eliminate all the problems that appear in the QCD and electroweak theory in the lowenergy
regime.
Equations relying on time should describe the motions and interactions, however, such
equations are already in existence. The string/M theory based on vibrations of a flexible
closed string leads to too many solutions. We need a theory describing phase transitions of the
Newtonian spacetime. This should lead us to understanding the internal structures of stable
objects and fields and to the postulates applied in the general theory of relativity (constancy of
the speed of light in the Einstein spacetime and equivalence of the inertial and gravitational
masses) and quantum physics (physical meaning of the uncertainty principle and the wave
function). We also need a correct and detailed theory relating to baryons. There appear the
reformulated QCD and theory of chaos.
The phase transitions of the Newtonian spacetime lead to the useful Mtheory. The useful
Mtheory is the part of the Everlasting Theory. To describe the internal structure of baryons,
we need something beyond the useful Mtheory i.e. the TitiusBode law for the strong
interactions.
References
[1] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)
[2] J Stachel; Has the QuarkGluon Plasma been seen?; http://arxiv.org/abs/nuclex/0510077
(2005).
10
11
Phase Transitions of Newtonian Spacetime, Neutrinos, Nucleons,
Electrons, Pions and Muons
Introduction
In the previous chapter, I set forth the experimental data suggesting how the ultimate theory
should look. I also formulated the program of the Everlasting Theory i.e. the lacking part of
the ultimate theory. Here I described the phase transitions of the gaslike Newtonian
spacetime and the internal structure of main particles.
Assume that the Newtonian spacetime is an ideal gas in the zerodimensional infinite
volume. The gas is composed of structureless tachyons that have a positive mass. Mass of
tachyon is directly proportionate to its volume. Assume that the Einstein spacetime is a gas
composed of binary systems of neutrinos.
Initial conditions are the six parameters describing physical state of the Newtonian
spacetime plus mass density of the Einstein spacetime. The mass density of the Einstein
spacetime is the seventh parameter because it does not follow from the six parameters
defining the Newtonian spacetime. Particles consist of the Einstein spacetime components.
Creations and annihilations of particles change local mass density of the Einstein spacetime.
The initial seven parameters listed in Fig. titled ‘The parameters in the Everlasting Theory’
describing the properties of the Newtonian and Einstein spacetimes can be replaced with a
new set of parameters listed below – as a result the ultimate theory is then mathematically at
its simplest. We can derive the new set of parameters from the initial set of parameters
describing the properties of the Newtonian and Einstein spacetimes. That means that these
sets of parameters are equivalent. The calculated values of the new parameters are in
accordance to the experimental data [1].
The calculated values of the new parameters are as follows:
Gravitational constant: G = 6.6740007·10 11 m 3 /(kg s 2 )
Halfintegral spin: h/2= 1.054571548·10 34 /2 Js
Speed of light in spacetimes: c = 2.99792458·10 8 m/s
Electric charge of electron: e = 1.60217642·10 19 C
Mass of electron: melectron = 0.510998906 MeV
Mass of free neutral pion mpion(o),free = 134.97674 MeV
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Mass of charged pion: mpion(+) = 139.57041 MeV.
The phase transitions of the Newtonian spacetime
Since tachyons have linear and rotational energies the rotary vortices appear, i.e. the closed
strings having internal helicity (see Fig. titled “Anticlockwise internal helicity”). A closed
string is stable because the internal helicity and dynamic viscosity cause the Newtonian
spacetime near the closed string to thicken. Because of the shape of a closed string, the
pressure is lowest on its internal equator (see Fig. titled “Stable tori”). This means that the
thickened Newtonian spacetime becomes detached from the closed string on the internal
equator of it which leads to a negative pressure inside the closed string near it. There appears
a collimated jet in the Newtonian spacetime.
Closed strings appear on the surfaces of regions with tachyons packed to the maximum. The
probability of creating a maximum dense Newtonian spacetime is extremely low, however,
not equal to zero. Such a state of spacetime behaves as incompressible liquid. Stable closed
strings appear on the surface of a maximum dense Newtonian spacetime only if outside it the
gaslike Newtonian spacetime has a strictly determined mass density. The Reynolds number
NR for maximum dense Newtonian spacetime is
NR = ρtvt(2rt)/η = 1.0076047·10 19 . (1)
In this definition the ρt denotes the maximum density of the Newtonian spacetime – this is
the mass density of a tachyon and is ρt=8.32192436·10 85 kg/m 3 . The (2rt) is the size of the
element of a closed string or distance between the layers in the liquid.
Because NR=0 is for infinitely viscid fluid, the liquid behaves as a solid body and the radius
of a vortex can be infinite. On the other hand, the radius of a vortex should be directly
proportional to the size of the element of a vortex. We can define the radius of the spinning
closed string r1 as follows
r1 = (2rt)/NR = 0.94424045·10 45 m. (2)
Only closed strings that have such a radius can arise in the Newtonian spacetime but such
strings are stable when the density of the gaslike spacetime is strictly determined. We see
that phase transitions of the gaslike Newtonian spacetime are not always possible. The closed
strings are inflexible. We can now calculate the number of tachyons K 2 a closed string
consists of as follows:
K 2 = 2πr1/(2rt) = (0.7896685548·10 10 ) 2 . (3)
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The spin of each closed string is halfintegral
spin = K 2 mtvtr1 = h/2 = (1.054571548·10 34 /2) Js. (4)
We see that a closed string is composed of K 2 adjoining tachyons (the square of the K
means that calculations are far simpler). The stable objects created during the phase
transitions of the Newtonian spacetime should contain K 2 , K 4 , K 8 , K 16 tachyons. That
saturates the interactions of stable objects via the Newtonian spacetime. The mass of the
stable objects are directly proportional to the number of closed strings. This means that the
stable objects contain the following number of closed strings: K 0 , K 2 , K 6 , and K 14 and means
that the mass of the stable objects are directly proportional to K 2(d1) , where d=1 for closed
strings, d=2 for neutrinos, d=4 for the cores of baryons and d=8 for objects before the ‘soft’
big bangs suited to life. The cosmic objects defined by d=8 I will refer to as the protoworlds.
The early Universe and the precursors of the DNAs arose inside the Protoworld as the cosmic
loop then there appear the early universes (i.e. the cosmic loops) ‘suited to life’ – I will
explain it later on.
Surface mass densities for all stable objects should have the same value. Furthermore,
nature immediately repairs any damages to stable objects – so they are the stable objects. This
means that the radii of the stable objects should be directly proportional to K (d1) .
The first phase transition of the Newtonian spacetime leads to the closed strings with
internal helicity. This suggests that all the stable objects arising due to the phase transitions of
the Newtonian spacetime should have internal helicity. Spheres cannot have internal helicity.
Torus is the simplest object, which can have an internal helicity.
The mean radii of the tori of stable objects are
rd = r1K d1 . (5)
The rest mass of the tori of the stable objects are
md = m1K 2(d1) , (6)
where m1 is for the closed string.
We know that following equation defines a torus:
(x 2 + y 2 + z 2  a 2  b 2 ) 2 = 4b 2 (a 2  z 2 ). (7)
Tori are most stable when b=2a (see Fig. titled “Stable tori”). Therefore, the radius of the
internal equator is equal to a. A most distant point of such torus (i.e. a point on the equator of
torus) is in distance 3/2 of the mean radius resulting from (5). The radius of the equator I also
refer to as external radius of torus. Spin speed on the equator of a resting torus in spacetime is
14
equal to the natural speed of the components of the torus in the spacetime. This means that for
b=2a the mean spin speed of whole torus is 2/3 of the natural speed of the components of a
torus in spacetime. All components of a torus must have the same resultant speed in
spacetimes. Because the mean spin speed is 2/3 of the natural speed in spacetime then there
appear the radial speeds of the components of a torus. From the Pythagorean’s theorem
follows that the mean radial speed is Z1=0.745355992 of the natural speed in the spacetimes.
Due to the radial speeds of the components of a torus, the components are going through the
circular axis of torus or through the centre. Due to the b=2a the mean time of such exchanges
is the same for both paths. Additional stabilization of the tori is due to the negative pressure
created in thickened beams of the Newtonian and Einstein spacetimes when the beams are
going through the surface of a torus and due to the exchanges of the beams created on the
equators of the components of a torus.
Neutrinos, electrons, cores of baryons, and the protoworlds appear similar to the NGC 4261
galaxy i.e. there is ‘point’ mass in the centre of a torus. The surface of a torus looks similar to
the Ketterle surface for a strongly interacting gas [2]. The tori consist of binary systems of
smaller tori. A torus is a stable object because the smaller tori exchange loops created on the
equators of them. The distances between the smaller binary systems of tori are about 2πr,
where r is the radius of the equator of the component. The charges and spins of particles
depends on the internal structure of the tori. The torus of the neutrino consists of binary
systems of closed strings. The torus of the core of baryons and electrons (electron is only
polarized in a specific way in the Einstein spacetime) are composed of binary systems of
neutrinos. The torus of the Protoworld (the Protoworld arose after the period of inflation) is
composed of deuterium. There is attraction between closed strings in a binary system when
the closed strings produce not overlapping antiparallel jets. Due to internal helicity of the
closed strings in a binary system, therefore, in the Newtonian spacetime between the closed
strings arises negative pressure. All spins are perpendicular to surface of the torus of a
neutrino. There are four possibilities. In the weak charge of a neutrino, the senses of all spins
of the closed strings are towards the circular axis of the neutrino whereas in its weak
anticharge all have opposite senses. In these two cases the binary systems are the dipoles
15
(spin=1). There are also two possibilities for the antiparallel spins of the neutrinos in a binary
system. In both the binary systems are the scalars (spin=0). Probability of creation of the
dipoles is much higher (the components of a pair are much closer) than the scalars but the
dipoles can appear only when interacts matter with antimatter. The exchanged binary systems
of the neutrinos that the electrons and cores of baryons consist of make halfturns on the
circular axis and in the centre of torus. Due to the law of conservation of energy, the halfturns
decrease the linear speeds of the exchanged particles so decrease also the local pressure
in the Einstein spacetime. It leads to the locally thickened spacetime i.e. this means circular
mass on the circular axis and the point mass in centre of torus appears. Similar phenomena
take place in the neutrinos and protoworlds. The surfaces of tori of neutrinos have also
internal helicity. Since the neutrinos can appear as the neutrinoantineutrino pairs then the
components of the surfaces of tori of neutrinos are the weak dipoles. It leads to the four states
of neutrinos (there are the two orientations of the dipoles and two different helicities of the
surfaces of the tori of the neutrinos).
Inside the tori, from the components of spacetimes and other fields, are produced loops.
From the Uncertainty Principle, for loop having spin equal to 1, we obtain that mass of a loop
mloop,d is Xo times smaller than the mass of torus calculated from (6)
Xo = md/mloop,d = 3πmdvdrd/h = 3π/2 = 4.71238898. (8)
For example, the large loops produced inside the tori in the cores of baryons, which are
responsible for the strong interactions, have mass mLL=67.5444107 MeV.
The strings, neutrinos, cores of baryons and protoworlds should have the same spin. This
leads to conclusion that time of an interaction depends only on involved energy so the
unification of all interactions is possible. Because all elementary objects have the same spin
then from following formula
mvr = h/2, (9)
we can calculate the natural speeds of the elementary objects in the spacetimes (the spin speed
of a component of a torus on equator of the resting torus is equal to the natural speed of the
component in the spacetimes). The binary systems of neutrinos on equator of the core of
baryons are moving with speed equal to the c (i.e. with speed 3/2 of the spin speed resulting
from (9)) and it is the natural speed of the entangled binary systems of neutrinos in the gaslike
Newtonian and Einstein spacetimes
c = 3h/(4m4r4) = 3h/(4mtr1K 11 ) = 299792458 m/s, (10)
where mass of torus in core of baryons is X=m4=318.295537 MeV whereas radius of equator
of torus in core of baryons is A=3r4/2=0.69744247 fm. The torus in the core of baryons
behaves as the strong charge/mass that carries electric charge the same as positron whereas
outside the strong field, due to the gluonphoton transitions, it behaves as electric charge of
positron. The neutrinoantineutrino pairs are the carriers of the elementary gluons and
photons. The rotatingspin pairs have three internal helicities (the three colours) but their
internal structure is disclosed in the strong field only because this field in contrary to the
electromagnetic field has internal helicity due to the properties of the strong charge/mass.
Maximum distance of a point on internal equator of a torus from the equator of the torus is
4/3 of the distance of the point mass from the equator. Energy is inversely proportional to
length of a wave. This means that we can assume that the point mass has mass about 4/3 of
the mass of torus calculated from (6). The exact calculations resulting from the atomlike
structure of baryons lead to Z2=1.3324865 – see the discussion below formulae (49) and (51)
concerning the point mass of baryons.
The internal helicity of closed string resulting from the angular speeds of the tachyons and
their dynamic viscosity means that the closed strings a torus of neutrino consists of transform
outside the torus the chaotic motions of tachyons into divergently moving tachyons. The
direct collisions of divergently moving tachyons with tachyons the Newtonian spacetime
16
consists of produce a gradient in this spacetime. The gravitational constant is associated with
gradient produced by the all closed strings a neutrino consists of. Because the constants of
interactions are directly proportional to the mass densities of fields carrying the interactions
then the G we can calculate from following formula
G = g·ρN = 6.6740007·10 11 m 3 /(kg s 2 ), (11)
where the g has the same value for all interactions and is equal to
g = vst 4 /η 2 = 25,224.563 m 6 /(kg 2 s 2 ). (12)
The gradients in the Newtonian spacetime, produced by the internal helicity of the closed
strings the neutrinos consist of, produce also gradients in the Einstein spacetime.
Due to the binding energy mass of the core of baryons (it is 727.440 MeV – see Table 1) is
14.980 MeV smaller than the sum of the masses of the torus and point mass (see the
discussion below formula (51)). This leads to conclusion that the masses of neutrinos, cores of
baryons and protoworlds are about Z3=2.2854236 times greater than the mass of tori
calculated from (6). For example, the mass of neutrino is mneutrino=3.3349306·10 67 kg.
The number of binary systems of neutrinos Z4 on torus in core of a baryon is
Z4 = m4/(2mneutrino) = 8.50712236·10 38 . (13)
Mean distance L1 of binary systems of neutrinos on surface of torus in core of a baryon is
L1 = (8π 2 A 2 /(9Z4)) 1/2 = 7.08256654·10 35 m. (14)
Mean distance L2 of binary systems of neutrinos in the Einstein spacetime is
L2 = (2mneutrino/ρE) 1/3 = 3.92601594·10 32 m. (15)
The ratio Z5 of the mean distances is
Z5 = L2/L1 = 554.321081. (16)
The Compton length λbareelectron of the bare electron is
λbare(electron) = AZ5 = 3.8660707·10 13 m. (17)
The bare mass of electron is
mbare(electron) = h/(cλbare(electron)) = 0.510407011 MeV. (18)
Knowing that melectron=(1.0011596521735)mbare(electron) (see formula (69)), we obtain
following mass of electron melectron=0.510998906 MeV (for 1MeV=1.78266168115·10 30 kg).
On comparing the two definitions of the finestructure constant for low energies αem, we
arrive at the relation
ke 2 /(hc) = Gemmelectron 2 /(hc), (19)
where k=c 2 /10 7 whereas Gem=GρE/ρN=2.78025274·10 32 m 3 /(kg s 2 ).
From formula (19), we can calculate the electric charge e of electron
e = melectron(GρE10 7 /ρN) 1/2 /c = 1.60217642·10 19 C, (20)
and next the finestructure constant
αem = e 2 c/(10 7 h) = 1/137.036001. (21)
Binding energy of the large loop ΔELL, resulting from creations of the electronpositron
pairs, to the mass of large loop mLL is (energy is inversely proportional to a length)
ΔELL/mLL = A/(2λbare(electron)). (22)
From this formula we obtain ΔELL=0.06092535 MeV.
During creation of the neutral pion from two large loops, due to the electromagnetic
interactions, is released energy equal to 2ΔELLαem. The total binding energy of neutral pion is
ΔEpion(o) = 2ΔELL(1 + αem) = 0.12273989 MeV. (23)
This means that the mass of bound neutral pion (i.e. placed in strong field) is mpion(o) =
134.96608 MeV.
The energy of opened large loop is the portion of the electromagnetic energy inside baryons.
Near the torus in core of baryons can appear at the same time nine opened large loops (the 8
closed large loops responsible for the strong interactions, see the discussion below formula
(32), and 1 responsible for electromagnetic interactions) exchanged between nine real
electronpositron pairs. Since with the rest mass of electron at the same time is associated one
17
bare electronpositron pair then the nine electronpositron pairs force production of contracted
electron having mass Z6=9·1.0011596521735=9.01043687 times greater than the rest mass of
electron. It is realized when with the point mass of electron interacts electron antineutrino (see
discussion concerning Table 8). Sometimes negatively charged pion decays to neutral pion,
electron and electron antineutrino so mass of the charged pion is
mpion(+) = mpion(o) + melectronZ6 = 139.57041 MeV.
Outside the strong field the radiation mass of the neutral pion disappears so the measured
mass of the free neutral pion is mpion(o),free = mpion(+)  9·mbare(electron) = 134.97674 MeV.
The αorder correction for the radiation energy created in the interactions of the virtual or
real electronpositron pairs (created by the virtual or real photons emitted by an electrically
charged particle) is
memc 2 = ke 2 /C, (24)
where k=c 2 /10 7 , the C is the Compton wavelength of particle.
The Compton wavelength of electrically charged particle is
C = 2h/(cm). (25)
Then from (24) and (25) we obtain
mem = Cm, (26)
where C=e 2 c/( h).
The simplest neutral pion consists of four energetic neutrinos. The charged pion more often
than not, decays into a muon and a neutrino. If we assume that these two particles arise from
the bare mass of a charged pion and that the neutrino has energy equal to the one quarter of
the mass of a neutral pion then the calculated mass of a bound muon is
mmuon = mpion(+)  mempion(+)  mpion(o)/4 = 105.666974 MeV. (27)
Due to the strong interactions, in the decays of particles most often appear the neutral and
charged pions. The charged pions decay to muons. We can assume that the free neutral pions
gain the mass at the cost of the mass of the free muons. It leads to conclusion that mass of free
muon is mmuon,free = mmuon – (mpion(o),free  mpion(o)) = 105.656314 MeV.
Simultaneously there can appear the virtual bare particleantiparticle pair(s) that total
positive mass is the sum of two the bare masses of the real particle (see definition “Virtual
particles”) and the emitted binding energy by the bare real particle.
Baryons
Key points:
*The core of baryons is the black hole in respect of the strong interactions.
*Outside of the core of baryons, the TitiusBode law for strong interactions is obligatory.
Between the core and pion, lying under the Schwarzschild surface for strong interactions,
electric charge is exchanged. A pion (two large loops) in strong field behaves similarly to two
electrons in the ground state of an atom. This means that the selection rules for the pions and
loops created in baryons appears.
*A neutral pion is a binary system of two large loops composed of binary systems of
neutrinos. Large loops arise on the circular axis inside the torus of the core.
For the TitiusBode law for strong interactions we can use the following formula:
Rd = A + dB, (28)
where Rd denotes the radii of the circular tunnels, the A denotes the external radius of the
torus, d=0,1,2,4; the B denotes the distance between the second tunnel (d=1) and the first
tunnel (d=0). The first tunnel is in contact with the equator of the torus.
Hyperons arise very quickly because of strong interactions. They decay slowly due to the
tunnels.
18
The pions in the tunnels circulate the torus. Such pions I refer to as W pions because they
are associated with strongWeak interactions. The pions behave in a similar way both in
nucleons and in hyperons. Their mass is denoted by mW(+o),d.
The B we can calculate on the condition that the charged W pion in the d=1 state, which is
responsible for the properties of nucleon, should have unitary angular momentum because this
state is the ground state for W pions:
mW(+),d=1(A + B)vd=1 = h, (29)
where vd=1 denotes the speed of the W pion in the d=1 state.
We can calculate the relativistic mass of the W pions using Einstein’s formula
mW(+o),d = mpion(+o)/(1  vd 2 /c 2 ) 1/2 . (30)
We know that the square of the speed is inversely proportional to the radius Rd (for d=1 is
v 2 d=1=c 2 A/(A+B)) so from (28) and (30) we have:
mW(+o),d = mpion(+o)(1 + A/(dB)) 1/2 . (31)
Since we know the A then from formulae (29)(31) we can obtain the B=0.5018395 fm. We
see that the d=1 state is lying under the Schwarzschild surface for the strong interactions. The
large loops are responsible for the strong interactions then range of such interactions cannot
be greater than the circumference of the large loop i.e. should be shorter than 2.915 fm. It
leads to conclusion that the radius of the last orbit for the strong interactions is A+4B=2.7048
fm. I will prove that the second solution B’=0.9692860 fm is not valid.
The creation of resonance is possible when loops overlap with tunnels. Such bosons I call S
bosons because they are associated with Strong interactions. Their masses are denoted by
mS(+o),d=0. The spin speeds of S bosons (they are equal to the c) differ from the speeds
calculated on the basis of the TitiusBode law for strong interactions – this is the reason why
the lifetimes of resonances are short.
The mass of the core of resting baryons is denoted by mH(+0). The maximum mass of a
virtual S boson cannot be greater than the mass of the core so I assume that the mass of the S
boson, created in the d=0 tunnel, is equal to the mass of the core. As we know, the ranges of
virtual particles are inversely proportional to their mass. As a result, from (28) we obtain:
mH(+0)A = mS(+o),d(A + dB). (32)
19
There is some probability that virtual S boson arising in the d=0 tunnel decays to two parts.
One part covers the distance A whereas the remainder covers the distance 4B. The large loops
arise as binary systems (i.e. as the neutral pions) because then the strong field is more
symmetrical. The part covering the distance A consists of four virtual neutral pions (i.e. of the
eight large loops). Then the sum of the mass of the four neutral pions (539.87 MeV) and the
mass of the remainder (187.57 MeV) is equal to the mass of the core of baryons and is equal
to the mass of S boson in the d=0 state (727.44 MeV).
Denote the mass of the remainder (it is the S boson) by mS(+),d=4, then:
mS(+),d=4 = mH(+)  4mpion(o). (33)
Since there is the positroncoreof proton transition, we should increase the mass of core
by the electromagnetic energy emitted due to this transition. From this condition and using
formulae (32) and (33) we have
mH(+) = mpion(o)(A/B + 4) + αemmbare(electron) =727.440123 MeV. (34)
There is some analog to the energy appearing during this transition. The weak energy of the
large loop is αw(proton)mLL=1.265 MeV (see formula (51)) and such energy is needed in the
protonneutron transition.
The nucleons and pions are respectively the lightest baryons and mesons interacting
strongly, so there should be some analogy between the carrier of the electric charge
interacting with the core of baryons (it is the distance of masses between the charged and
neutral cores) and the carrier of an electric charge interacting with the charged pion (this is the
electron). Assume that:
(mH(+)  mH(o))/mH(+) = melectron/mpion(+). (35)
Formula (35) leads to the distance of masses between the charged and neutral core equal to
2.663 MeV. Similar value we obtain for electron (plus electron antineutrino) placed on the
circular axis of the core (i.e. the point mass of electron is placed on this axis). Then the
electromagnetic binding energy is 3ke 2 /(2Ac 2 )=3.097 MeV. If we subtract the mass of
electron we obtain Eb1=2.586 MeV. The weak binding energy of the Eb1 interacting with the
core of baryon is Eb2=3GwEb1·mH(+)/(2Ac 2 )=0.0831 MeV (see formula (50)). It leads to the
distance of masses between the charged and neutral core equal to Eb1+Eb2=2.669 MeV.
The results obtained from formulae (31)(35), with the value A/B=1.389772, are collected
in Table 1 (the masses are provided in MeV).
Table 1 Relativistic masses
d mS(+) mS(o) mW(+) mW(o)
0 727.440123 724.776800
1 423.043 421.494 215.760 208.643
2 298.243 297.151 181.704 175.709
4 187.573 186.886 162.013 156.668
The mass of group of four virtual remainders is smaller than the mass of the virtual field of
nucleon. This leads to conclusion that the symmetrical decays of the group of the four
remainders lead to the TitiusBode law for the strong interactions. The group of four virtual
remainders reaches the d=1 state. There it decays to two identical bosons. One of these
components is moving towards the equator of the torus whereas the other is moving in the
opposite direction. When the first component reaches the equator of the torus, the other one
stops and decays into two identical particles, and so on. In place of the decay, a ‘hole’ appears
in the Einstein spacetime. A set of such holes is some ‘tunnel’. The d=4 orbit is the last orbit
for strong interactions because on this orbit the remainder decays into photons so strong
20
interactions disappear. We see that there is not in existence a boson having range equal to the
B’.
There is a probability that the y proton is composed of H + and W(o),d=1 and a probability that
1y is composed of H o and W(+),d=1. From the Heisenberg uncertainty principle follows that
the probabilities y and 1y, which are associated with the lifetimes of protons in the abovementioned
states, are inversely proportional to the relativistic masses of the W pions so from
this condition and (31) we have
y = mpion(+)/(mpion(+) + mpion(o)) = 0.5083856, (36)
1  y = mpion(o)/(mpion(+) + mpion(o)) = 0.4916144. (37)
There is a probability that the x neutron is composed of H + and W(),d=1 and a probability that
1x is composed of H o , resting neutral pion and Z o . The mass of the last particle is
mZ(o)=mW(o),d=1mpion(o) (the pion W(o),d=1 decays because in this state both particles, i.e. the
torus and the W(o),d=1 pion, are electrically neutral). Since the W(o),d=1 pion only occurs in the
d=1 state and because the mass of resting neutral pion is greater than the mass of Z o (so the
neutral pion lives shorter) then
x = mpion(o)/mW(),d=1 = 0.6255371, (38)
1  x = 0.3744629. (39)
The mass of the baryons is equal to the sum of the mass of the components because the
binding energy associated with the strong interactions cannot abandon the strong field.
The mass of the proton is
mproton = (mH(+) + mW(o),d=1)y + (mH(o) + mW(+),d=1)(1  y) = 938.2725 MeV. (40)
The mass of the neutron is
mneutron = (mH(+) + mW(),d=1)x + (mH(o) + mpion(o) + mZ(o))(1  x) = 939.5378 MeV. (41)
The proton magnetic moment in the nuclear magneton is
proton/o = mprotony/mH(+) + mproton(1  y)/mW(+),d=1 = +2.79360. (42)
The neutron magnetic moment in the nuclear magneton is
neutron/o = mprotonx/mH(+)  mprotonx/mW(),d=1 = 1.91343. (43)
The mean square charge for the proton is
= e 2 [y 2 + (1  y) 2 ]/2 = 0.25e 2 (quark model gives 0.33e 2 ) (44)
The mean square charge for the neutron is
= e 2 [x 2 + (x) 2 ]/(2x + 3(1  x)) = 0.33e 2 (quark model gives 0.22e 2 ), (45)
where [2x+3(1x)] defines the mean number of particles in the neutron.
The mean square charge for the nucleon is
= [ + ]/2 = 0.29e 2 (quark model gives 0.28e 2 ). (46)
21
Inside baryons are produced particles carrying the fractional electric charges so arithmetic
mean of both results should lie inside the interval determined by the experiment (the
measured values of the are (0.25, 0.31)e 2 ). We see that it is true. But there is the place
for the quarks too  see Chapter titled “Reformulated Quantum Chromodynamics”.
Notice that the ratio of the distance of masses between the charged and neutral pions to the
mass of an electron is equal to the ratio of the masses of a charged core of baryons H + and Z + ,
where mZ(+)=mW(+),d=1mpion(o). This should have some deeper meaning. Assume that the
increase in the mass of electrons and Z + boson are realized in the d=0 state because this tunnel
has some width resulting from the diameter of the point mass of the virtual H + created on the
equator of the torus of the core of baryons. The width of the d=1 tunnel means that the
mentioned particles in this tunnel do not move with a speed equal to the c. The relativistic
masses of the W pions can be calculated using Einstein’s formula (30). Definition of the
coupling constant for the strongweak interactions sw (the core of baryons is the black hole
with respect to the strong interactions i.e. on the equator of torus the spin speed is equal to the
c) leads to following formula
sw = GswMm/(csd) = mvd 2 rd/(csd) = vd/c, (47)
where Gsw denotes the strongweak constant, sd is the angular momentum of particle in the d
state whereas vd is the speed in the d tunnel. In the Einstein spacetime can appear particles or
binary systems of particles having spin equal to 1 because such spin have the components of
the Einstein spacetime i.e. the binary systems of neutrinos. For example, for the large loop
responsible for the strong interactions is sd=h and vd=c – it leads to sw(largeloop)=1.
From formulae (30) and (47) we obtain
sw(Z(+),d=0) = vd=0/c = (1  (mZ(+)/mH(+)) 2 ) 1/2 = 0.993812976. (48)
The rp(proton) denotes the radius of the point mass of a proton and the range of the weak
interactions of the point mass of a proton because the range of weak interactions of a single
neutrino is 3482.87 times bigger than the external radius of its torus (see Chapter
“Interactions”) so this radius is much smaller than the radius of the point mass of a proton.
Because v 2 =GswmH(+)/r and because the particle Z(+o),d=0 is in distance r=rp(proton)+A from the
centre of torus then from formula (48) we obtain
A/(rp(proton) + A) = (vd=0/c) 2 = 1  (mZ(+)/mH(+)) 2 . (49)
Then rp(proton)=0.8710945·10 17 m.
We calculated the sum of the circular mass and the mass of the torus:
X=mc(proton)=318.295537 MeV. Notice that the mass of H + is greater than the doubled value of
X. This means that the core of a baryon behaves in a different way to the bare electron. To
obtain the exact mass of core of baryons, the point mass Y must be Y=424.124493 MeV. We
see that the point mass of core of baryons Y is approximately the sum of the X and mass of
charged pion and minus one quarter of the mass of the neutral pion (424.124421 MeV). Since
on the equator of the point mass the spin speed of the binary systems of neutrinos must be
equal to the c then we can calculate the constant for the weak interactions
Gw = c 2 rp/Y = 1.0354864·10 27 m 3 s 2 kg 1 . (50)
The coupling constant for weak interactions of protons w(proton) can be calculated using the
formuladefinition
w(proton) = GwY 2 /(ch) = 0.0187228615. (51)
Y is the mass of the source and the carrier of weak interactions.
The distance of mass between X+Y and H + is equal to the binding energy resulting from the
weak interactions of the point mass of the core of baryons with the virtual large loops arising
at a distance of 2A/3 from the point mass and with the virtual particles arising on the surface
of the torus. There are exchanged the weak masses i.e. the volumes filled with a little
compressed Einstein spacetime. There arises the virtual H +, particles and the particles having
masses equal to the distance of masses between charged and neutral pions. They arise as
22
virtual pairs so the axes of these dipoles converge on the circular axis of the torus so they
were also at a distance of 2A/3 from the point mass. Binding energy, E = mc 2 , is equal to the
sum of the mass of these three virtual particles (M = 727.440 + 67.544 + 4.604 = 799.59
MeV) multiplied by the mass of the point mass Y and the Gw and divided by 2A/3. This leads
to 14.980 MeV and to the mass of the charged core of baryons that is equal to 727.440123
MeV and this result is consistent with the original mass of the H + .
The new electroweak theory
Structure of muon and magnetic moment of electron
The external radius of the torus of an electron is equal to the Compton wavelength for the
bare electron which is rz(electron)=3.8660707·10 13 m (see formula (17)).
From (50) for a point mass Mp we have
GwMp = rpc 2 , (52)
where rp denotes the range of weak interactions.
Since
w = GwMpmp/(ch), (53)
where mp denotes a mass interacting weakly with the Mp, so
w = mprpc/h. (54)
To calculate the radius of the point mass of an electron we should divide the point mass of
an electron by the mass of Y and extract the cube root of the obtained result and next multiply
it by the radius of the point mass of a proton. The radius of the point mass of an electron
rp(electron) is
rp(electron) = 0.7354103·10 18 m. (55)
The point mass of electron is the half of the bare mass of electron (see formula (18)).
The density of the Einstein spacetime inside the point mass of an electron is the same as the
point mass of a proton. This means that the speed on the equator of the point mass of an
electron cannot be the c. Using the formula c 2 =GwM/rp(electron), we can calculate the virtual or
real energy/mass E of neutrinos which should be absorbed by the point mass of electron
M=E+mp(electron)=35.806163 MeV. A muon is an electronlike particle i.e. the point mass of a
muon is equal to the circular mass of it i.e. about (mmuon,freemradiation(muon))/2=52.8282mradiation(muon)/2
MeV. The point mass of a muon consists of three particles: two energetic
neutrinos and the point mass of the contracted electron (the two neutrinos means that the
muon is stable). The additional point mass of the contracted electron is outside the circle
having the spin speed equal to the c. If we assume that the all three particles have the same
mass, then to obtain the mass of free muon the weak binding energy of the point mass of a
muon should be 0.498281845+mradiation(muon)/2. The energy lost by a free muon increases the
mass of the virtual field. This means that the mass of virtual field of a free muon is greater
than the bare mass of muon due to the emitted binding energy and due to the energy lost by
the free muon. We can see that mass of muon depends on mass density of point mass of
electron and the size of the point mass of the not contracted electron.
From (54) we obtain following value for the coupling constant for the electronmuon
transformation
w(electronmuon) = 9.511082·10 7 . (56)
We see that
Xw w(proton)/w(electronmuon) = (M/mp(electron)) 2 = 19,685.3. (57)
Because the state of an electron describes the wave function filling the entire Universe and
because the torus of an electron is a part of the Einstein spacetime we must take into account
the matter and dark energy in our Universe. Dark energy is a sphere filled with binary systems
of neutrinos created from the Protoworld. The mass of the dark energy is so many times
greater than the baryonic mass of our Universe and how many times greater the bare mass of
23
the proton (it is the core of the proton) is than the mass of the large loop created on the
circular axis of the torus of the proton – see Chapter titled “New Cosmology”. The ratio of
these values is =10.769805. The ratio of the energy of matter (visible and dark) and dark
energy to the energy of matter is +1. In understanding that the Y is the carrier of the weak
interactions of electrons, for the coupling constant of the weak electronproton interactions we
obtain: ’w(electronproton)≈Gw(Ygw)mp(electron)/(ch)=1.119·10 5 , where gw is the weak binding
energy of the Y and mp(electron) i.e. gw=GwYmp(electron)/rp(electron)=3.0229 MeV. There can be
virtual or real mass of Y. The real mass Y appears when the electron transforms into an
antiproton. A value close to the +1, we obtain for the ratio of the mass Ygw to the mass
M=35.806163. This similarity leads to conclusion that the electronmuon transformation (due
to the weak interactions) is associated with the electronmatter interactions whereas the
electronproton weak interactions are associated with the electronmatterdarkenergy weak
interactions.
The exact value for the coupling constant of the weak interactions of an electron placed in
the matter and dark energy is
’w(electronproton) = ( + 1)w(electronmuon) = 1.11943581·10 5 . (58)
The mass of a resting electron is equal to the mass of a bare electron and the
electromagnetic and weak masses resulting from the interaction of the components of virtual
electronpositron pairs (it is the radiation mass of pairs) plus the weak mass resulting from the
interaction of the point mass with the radiation mass of the virtual pairs. Virtual pairs behave
as if they were in a distance equal to 2rz(torus)/3 from the point mass. We neglect the pairelectron
electromagnetic interactions because the pairs are electrically neutral.
The formula for the coupling constants of the gravitational, weak and strong interactions is
as follows:
i = GiMm/(ch). (59)
The energy of the interaction defines the formula
Ei = GiMm/r, (60)
then from (59) and (60) we obtain
Ei = ich/r = mic 2 . (61)
On the other hand the Compton wavelength of the bare particle is equal to the external
radius of a torus and is defined by the formula
= rz(torus) = h/(mbarec), (62)
then from (61) and (62) we obtain
mi = imbare/(r/rz(torus)). (63)
Most often the point mass of an electron appears near the point mass of a nucleons because
there is a higher mass density of the Einstein spacetime. From (58) we have
’w(electronproton) = 1.11943581·10 5 . (64)
As a result, we can introduce the symbol
= em/(’w(electronproton) + em), (65)
where denotes the mass fraction in the bare mass of the electron that can interact
electromagnetically, whereas 1 denotes the mass fraction in the bare mass of the electron
that can interact weakly. Whereas the electromagnetic mass of an bare electron is equal to its
weak mass.
Since the distance between the constituents of a virtual pair is equal to the length of the
equator of a torus (because such is the length of the virtual photons) so the ratio of the
radiation mass (created by the virtual pairs) to the bare mass of electron is
= em/2 + (1  )’w(electronproton)/2 = 0.00115963354. (66)
24
The ratio of the total mass of an electron to its bare mass, which is equal to the ratio of the
magnetic moment of the bare electron to the Bohr magneton for the electron, describes the
formula
= 1 + + ’w(electronproton)/(2/3). (67)
Due to the virtual pairs annihilations, in the Einstein spacetime are produced holes
decreasing mass density of the radiation field. Since for virtual electron the product
mbare(electron)’w(electronproton) is about 7.2·10 7 times smaller than the mp(proton)w(proton) for proton
so we obtain that the final result is lower than it follows from (67) by the value
Δεelectron = (  1)·7.2·10 7 = 8.344077·10 10 . (68)
Then we obtain following value
’ = ε – Δεelectron = 1.0011596521735 (69)
Summary
The Everlasting Theory is the lacking part and foundations of the ultimate theory.
The phase transitions of the Newtonian spacetime lead to the physical constants, to an atomlike
structure of baryons and new cosmology.
My theory is very simple because it is based on only seven parameters and three formulae –
two formulae are associated with the phase transitions and one formula is associated with the
TitiusBode law for strong interactions – and concerns the stable stages of bare particles.
This theory is an extension to Einstein’s theories of relativity and of the correct part of the
quantum theory. Gravity needs inflexible neutrinos. The G then has the same value for all
masses. Newtonian spacetime is classical and leads to the correct part of the quantum theory.
The Everlasting Theory provides very good results. The exotic particles and tau neutrinos are
not in existence.
Two of the seven parameters, i.e. the inertial mass density of tachyons and the dynamic
viscosity, do not change with time. The other five can have different values in different
cosmic bulbs which walls are composed of the pieces of space packed to maximum. Then, the
walls are hermetic for the Newtonian spacetime. The values of the seven parameters in our
bulb lead to the fundamental laws of conservation of energy and spin, and to the principle of
relativity. Today, of course in a cosmic scale, almost all closed strings in our bulb are inside
the masses so there are only two spacetimes leading to the gravity and electromagnetism. All
particles greater than the neutrino are built of the very stable neutrinos. The lacking dark
energy is inside the neutrinos because they are composed of the closed strings moving with
superluminal speeds. Exchanges of the binary systems of the closed strings are responsible for
the entanglement of particles.
There can be infinite number of the cosmic bulbs.
Three conditions must be satisfied in order to create life. First, the mass densities of the
spacetimes must be specific the creations of the stable objects were possible. The laws of
physics should not vary. Next, the Protoworld must have strictly determined the mass of the
Protoworldneutrino transition was possible. Because universes arise as the universeantiuniverse
pairs then the distance between the constituents of a pair must be sufficiently
distant.
25
Table 2 Theoretical results
Physical quantity Theoretical value*
Gravitational constant 6.6740007 E11 m 3 /(kg s 2 )
Halfintegral spin (1.054571548 E34)/2 Js
Speed of light 2.99792458 E+8 m/s
Electric charge 1.60217642 E19 C
Mass of electron 0.510998906 MeV
Finestructure constant for low energies 1/137.036001
Mass of bound neutral pion 134.96608 MeV
Mass of free neutral pion 134.97674 MeV
Mass of charged pion 139.57041 MeV
Radius of closed string 0.94424045 E45 m
Linear speed of closed string 0.7269253 E+68 m/s
Mass of closed string 2.3400784 E87 kg
External radius of neutrino 1.1184555 E35 m
Mass of neutrino 3.3349306 E67 kg
Mass of Protoworld 1.961 E+52 kg
External radius of Protoworld 287 million lightyears
Mass of the Universe 1.821 E+51 kg
Radius of the early Universe loop 191 million lightyears
External radius of torus of nucleon 0.697442473 fm
Constant K 0.7896685548 E+10
Binding energy of two large loops 0.12273989 MeV
*E15=10 15
26
Table 2a Theoretical results
Physical quantity Theoretical value
Mass of large loop 67.5444107 MeV
Mass of torus of core of baryons 318.295537 MeV
Point mass of the nucleon 424.124493 MeV
Range of weak interactions of the proton 8.710945 E18 m
Weak binding energy of core of baryons 14.980 MeV
Mass of charged core of baryons 727.440123 MeV
Ratio of mass of core of baryons to mass of large loop 10.769805
Mass of electron to mass of bare electron 1.0011596521735
Mass of bound muon 105.666974 MeV
Mass of free muon 105.656314 MeV
The A/B in the TitiusBode law for strong interactions 1.38977193
Mass of proton 938.2725 MeV
Mass of neutron 939.5378 MeV
Proton magnetic moment in nuclear magneton +2.79360
Neutron magnetic moment in nuclear magneton 1.91343
Radius of last tunnel for strong interactions 2.7048 fm
Mean square charge for nucleon 0.29
Mean square charge for proton 0.25
Mean square charge for neutron 0.33
External radius of torus of electron 386.607 fm
Range of weak interactions of electron 0.7354103 E18 m
Weak constant 1.0354864E+27 m 3 /(kg s 2 )
Electromagnetic constant for electrons 2.7802527E+32 m 3 /(kg s 2 )
Coupling constant for weak interactions of the proton 0.0187228615
Coupling constant for the electronproton weak
interaction
1.11943581 E5
Coupling constant for the electronmuon weak
0.9511082 E6
interaction
Coupling constant for strongweak interactions inside
the baryons
d=0: 0.993813
d=1: 0.762594
d=2: 0.640304
References
[1] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)
[2] M W Zwierlein, J R AboShaeer, A Schirotzek, C H Schunck, and W Ketterle; Vortices
and superfluidity in a strongly interacting Fermi gas; Nature 435, 10471051 (2005).
27
Interactions
Here I show mathematical and physical relations between different interactions.
Name of
source
St
at
es
Types of interactions and phase spaces
Table 3a Interactions
What produces gradients in fields? Name of interaction
Tachyons 1 Fundamentaldirect collision
Range=0.5·10 64 m
Closed 2 Tachyon jet (line of
string
gravitational field)
Range=2·10 36 m
Neutrino 4 Divergently moving tachyon jets; they produce the Gravitational
gradients in the Newtonian spacetime
Range=2·10 36 m
Core of
baryon
The binary systems of closed strings a neutrino
consists of suck up Newtonian spacetime from some
volume
Exchanged small loops produced on the equator of a
neutrino and composed of the superluminal binary
systems of closed strings
2 Divergently moving binary system of neutrinos fluxes
(the binary systems are the carriers of massless
photons and gluons) produced in annihilations of
electronpositron pairs appearing in Einstein
spacetime (the pairs are produced by the virtual or
real photons)
Exchanged volumes filled with additional binary
systems of neutrinos
Exchanged large single loops composed of carriers of
gluons (in mesons) or binary systems of loops
(between baryons) appearing on circular axis of torus;
the 8 different carriers of gluons are the Feynman
partons; the three internal helicities of a carrier of
gluons cause that the gluons are the threecoloured
particles; due to the internal helicities of the core of
baryons and the particles produced inside it, we
cannot neglect the internal structure of the carriers of
gluons in the strong fields; outside strong field the
gluons become the photons
Weak
Range of confinement=
=3482.87R(neutrino)
Entanglement
Range=size of the Universe
Electromagnetic
Range=2·10 36 m
Weak
Range for proton=
=0.871·10 17 m
Range for electron=
=0.735·10 18 m
Strong
Range=2.92·10 15 m
(circumference of the large
loop)
Protoworld 2 Divergently moving tachyon jets Gravitational
Range=2·10 36 m
Charge
(source)
(gravitational mass
i.e. composed of weak
bidipoles)
Weak
(torus of neutrino)
Strong
(torus of core of
baryons)
Electric
(torus of core of
baryons; only outside
the strong field due to
the transition of
gluons into photons)
Electric
(torus of electron i.e.
the polarized part of
the Einstein
spacetime)
Superstrong
(cosmic torus of
protoworld)
Kasner
solution
and
BKL
model
28
Table 3b Interactions
Emitted
massless
rotational
energy
+ Gravitons
(they behave
as two
entangled
photons)
Mass carrier of emitted
massless rotational
energy
Weak bidipoles (two
binary systems of
neutrinos i.e. two weak
dipoles; spin = 2; today
the classical gravity)
+ Entanglons Binary systems of closed
strings i.e. halfjet
dipoles (spin = 1)
Quantum particles
Weak bidipoles (only
in the era of inflation;
Quantum Gravity)
Binary systems of
closed strings (only in
the era of inflation)
Entanglons
+ Gluons Entangled weak dipoles Weak dipoles (only in
the era of inflation)
Gluons
+ Photons Entangled weak dipoles Photons
– Photons Entangled weak dipoles Electrons and
Electronpositron pairs
+ – – –
Table 4 Phase spaces
Stable object Coordinates and quantities needed to
describe position, shape and motions
Tachyon 6 (5 + time)
Closed string
10 (9 + time)
Closed stringantistring pair
Neutrino
Neutrinoantineutrino pair
26 [9(large torus) + 7(small tori on the surface
of the large torus) + 9(small tori on the surface
of the point mass) + time]
58 (9 + 23 + 25 + time)
Core of baryons
Electron
Protoworld 122 (9 + 55 + 57 + time)
We see that for stable objects we have N=(d1)·8+2, where N denotes the numbers of needed
coordinates and quantities whereas d=0, 1, 2, 4, 8, 16. Then for the N we obtain 6 (the
Newtonian spacetime is the imaginary spacetime), 2 (for rotating spin), 10, 26, 58 and 122.
For example, to describe the position, shape and motions of a closed string we need three
coordinates, two radii, one spin speed, one angular speed associated with the internal helicity
and the time associated with the linear speed. To describe the rotation of the spin we
additionally need two angular speeds. This means that the phase space of a closed string has
ten elements whereas the stringantistring pair has eleven. We can see that we can replace the
higher spatial dimensions (i.e. the more than three) for the enlarged phase spaces.
29
The weak interactions of baryons lead to the fundamental force
Now, verify whether the mass Y leads to the stable closed strings. Gravitational mass is
directly proportional to the number of closed strings a mass consists of. Then using the
following formula we can calculate the number of closed strings Ncs that the point mass of the
core of baryons is composed of
Ncs = Y/m1. (70)
Assume that the radius of the point mass has a strictly determined value because the closed
strings suck up the Newtonian spacetime from the interior of it. To calculate the volume of the
spacetime Vs a closed string sucks it up we can use
Vs = 4πrp(proton) 3 /(3Ncs). (71)
Due to the shape of closed string, inside it pressure of the Newtonian spacetime is a little
lower so the sucked up spacetime separates from closed string on the internal equator. There
is produced tachyon jet. The sucked up tachyons have the radial speeds equal to the linear
speeds of the tachyons. Volume of one separated portion of the thickened spacetime is
Vcs = 2πrt πrt 2 . (72)
In knowing the inertial mass density of the Newtonian spacetime ρN, we can calculate the
mass density of the thickened Newtonian spacetime ρts
ρts = ρNVs/Vcs. (73)
Centripetal force acting on one tachyon depends on the pressure difference between the
interior and exterior of the closed string. Because ρts>>ρN then the centripetal force Fcpt is
Fcpt = πrt 2 ρtsvt 2 /2. (74)
Next, compare the obtained centripetal force with the centrifugal force Fcft acting on the
tachyons that a closed string is composed of
Fcft = mtvt 2 /r1. (75)
For both forces we obtain about 2.2·10 133 N. It means that closed strings are stable particles.
In knowing the point mass of proton Y and applying formula (49), we can calculate the
mass density of the point mass. The mass density of the Einstein spacetime is the parameter
then the ratio of the mass densities of the Einstein spacetime and the point mass Y is 40,363.
The formula (15) defines the mean distance between the neutrinoantineutrino pairs in the
Einstein spacetime. The mean distance between the neutrinoantineutrino pairs in the point
mass Y is (40,363/(40,363 + 1)) 1/3 = 0.9999917 times smaller than in the Einstein spacetime.
This means that the mean distance is 3482.87rneutrino. It is the range of the weak interactions of
a single neutrino i.e. the range of the confinement of the carriers of gluons and photons.
Homogeneous description of all interactions
Constants of interactions are directly proportional to the inertial mass densities of fields
carrying the interactions. The following formula defines the coupling constants of all
interactions
αi = GiMimi/(ch), (76)
where Mi defines the sum of the mass of the sources of interaction being in touch plus the
mass of the component of the field whereas mi defines the mass of the carrier of interactions.
We know that the neutral pion is a binary system of large loops composed of the binary
systems of neutrinos. This means that inside the neutral pion the binary systems of neutrinos
are exchanged whereas between the neutral pions the large loops are exchanged. We can
neglect the mass of the binary system of neutrinos in comparison to the mass of the neutral
pion. On the other hand, from (47) it follows that coupling constant for the large loop is
unitary because its spin speed is equal to the c. Due to the formula E = mc 2 , the massless
energy frozen inside a pion is equal to its mass. Then for strongly interacting neutral pion is
S = GS(2mpion(0))(mpion(0)/2)/(ch) = v/c = 1, (77)
30
where v denotes the spin speed of the large loop. Then the constant of the strong interactions
is GS=5.46147·10 29 m 3 s 2 kg 1 .
Coupling constant for strongly interacting proton, for low energies, is
S pp = GS(2mproton + mpion(0)/2)mpion(0) /(ch) =14.4038. (78)
In a relativistic version, the GS is constant. When we accelerate a baryon, then there
decreases the spin speed of large loop so its mass also decreases:
E(loop)2πr(loop)/v(spinspeedofloop)=h. This means that the mass of the carrier decreases
whereas when nucleons collide, the number of the sources increases. These conditions lead to
the conclusion that the value of the running coupling decreases when energy increases (see
Paragraph titled “Running couplings”).
The other constants of interactions for low energies i.e. the gravitational constant G,
electromagnetic constant for electrons Gem and weak constant Gw I calculated before – see
respectively formulae (11), (19) and (50).
Running couplings
We can calculate the coupling constants from the formula (76). Using the formulae (11) and
(12) we know that the constants of interactions depends linearly on the mass densities of
appropriate fields.
Strong and strongweak interactions of colliding nucleons
The formula (78) defines coupling constant for two strongly interacting nonrelativistic
protons. The scale in my theory is as follows. When energetic nucleons collide the Titius
Bode orbits for strong interactions are destroyed i.e. the strong field. This means that colliding
nucleons interact due to the weak masses of the large loops responsible for strong interactions.
The strongweak interactions of the colliding nucleons depend on the properties of the pions
i.e. of the binary systems of large loops. The weak mass of virtual particles produced by
binary system of large loops is f=2αw(proton)=1/26.7053=0.0374457 times smaller than rest
mass of the large loop and this value is the scale/factor for the running coupling of the strongweak
interactions for colliding nucleons. This means that the running constant of the strongweak
interactions for colliding nucleons αsw defines the following formula
αsw = fαs, (79)
where f=2αw(proton).
When the energy of a proton increases then, due to the uncertainty principle, the mass of
components of fields decreases (energyofcomponentoffield multiplied by spinperiod is h;
the spinperiod increases when the energy of the proton increases). We can calculate the mass
of the carrier msw using the following formula (there are calculations analogous to the
formulae (103)(105))
msw = mpion(o)β, (80)
where
β = (1 – v 2 /c 2 ) 1/2 , (81)
where v denotes the relativistic speed of the nucleon. When energy of collision is E = nmproton
then β = 1/n.
When the energy of colliding protons increases, more sources interacting strongly appear.
The sources are in contact because there is a liquidlike substance composed of the cores of
baryons. There is the destruction of the atomlike structure of baryons. This means that a
colliding nucleon and the new sources behave as one source. Strongweak interactions are
associated with the torus (the mass of the torus is X=318.3 MeV) whereas the mass of the
core is mH(+)=727.44 MeV) then the mass of the source Msw for colliding proton is
Msw = 2mproton + mpion(o)β/2 + X·\integerof\{(1/β  1)2mproton/(2mH(+))}. (82)
Due to the frozen energy, one charged torus is associated with energy 2mH(+).
31
This means that there are separated fragments of the curve representing the running
coupling for strongweak interactions of colliding nucleons. When we neglect the \integerof\
in the formula (82) then from (76), (78) and the formulae (79)(82), we obtain the following
function for strongweak runningcoupling
αsw = auβ 2 + buβ + cu, (83)
au = 0.0187229 = αw(proton),
bu = 0.4067,
cu = 0.1139.
This curve starts from 1.67 GeV and leads through the upper limits of the sectors
representing the successive ‘jumps’ of the running coupling. The ‘jumps’ appear for the
following energies
En[GeV] = mproton + n·mH(+), (84)
where n=2, 3, 4, 5,….. For the n=1 we observe the drop in value of the running constant from
8.113 to 0.349. You can see in Chapter “Reformulated Quantum Chromodynamics” how the
mass of the charm quark defines the energy E1. The widths of the ‘jumps’ can be calculated
using the following formula
Δαsw = fGsΔMm/ch = djβ, (85)
where dj=0.0883096 whereas ΔM=X and m=mpion(o)β and should be expressed in kilograms.
For the curve leading through the lower limits of the sectors representing the successive
‘jumps’ we obtain
αsw = alβ 2 + blβ + cl, (86)
al = 0.01872,
bl = 0.3184,
cl = cu = 0.1139.
32
We can see that there is an asymptote for αsw=0.1139. This means that there is asymptotic
packing of the cores of baryons, not asymptotic freedom of the quarks and gluons. The
asymptotic freedom leads for high energies to gaslike plasma whereas the asymptotic
packing leads to liquidlike plasma and is consistent with experimental data. It proves that
baryons do not consist of point quarks. This asymptotic packing suggests that baryons have a
massive core which is what I propose and support in my theory. We can also see from my
theory the beta function is negative for the separated fragments, is infinite for the jumps and
practically equal to zero for energies close to the maximum energy of proton (about 18 TeV).
A closer experiment should show the internal structure of the curve for running coupling of
the strongweak interactions for colliding nucleons.
The internal structure of the core of baryons should be overcome when the surface of the
point mass attains the torus i.e. when the radius of the point mass increases 1/f=26.71 times. It
is when the mass of the proton increases (1/f) 3 =1.9·10 4 times i.e. for energy about 18 TeV.
Above this energy, the proton loses the surplus energy. The mass of the region of the Einstein
spacetime inside the nonrelativistic point mass in the centre of the core of baryons is in
approximation 17.1 TeV so probably there is in existence the Type W boson carrying such
mass.
Weak interactions
Since Gw=const. then from formula (51) we obtain that coupling constant for weak
interactions of nucleons does not depend on their energy because the point masses Y of the
cores of baryons do not adhere in the liquidlike substance.
Electromagnetic interactions
Within the liquidlike plasma (it consists of the cores of baryons and antibaryons; inside
such plasma the d=1, 2, 4 states are destroyed) in the d=0 states, i.e. on equators of the cores
of baryons, the contracted electronpositron pairs appears. The mass of contracted pair is
33
xm=9.0104369 times greater than the mass of the electronpositron pair (see discussion below
formula (23)). From formula αem=Gemm 2 electron/ch, we obtain that at the highenergy collisions
of nucleons the coupling constant for the electromagnetic interactions of the contracted
electrons is xm 2 =81.18797 times greater than the finestructure constant. There appears one
more contracted pair per each new coreanticore pair. It leads to conclusion that probability of
the electronpositron pair creation is Z7=727.440/0.5109989=1423.6 times higher than the
contracted pair. This means that the value of the coupling constant for the electromagnetic
interactions inside the liquidlike plasma should be
αem(xm 2 + Z7)/(1 + Z7) = 1/129.7. (87)
Gravitational interactions
Closed strings a neutrino consists of transform the chaotic motions of tachyons into the
divergently moving tachyons. Due to the dynamic viscosity of the closed strings, the mass
density of the Newtonian spacetime rapidly increases only on the surface of the closed string
(about 10 82 times – see (11) and (73)). Since torus of neutrino produces about 6·10 19 divergent
tachyon jets then for distances greater than about 3.9·10 32 m (this distance is the range of the
weak interactions of single neutrino), the gravitational constant is constant. Due to the density
of the Newtonian spacetime and tremendous pressure (about 10 180 Pa), the neutrino stretches
the gravitational field to distance 2·10 36 m. The total cross section of all tachyons in volume
of a rectangular prism 1m·1m·2·10 36 m is 1m 2 so all divergently moving tachyons are
scattered.
The neutrinos are the ‘carriers’ of the gravitational constant. There are only 4 different
neutrinos (the electron neutrino and its antineutrino and the muon neutrino and its
antineutrino). The graviton could be the rotational energy (its mass is zero) of particle
composed of the four different neutrinos in such way that the carrier of graviton is the binary
system of binary systems of neutrinos with parallel spins, i.e. spin of carrier of gravitational
energy is 2. The rotating neutrino bidipole behaves as two entangled photons, not as graviton.
Gravitational energy is emitted via the flows in the Einstein spacetime composed of the nonrotatingspin
neutrino bidipoles.
The neutrinos, binary systems of neutrinos, bidipoles of neutrinos, and so on, produce the
gradients in the Newtonian spacetime that is impressed on the Einstein spacetime too. We can
describe the gravity via such gradients. When time of an interaction is longer than about 10 60
s then the Newtonian spacetime looks for interacting particleas a continuum and we can apply
the Einstein equations and the Noether theorem. Such continuum leads to the symmetries and
the laws of conservation.
Since spin of the neutrino bidipoles is 2 whereas of the neutrinos 1/2 then the gravity leads
to conclusion that the neutrinos have only two flavours i.e. there are in existence only four
different neutrinos. The tau neutrinos are not in existence.
Finestructure constant for quasars
Due to the internal helicity of the Protoworld and the cosmic loop (see Chapter “New
Cosmology”), there was produced jet in the Einstein spacetime. The jet and the protuberances
on surface of our early Universe led to high redshift for quasars. The jet and the protuberances
produced regions in the Einstein spacetime with increased or decreased mass density in
comparison with its mean mass density. The spatial dependence of the fine structure constant
arose just at the beginning of the ‘soft’ big bang. Its dipolar part arose due to the jet. The
monopole part is due to the protuberances. The total spatial dependence should be positive
because in the deep past the thickened Einstein spacetime had higher mass density than today.
The finestructure constant is proportional to the mass density of the Einstein spacetime to
the power of five third (see formulae (15)(21)) whereas the mass of the electronpositron
34
pairs, produced by the photons appearing in the decays of the neutral pions, is proportional to
the mass density of the Einstein spacetime to the power of three (see formulae (15)(18)). The
production of the neutral pions and next the electronpositron pairs and next their
annihilations decreased the mass density of the Einstein spacetime. This means that the
changes in the mass of the pairs should not exceed Δm/m=mneutralpion/mnucleon≈0.144. Such
maximum changes are possible due to following changes of the density of the Einstein
spacetime ΔρE/ρE≈±3.0·10 3 . Such changes were possible only just at the beginning of the
‘soft’ big bang. We see that the maximum changes of the finestructure constant should not
exceed Δαem/αem≈±6.2·10 5 . This means that all measurements for the quasars with high
redshift (in the Everlasting Theory the high redshift begins from z=0.6415), i.e. from the Keck
telescope and the ESO Very Large Telescope, can be correct [1].
The Everlasting Theory leads also to conclusion that we should not observe spatial
dependences of the gravitational constant, of the speed of light in ‘vacuum’ and of spin
because these physical constants do not depend on mass density of the Einstein spacetime.
These physical constants depend on the properties of the more fundamental spacetime i.e. the
Newtonian spacetime composed of the structureless tachyons that have a positive mass.
Homogeneous description of the lifetimes
Suppose that the binary systems of neutrinos inside the point masses of particles behave
similarly to ionized gas (at the assumption of the gas) in the stars. The theory of such stars
says that the radiation pressure p is directly in proportion to the absolute temperature T to the
power of four
p T 4 . (88)
The analogous relation ties the total energy emitted by a black body with its temperature.
This theory also suggests that the absolute temperature of a star is directly in proportion to its
mass. From it follows that total energy emitted by a star is directly proportional to its mass to
the power of four. On the other hand, the maximum energy of the created virtual particle, in
the surrounding of a point mass, is equal to the point mass multiplied by 2. However, because
the Heisenberg uncertainty principle results that the lifetime of a particle is inversely
proportional to its energy we obtain that the lifetime of a point mass is inversely in proportion
to the mass to the power of four
t 1/m 4 . (89)
The same relation concerns circular masses.
From the uncertainty principle and formula (61) we obtain
t 1/α. (90)
On the basis of the formulae (89) and (90), we can calculate the lifetimes of particles.
The time the large loop reaches the equator of torus is
tstrongminimal = temminimal(proton) = (A/3)/c = 0.7755 . 10 24 s. (91)
This is the minimum time of the strong interactions and is equal to the time needed for a
photon to cover the distance between the ‘electric charge’, placed on the circular axis, and the
equator of torus.
The tau in weak interaction behaves in the same way as the electron in the electromagnetic
interaction (see formula (136)). As a result, we have:
tw(tau)/temminimal(proton) = (mc(proton)/mc(electron)) 4 = 2.42·10 12 , (92)
where the lifetime of tau is tw(tau)=1.88·10 12 s.
The weak mass of tau is about 1782 MeV. The weak interactions are responsible for the
decay of a muon and mp(muon)=mmuon/2 so the lifetime of a muon is
tw(muon) = tw(tau)(mp(tau)/mp(muon)) 4 = 2.44·10 6 s. (93)
35
The weak interactions are responsible for the decay of the hyperons and because of these
interactions they behave as a nucleon, whereas the muon behaves as an electron, so the
lifetime of the hyperons are equal to
tw(hyperons) = tw(muon)/(w(proton)/w(electronmuon)) = 1.24·10 10 s. (94)
The weak interactions are responsible for the beta decay of a neutron, however, in such a
decay a neutron behaves like an electron (the electron appears in this decay), whereas it is
impossible for the proton to decay as such the lifetime of neutron is:
tw(neutron) = tw(hyperons)(mp(proton)/mp(electron)) 4 = 946 s. (95)
The lifetime of the charm hyperon c( is:
tw((2260)) = tw(hyperons)(mp(proton)/mp((2260))) 4 = 6.5·10 13 s, (96)
where mp((2260))= m(2260)m(1115)+Y=1573 MeV.
The lifetime of the large loop created on the circular axis of the torus of the nucleon can be
calculated using the uncertainty principle ELL·tLL=h, where mLL=67.5444119 MeV. The
neutral pion decays in respect of the weak interaction. The weak mass of virtual particles
produced by the large loop we can calculate using the formula mLL(weak) = mLL·w(proton) =
1.26462 MeV. This is the distance of masses between a neutron and a proton. Consequently
the lifetime of the neutral pion is:
tpion(o) = tLL(mLL/mLL(weak)) 4 = 0.793·10 16 s. (97)
The charged pion decays because of the electromagnetic interaction of the weak mass,
therefore:
tpion(+) = tpion(o)(1/em) 4 = 2.78·10 8 s. (98)
Fourneutrino symmetry
Entanglement of neutrinos is due to the exchanges of the binary systems of closed strings.
Particles composed of the four different neutrinos have the resultant weak charge equal to
zero. Furthermore, the resultant internal helicity and spin also can be equal to zero. As a
result, the neutral object should be built of the 4n different neutrinos where the n denotes the
integers. In order for the interactions of elements where an object composed were saturated
the number of the elements in this object must be equal to the number of neutrinos in each
element. Therefore, if the smaller object contains x neutrinos the larger object must contain x 2
neutrinos (4 d , where d = 1, 2, 4, 8, 16, 32…). The flat structures of the neutral pions should,
therefore, contain 4, 16, 256, etc. neutrinos. In the surroundings of torus of a real particle,
there appear virtual particles and the total mass of them cannot be greater than the mass of the
real particle multiplied by 2 and increased by the emitted binding energy. It is easily
noticeable that within a nucleon there can be created at the same time at most 6 virtual pionantipion
pairs. These pairs must differ by the number of the neutrinos because the neutrinos
are the fermions. This means that, for example, the typical gravitational black hole built of the
neutrons (i.e. photons on the equator of the typical black hole are moving with the speed c;
see formulae (99)(101)) can interact with 2·4 32 other typical black holes because at most such
a number of the neutrinos, having weak charges, contain a virtual pionantipion pair created
inside the neutron. Therefore, in our early Universe there were around 3.69·10 19 typical black
holes. The typical black hole built of neutrons (i.e. the biggest neutron star) has mass about 25
times greater than that of the sun. The total mass of all of these biggest neutron stars was
equal to about 1.821·10 51 kg. Such mass has the baryonic matter (visible and dark) in our
Universe. The typical early massive galaxy, which I call the protogalaxy, contained 4 16 typical
black holes. There were 2·4 16 protogalaxies. Associations containing 4, 16, 256, etc. binary
systems of massive galaxies are a flattened spheroidlike structures. Notice that the above
described rules lead to the fourneutrino symmetry. This symmetry is obligatory for also
following a sequence of numbers: 64 = (2·4 1 ) 2 (for example a meson built of four groups, each
36
group built of four pions and each pion built of 4 neutrinos), 64 2 , 64 4 , etc. Such associations
are the chainlike structures.
Our Universe appeared analogically as a large loop inside the torus of baryons but we must
replace the neutrinos in binary systems of neutrinos with the biggest neutron stars.
The objects which contained most of the binary systems of neutrinos (they are an analog to
our early Universe), created in the nuclear transformations, decayed to ‘galaxies’ (which carry
energy of entangled photons) similarly as our early Universe decayed to the massive galaxies.
Each such object decayed to the 2·4 16 photon galaxies. It leads to 300 million photons in cubic
meter in our Universe (see Chapter “New Cosmology”).
Some results associated with the constant K
Calculate the mass of a typical gravitational neutron black hole. On the equator of such a
black hole the neutrons are moving with a speed equal to the c but such an object is ballshaped
because inside it the field composed of the binary systems of neutrinos rotates with the
same angular speed – it means that the black hole is in rest in relation to the Einstein
spacetime. The nucleons in such an object are placed in vertices of cubes and the lattice
constant is equal to ac=(A+4B)/2 1/2 (see formula (183)).
The radius of such a black hole is rbh and the mass mbh that satisfies the following formula:
rbh = Gmbh/c 2 . (99)
If N1 denotes the number of neutrons in such black hole then
4rbh 3 /3 = N1ac 3 , (100)
and
mbh = N1mneutron. (101)
Solving the set of formulae (99)(101) we get
N1=2.946·10 58 ,
mbh=4.935·10 31 kg i.e. about 25 masses of the sun,
rbh=3.664·10 4 m i.e. about 37 km.
On the other hand the fourneutrino symmetry follows that the early Universe contained
2·4 32 gravitational neutron black holes. This means that the baryonic mass of the Universe is
1.821·10 51 kg. The baryonic mass in our Universe should be K 8 times greater than the rest
mass of the large loop (mLL=67.5444 MeV), which means that is satisfied using the following:
mLLK 8 = 2·4 32 N1mneutron. (102)
The question as to why the value of the dark energy mass density calculated within the
quantum theory is approximately 10 120 times greater than that measured can be answered as
follows. We know that the spin of stable particles defines the expression mvr. Knowing the
natural speed of the closed strings, we can then calculate the internal energy of the neutrino.
The mneutrinov 2 plus the rest energy mneutrinoc 2 is equal to the calculated rest mass of the
Protoworld (which is equal to the msc 2 where ms=1.961·10 52 kg). This means that there is a
possibility of the Protoworldneutrino transition that is the reason why our Universe exited
from a black hole state. It also means that the measured energy of a nonrotatingspin neutrino
should be K 12 =0.59·10 119 times smaller than the energy (not mass) frozen inside the neutrino.
The Protoworldneutrino transition leads to the creation of a sphere filled with the surplus
binary systems of neutrinos, which is the dark energy.
The gravitational field propagates with a speed equal to 2K 9 c/3 i.e. 8·10 88 times higher than
the c.
The properties of Newtonian and Einstein spacetimes lead to relativistic mass
Inertial and gravitational mass of a particle I define as directly proportional to the number of
all closed strings (or to the total volume of all closed strings) which the particle consists of. It
also concerns the relativistic mass. The mean speed of bound and free tachyons cannot
37
change, therefore, the spin speed of an accelerated particle decreases. It causes the pressure
inside the particle to also decrease and the particle absorbs the free binary systems of
neutrinos, composed of the closed strings, from the Einstein spacetime. The Einstein formula
E=mc 2 is obligatory for such mechanism for particles composed of the binary systems of
neutrinos. Generally, the mass and energy do not have the same origin.
The unsolved basic problem associated with spin is as follows. What spontaneous
phenomena lead to the law of conservation of spin?
Fluctuations of spacetime and fields cause compressions and rarefactions to arise. To extend
the lifetime of a compression the pressure inside it must decrease. Because the mean speed of
particles inside the compression cannot change then only the creation of a vortex will cause a
reduction in the pressure. When we accelerate a vortex then its spin speed decreases which as
a result also causes the pressure to also decrease. This means that to increase the pressure, the
density of the Einstein spacetime inside the vortex must also increase. When we accelerate the
proton for example, the spin speed of it must then decrease because the resultant speeds of the
components of which the proton is composed of cannot change. This causes the pressure
inside the proton to decrease and the additional energy accumulated in the Einstein spacetime
flows into the proton and transforms it into a vortex in such a way that the spin is always halfintegral.
When we accelerate some particles, the spin of the torus must be parallel or antiparallel to
the linear velocity. Then spin of the particle does not change. This means that the spin angular
velocity is always parallel or antiparallel to the relativistic velocity. When we accelerate some
particles, for example, protons (the spin speed of the binary systems of the neutrinos on the
equator of the resting torus will be equal to the c), therefore, the spin speed of the torus
decreases. This is because in spacetimes and inside particles the law of conservation of energy
is obligatory. In this case, the total energy is conserved of the binary systems of neutrinos that
the torus is composed of. Rotations of the spin vectors of the binary systems of neutrinos of
which the torus is built of, are impossible because electric charge must also be conserved (all
spins of the binary systems of neutrinos the torus is built of must be perpendicular to its
surface).
Because the mean spin velocity of the proton v(spin) is perpendicular to the relativistic
velocity of the proton v(relativistic) then binary systems of neutrinos placed on the equator
have:
nv 2 (spin) + nv 2 (relativistic) = nc 2 , (103)
where the letter n denotes the number of binary systems of neutrinos within a relativistic
proton.
Because it is obligatory that the law of conservation of spin exists then for binary systems of
neutrinos placed on the equator (similarly for all other binary systems of neutrinos) we have:
Nnc = nv(spin), (104)
where Nn denotes the number of binary systems of neutrinos in a resting proton. The size of
the torus also cannot change because the spin and charge are continuously not changing.
Transformations of a very simple nature lead to following formula:
n = Nn/(1  v 2 /c 2 ) 1/2 . (105)
Since the relativistic mass is directly proportional to the n whereas the rest mass to Nn, we
subsequently obtained the very well known Einstein formula. We can see that this formula is
correct only when:
the halfintegral spin is associated with the torus having a surface similar to the Ketterle
surface for a strongly interacting gas,
there is an obligatory laws of conservation of spin and energy.
This means that a relativistic proton is built up of more binary systems of neutrinos i.e. the
thickness of the surface of torus is greater – next are created layers built up of the same
38
number of binary systems of neutrinos because the number of lines of electric forces, created
by the torus, cannot change over time. As the point mass must be about 4/3 greater than the
mass of torus this mass also increases when we accelerate a proton.
The neutrinos do not have a relativistic mass because the density of the field composed of
the free binary systems of closed strings is practically equal to zero  we do not observe
interactions associated with such field.
Characteristic total cross sections for NN and π –N scattering
In knowing the internal structure of particles, we can calculate the coupling constants for
interactions and define what is needed in the calculations for scattering potentials. Sometimes
the calculations are very simple, for example, in protonproton total cross sections. The
resting torus is composed of one layer of the binary systems of neutrinos and they are at a
distance of about 2πrneutrino. This means that during the penetration of the tori of the protons
the target consists of by moving protons is possible. The range of strong interactions for a
resting proton is a little greater than the radius of the last tunnel (A+4B=2.7048 fm) and is
equal to the circumference of the large loop (4πA/3=2.9215 fm). In fact, the range is slightly
greater because the opened loop is tangential to the circular axis – the correct value being
drangestrong=2.958 fm. To neglect the cross section resulting from the electromagnetic
interactions of nucleons they should be at a distance smaller than A+4B. The nucleons in a
beam and target have a tendency to collect in vertices of squares having a diagonal equal to
A+4B. The exchanged pions are most often found in the centres of the squares. The
volumetric binding energy for such nucleons is 14.952 MeV (see the explanation above
formula (183)). This means that we can neglect the electromagnetic interactions of nucleons
in comparison to the strong interactions when the nucleons in a beam have energy of about 15
MeV. For kinetic energy of a proton of about 15 MeV, due to the possible turns of the spins
(thermal motions), the strong field fills the sphere having a radius equal to the range of the
strong interactions. When distance between falling protons and the resting tori is less than the
sum of the range of the strong interactions and the radius 2A/3 of the large loop then the
protons are scattered on the circular axes of resting tori of the protons that the target consists
of (i.e. on the large loops having the highest energy density in the resting nucleons). In this
case the pp cross section is
σ15MeV(pp) = π(drangestrong + 2A/3) 2 = 368 mb. (106)
For medium kinetic energies (a few hundred MeV, for example) the total cross section
rapidly decreases due to following reasons:
1 The spin of the falling proton must be parallel or antiparallel to the relativistic velocity.
2 The spin speed of the proton decreases when relativistic speed increases  that causes the
spin period of the large loops to increase whereas the mass of it decreases. This causes strong
interactions outside of the torus of the proton to vanish. Therefore, the colliding protons are
scattered on their circular axes which means that in this case the total cross section is
σmedium(pp) = π(2A/3 + 2A/3) 2 = 27 mb. (107)
For kinetic energies a few times higher than the rest mass of the proton, there arises on the
surface of torus of the proton a few new layers and the torus becomes nontransparent. During
collisions of such protons with the resting target the cross section is (tori of the protons the
target is composed of are transparent)
σhigh(pp) = π(A + 2A/3) 2 = 42 mb. (108)
For kinetic energies a few times higher than the rest mass of the proton for antiparallel
beams of nucleons is:
σhighantiparallel(pp) = π(2A) 2 = 61 mb. (109)
The np scattering differs from the pp scattering. The negative pion in the neutron (due to
electric attraction) looks for the electric charge of the proton. This means that the proton can
39
see the mass of a negative pion. Because the centres of the large loops of which the negative
pion consists of are in the d=1 tunnel (r=A+B) and because the radius of the large loop is
2A/3 for energy about 15 MeV and for the np scattering we consequently obtain:
σ15MeV(pn) = π(drangestrong + A + B + 2A/3) 2 = 671 mb. (110)
Furthermore, a highly energetic pn scattering mass of the negative pion is very small so for
both total cross sections, i.e. for pp and pn, they should have the same value.
It is easy to calculate that for very energetic πp scattering the total cross section is
approximately 27 mb – see formula (107). There should be a significant reduction of the cross
section for the negative pionproton scattering for energies of the pion equal to the energies of
the S bosons in the d=0 and d=1 tunnels i.e. in the tunnels lying under the Schwarzschild
surface for the strong interactions. These energies are equal to approximately 423 MeV and
727 MeV. These reductions are associated with the production of the resonances.
Lengths of NN scattering
The effective ranges are as follows
rsing(pn) = r1(nn) = r(pp) = A + 4B = 2.7 fm. (111)
For the nn scattering there is also the second effective range. In nucleons the relativistic
pions are in the d=1 state. Since pions consist of the large loops having radius equal to 2A/3
then the effective range for this state is A+B+2A/3.
r2(nn) = A + B + 2A/3 = 1.7 fm. (112)
For the triplet pn scattering, the effective range is:
rtrip(pn) = A + B +2A/3 = 1.7 fm. (113)
Se also the theory of deuteron in Chapter titled “Fourshell Model of Atomic Nucleus”.
When we scatter neutral particles or charged particles on neutral particles the most distant
closed photons on the circle having radius equal to the effective range appears. Assume that
the circular axes of nucleons are on the same plane. To calculate the lengths of the pn and nn
scattering (the lengths are the ranges of bosons), we should to the length of a closed photon
add the multiplied by two the range of strong interactions.
asing(pn) = 2π(A + 4B) + 2(A + 4B) = 22.4 fm, (114)
a(nn) = 2π(A + B + 2A/3) + 2(A + 4B) = 15.9 fm. (115)
In the pn triplet state, the directions of the spins overlap and have the same senses.
atrip(pn) = 2(A + 4B) = 5.4 fm. (116)
See also the theory of deuteron. The exact result is 5.4343 fm.
In the pp scattering the length of the closed photons is equal to the range of strong
interactions.
a(pp) = (A + 4B) + 2(A + 4B) = 8.1 fm. (117)
New interpretation of the uncertainty principle
I will refer to and call real and virtual photons, electrons and the electronpositron pairs in
the Einstein spacetime as renewable particles, i.e. particles disappearing in one place of a field
and appearing in another and so on. This leads to the wave function. We can say the same
about real and virtual loops composed of the binary systems of neutrinos in a strongly
interacting field i.e. a field composed of virtual and real large loops, created on the circular
axis of the torus of the core of baryons, and bound states of large loops such as mesons. In
sum, the photons and electrons in the Einstein spacetime and the free and bound large loops in
a strongly interacting field behave as quantum particles. We can observe some distribution of
energy, mass or mass/energy of the renewable/quantum particles in the adequate field. Such
distribution can be described by means of the wave function. The value of the n (see Figure
titled “The uncertainty principle for state lifetime”) depends on the spins of the objects a field
is composed of. For elementary photons (elementary photon is the massless rotational energy
40
of a single neutrinoantineutrino pair), the electronpositron pairs and the large loops created
in the Einstein spacetime are n=1. This means that for electrons it equals n=1/2 but new free
electrons cannot be created in the Einstein spacetime (only the electronpositron pairs can be)
because for Einstein spacetime n=1. Total spin of the binary system is equal to 1. At first,
there appears a binary system of loops with different internal helicities composed of the
rotating binary systems of neutrinos. Due to the different internal helicities of the loops in a
binary system of loops, sometime the visavis binary systems of the neutrinos (the dipoles of
the weak charges) placed in different components of the binary system of the loops have
opposite orientation so there is the repulsion between the weak charges. Such state of the
binary system of loops is unstable and the system transforms into torusantitorus pair, for
example, into electronpositron pair. Such torusantitorus pairs are stable for the periods of
spinning and the radii of the equators are equal to the radii of the loops. The electrons
observed today (this not concerns the electrons in the electronpositron pairs) were created
during the era when the symmetry of the Einstein spacetime was broken  this is described in
more detail below. In the strong field can appear particles composed of the entangled large
and/or other loops.
There are different lifetimes associated with a quantum particle. For example, we can say
about statelifetime and lifetime of an entangled photon. From the uncertainty principle
relating to new shapes there results, for example, photon which can be the rotational energy of
only one binary system of neutrinos (i=1) or of the ‘i>1’ binary systems of neutrinos. For a
photon, the ‘i’ has a strictly determined value – it is the number of the entangled elementary
photons a photon consists of. A photon behaves as follows: the ‘i’ entangled elementary
photons disappear in some places of the Einstein spacetime and appear in other ‘i’ places and
so on. This leads to the conclusion that photons sometimes behave like particles (i=1) or as a
set of entangled elementary photons (i>>1). We can see that the uncertainty principle and
quantum physics are associated with the appearing/disappearing mechanism i.e. with the
changing distribution of the ‘i’ entangled elementary photons (in reality, there are entangled
the carriers of the elementary photons). The statelifetime is the time distance between
appearance and nearest disappearance. We see that the statelifetime of a renewable particle is
associated with the length of the circumference of the loop. The length of a wave is associated
with the radius of a loop so to obtain the statelifetime of a photon we must multiply the time
resulting from the length of the wave by 2π.
The inverse to the resultant frequency in the uncertainty principle is not a lifetime of a
renewable particle – it is the statelifetime in one state with a determined value of the ‘i’.
Statelifetime is the time of some distribution of the entangled photons which a photon is
composed (i = const) whereas the lifetime of a photon is the time after which the photon
41
decays to nonentangled photons composed of entangled elementary photons i.e. the ‘i’
changes value. A photon, after its lifetime, decays to more entangled photons containing less
entangled elementary photons. The fourneutrino symmetry determines the number of new
photons. The uncertainty of energy does not define the sum of the energies of the entangled
photons – it is the uncertainty of the distribution of energy between the ‘i’ entangled
elementary photons a photon consists of. After the statelifetime, that follows from the sum of
the frequencies of the entangled photons, the distribution of energy of the entangled
elementary photons changes.
Emissions of photons composed of a greater number of entangled photons are more probable
because then each entangled photon carries less energy. This means that also the lifetime of a
photon should be longer. In describing the fourneutrino symmetry, I motivated that during
nuclear transformations are emitted superphotons each composed of i=2·4 32 entangled
elementary photons. Such photons, after its lifetime, decay into photons each composed of
less number of entangled photons, for example, to the photon galaxies (i=4 16 ), similarly as the
early Universe decayed into massive protogalaxies. Today massive galaxies dominate so we
can assume that subsequently photon galaxies dominate i.e. that the lifetime of photon
galaxies is equal to the lifetime of massive galaxies. When massive galaxies start to decay
into smaller objects then photon galaxies should also do the same. As a result the lifetime of
photon galaxies should, therefore, be 2·4 16 times longer than the lifetime of the original
photon.
Broken symmetry
We can derive entire nature from the physical properties of the Newtonian spacetime theory
and the mass density of the Einstein spacetime that is composed of the binary systems of
neutrinos.
In Einstein’s spacetime there appear spontaneous fluctuations. Because the fundamental
field, i.e. the Newtonian spacetime, is composed of tachyons that have linear and rotational
energy, then the thickened regions of the Einstein spacetime transform into the rotary vortices.
As a result, the helicity and spin of all created rotary vortices must be equal to zero. This
means that the rotary vortices arise as vortexantivortex pairs. We see that such phenomena
broken symmetry of the Einstein spacetime inside the vortices. In both components of the
vortexantivortex pair, the creation of electronpositron pairs is possible. When mass density
inside a vortex was sufficiently high, there appeared in the lefthanded vortex the positronproton
transitions whereas in the righthanded vortex the electronantiproton transitions.
When the mass of a vortex is strictly determined then there is the possibility of the vortex
Protoworld transition. Our rotary vortex was lefthanded so there the protons and next
neutrons were created because nucleons are the lefthanded particles. Next, on the circular
axis appeared the protogalaxies composed of the greatest neutron stars. Due to the fourneutrino
symmetry and the entangled neutrinos, the protogalaxies already grouped in larger
structures already before the ‘soft’ big bang. Furthermore, because the internal energy of a
neutrino is equal to the mass of the Protoworld, ‘one day’, there was the
Protoworldneutrino transition. The released dark energy in such transition caused the
expansion of the early Universe (i.e. of the cosmic loop). There appear in the beta decays
electronantineutrinos for the third time in the history of evolution of a lefthanded rotary
vortex broken symmetry of the Einstein spacetime. This means that the present symmetry of
the Universe is broken due to the same orientation of the angular velocities of massive spiral
galaxies in relation to their magnetic axes for majority of such galaxies, due to the electronproton
asymmetry and because the Einstein spacetime contains more the electronantineutrinos
than other neutrinos.
42
Summary
Stability of the closed strings leads to the point mass of baryons.
Point and circular mass behaves like ionized gas in stars. Such a model leads to lifetimes of
particles consistent with experimental data.
Constants of interactions are directly in proportion to the mass densities of the fields
carrying the interactions. The factor of proportionality has the same value for all interactions.
The changing running coupling for strongweak interactions follows from the Uncertainty
Principle for the virtual large loops responsible for the strong interactions.
The properties of the Newtonian and Einstein spacetimes lead to the relativistic mass.
The fourneutrino symmetry solves many problems associated with particle physics and
cosmology.
The calculated characteristic values for the pionN and NN scattering on the basis of an
atomlike structure of baryons are consistent with experimental data.
The new interpretation of the uncertainty principle leads to the evolution of the entangled
photons.
Throughout the history of the Universe, symmetry was broken three times.
The calculated binding energy of the core of baryons is 14.98 MeV. But there is also the
binding energy of the core following from the entanglement of the binary systems of
neutrinos the torus inside the core consists of. The exchanged binary systems of the closed
strings are moving with the superluminal speed so the involved energy is very high. It is very
difficult to destroy the cores of baryons. The binding energy of a neutrino is tremendous – it is
equivalent to about 4·10 50 kg so it is very difficult to destroy the neutrinos too. In our
Universe there are not in existence black holes having mass densities higher than the cores of
baryons.
Table 5 Theoretical results
Physical quantity Theoretical value
Centripetal force acting on the closed string 2.2 E+133 N
Lifetime of the proton Stable
Lifetime of the neutron 946 s
Lifetime of the muon 2.44 E6 s
Lifetime of the tau 1.88 E12 s
Lifetime of the hyperon 1.24 E10 s
Lifetime of the charm baryon c + (2260) 6.5 E13 s
Lifetime of the neutral pion 0.79 E16 s
Lifetime of the charged pion 2.8 E8 s
Coupling constant for strong interactions of the nonrelativistic
protons
14.4038
Coupling constant for strong interactions of the pions 1
Maximum change of the finestructure constant
*2.2 E+133=2.2·10
±6.2 E5
133
43
Table 6 Theoretical results
Physical quantity Theoretical value
Mass of a typical neutron black hole ~ 25 masses of the sun
Radius of a typical neutron black hole ~ 37 km
Total mass of the dark energy 1.961 E+52 kg
Mass of the baryonic matter 1.821 E+51 kg
Ratio of the hidden dark energy to mass of the neutrino 0.59 E+119
Ratio of the total mass of the dark energy to the mass of
baryonic matter (inside a sphere filled with baryons the
ratio has a different value)
10.769805
pp total cross section for kinetic energy about 15 MeV 368 mb
pp total cross section for kinetic energies approximately a
few hundred MeV
27 mb
pp total cross section for kinetic energies approximately a
few rest mass of protons
42 mb
pp total cross section for kinetic energies approximately a
few rest mass of proton for antiparallel beams
61 mb
pn total cross section for kinetic energy approximately 15
MeV
671 mb
pn total cross section for kinetic energies approximately a
few rest mass of the proton
42 mb
πp total cross section for very high energies 27 mb
Significant reduction of the cross sections for negative 423 MeV
pionproton scattering
727 MeV
Table 7 Values of the G(i)
Interaction Relative value of the G(i)
Strong 1 (for GS=5.46147·10 29 m 3 s 2 kg 1 )
Weak 1.9·10 3
Electromagnetic interaction of electrons 5.1·10 2 (it is not a mistake)
Gravitational 1.2·10 40
References
[1] J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell,
M. B. Bainbridge;
Evidence for spatial variation of the fine structure constant;
arXiv: 1008.3907v1 [astroph.CO] 23 Aug 2010
44
Structure of Particles (continuation)
Introduction
Previously, I described the internal structure of Newtonian spacetime, closed strings,
neutrinos, electrons, muons, pions and nucleons. The description of these structures is
associated with the phase transitions of the Newtonian spacetime, the Einstein spacetime, and
the symmetrical decays of particles in a strong field.
Photons and gluons are the massless rotational energies of the neutrinoantineutrino pairs
the Einstein spacetime consists of (E = hν, where h is the spin of a pair whereas ν is the
frequency of spinning). Certain parts of an entangled photon can be outside the occupied
states of an atom.
Multiplying the Compton length of an electron by 2π, we can calculate the statelifetime.
Slowly moving electrons have statelifetimes about 10 20 s. This means that within one second
an electron appears in 10 20 places of the Einstein spacetime. This leads to the wave function.
An electron, when going through a set of slits (an electron only appears whereas the wave
function is ongoing), appears many times in each slit. We cannot say for certain that an
electron is going through only one slit.
We can calculate the spin of stable objects (i.e. the closed strings, neutrinos, cores of
baryons and protoworlds) from the mvr. The renewable pairs arise in different ways. The
resultant internal helicity of the Einstein spacetime is not broken when there appear binary
system of entangled loops and each loop in a binary system has different internal helicity. The
resultant energy of the entangled loops multiplied by the period of spinning must be equal to h
(i.e. spin is 1) because such spin have the Einstein spacetime components. Then symmetry of
the Einstein spacetime is not broken  it is the reason why carriers of interactions associated
with this field have unitary spin. Entangled loops exchange the binary systems of the closed
strings. Since total spin of the Einstein’s spacetime cannot change then there arise the pairs of
the binary systems of loops i.e. the quadrupoles. The opposite internal helicities of the loops
in a binary system of loops enforce an immediate transition (possible because the Newtonian
spacetime is composed of tachyons moving at a speed approximately 8·10 88 times greater than
the light in spacetime) of the two entangled loops into the electronpositron pair. The
Compton length of an electron is the radius of the loop. The tori, i.e. the electric charges,
consist of the entangled and polarized binary systems of neutrinos the Einstein spacetime
consists of. Surfaces of the tori have an appearance similar to the Ketterle surface for a
strongly interacting gas discovered in 2005. The loops overlap with the equators of the tori.
The binary systems of the neutrinos that the loops are composed of make halfturns on the
circular axis of the torus and in the centre of it because in those places the lines of electric
forces, created by the polarized binary systems of neutrinos that the torus is composed of,
change their senses. The halfturns decrease the local pressure in the Einstein spacetime that
causes new binary systems of neutrinos to flow into a bare electron (the absorption). This
means that with the torus, i.e. with the electric charge, half of the mass of the bare electron
should be associated whereas the second half of the bare mass is associated with the centre of
the torus i.e. with the point mass of the electron. The torusantitorus pairs are the stable
structures for the period of spinning. On surface of the tori, all spins of the neutrinoantineutrino
pairs either have the senses pointed to the interior of the torus or pointed outside
the surface. This leads to the conclusion that there arises one divergent and one convergent
spin field. When torus/electriccharge of electron disappears in some place then the mass of
electron in this place vanishes due to the emissions of the surplus neutrinoantineutrino pairs.
The radius of the bare electron is 554.32 times greater than that of the core of baryons.
Outside of the bare electron, arise the virtual bare electronpositron pairs.
45
Muons consist of a contracted electron and the two different energetic neutrinos that interact
with the point mass of the electron. The point mass of the electron cannot be a stable structure
when it contains only one energetic neutrino because the resultant centrifugal force would not
be equal to zero. Because the simplest neutral pion consists of the two binary systems of
neutrinos and because the charged pion decays into a muon and neutrino, the mass of the
muon should be equal to the bare mass of the charged pion minus a quarter of the mass of the
neutral pion.
A tau lepton consists of an electron and massive particle, created inside a baryon, which
interact with the point mass of the electron.
Mesons, meanwhile, are binary systems of gluon loops that are created inside and outside
the torus of baryons. They can also be mesonic nuclei that are composed of the other mesons
and the large loops, or they can be binary systems of mesonic nuclei and/or other binary
systems.
A charged pion consists of an electron and three different energetic neutrinos that interact
with the point mass of an electron. This particle can transform into the neutral pion (i.e. into
the binary system of the large loops) interacting with the electronneutrino pair. The charged
pion is the fourparticle system. Fermions containing more than three different energetic
neutrinos do not exist because two or more of the components cannot have the same internal
helicity simultaneously and the sign of a weak or electric charge.
Calculated below are the masses of the selected mesons: of the lightest mesonic nuclei,
kaons, W and Z bosons, and the D and B mesons.
A particle placed in different fields does not look the same. In an electromagnetic field,
many charged pions occupy the same state when they are composed of a different number of
binary systems of neutrinos so they are in different states for the electromagnetic field. In a
strong field, the neutral and charged pions look the same because both contain the same two
strongly interacting large loops. The spins of the two large loops are antiparallel. This means
that pion in a strongly interacting field looks analogically as the electronelectron pair in a
ground state of atom. This means that in the ground state of baryons (d=1) there can be only
one pion. In the d=2 state there are more pions but due to their interactions with the strong
field components they do not look the same. The TitiusBode orbits for the strong interactions
and only leads to the S states. Here we will calculate mass of hyperons and also selected
resonances.
Here I also calculated the mass of the tau lepton. Within the new nonrelativistic
electroweak theory, I calculated the magnetic moment of a muon, the frequency of radiation
emitted by the hydrogen atom under a change of the mutual orientation of the electron and
proton spin in the ground state and the LambRetherford shift.
Mesons
Masses of the lightest mesonic nuclei
We can build three of the smallest unstable neutral objects containing the carriers of strong
interactions i.e. the pions (134.9661 MeV, 139.57040 MeV) and bound large loops
(134.9661/2 MeV). Each of those objects must contain the large loop because only then can it
interact strongly.
The letter a denotes the mass of the object built of a neutral pion and one large loop
a = m(neutral pion, loop) = 202.45 MeV.
The parity of this object is equal to P=+1 because both the pion and the large loop have a
negative parity so as a result the product has a positive value.
The letter b denotes the mass of the two neutral pions and one large loop
b = m(2 neutral pions, loop) = 337.42 MeV,
46
where b’ denotes the mass of the two charged pions and one large loop
b’ = m(2 charged pions, loop) = 346.62 MeV.
The parity of these objects is equal to P= 1.
In particles built of objects a, b, and b’, the spins are oriented in accordance with the Hund
law (the sign ‘+’ denotes spin oriented up, the sign ‘‘ denotes spin oriented down, and the
word ‘and’ separates succeeding shells)
For example, + and + +++ and + +++ +++++ and etc.
Because electrically neutral mesonic nuclei may consist of three different types of objects
whereas only one of them contains the charged pions the charged pions should, therefore, be
two times less than the neutral pions. It is also obvious that there should be some analogy for
mesonic and atomic nuclei. I will demonstrate this for the Ypsilon meson and the Gallion. The
Gal is composed of 31 protons and has an atomic mass equal to 69.72. To try to build a meson
having a mesonic mass equal to 69.5 we can use the following equation:
69.5 Ypsilon = 8a + 14b + 9b’ = 9463 MeV (vector).
Such a mesonic nucleus contains 18 charged pions, 36 neutral pions and contains 31 objects.
The mass of lightest mesonic nuclei is as follows:
The Eta meson is an analog to the Helion4. Since the Eta meson contains three pions there
are two possibilities. Such a mesonic nucleus should contain one charged pion but such
objects are not electrically neutral. This means that the Eta meson should contain two charged
pions or zero
4 Eta = a + b’ = 549.073 MeV (pseudoscalar),
4 Eta(minimal) = a + b = 539.864 MeV (pseudoscalar).
The Eta’ meson is an analog to Lithion7
Eta’ = 3a + b’ = 953.971 MeV (pseudoscalar).
We see that there is in existence the following mesonic nuclei (a + b’) and (3a + b’) – which
suggests that there should also be (2a + b’). However, an atomic nucleus does not exist which
has an atomic mass equal to 5.5. Such a mesonic nucleus can, however, exist in a bound state,
for example inside a binary system of mesons
X’ = 2a + b’ = 751.522 MeV (vector).
The mass of kaons
To calculate the mass of the particle created in the d=0 state in a nucleon for which the ratio
of its mass to the distance of mass between the charged and neutral pions is equal to
sw(d=0)/w(proton) we can use the following:
(mpion(+) mpion(o)(sw(d=0)/w(proton)) = 244.398 MeV. (118)
This mass interacts with the point mass of the particle which has a mass equal to
(mpion(+)mpion(o) Therefore, the total mass equals 249.003 MeV. Two such particles create
the binary system having mass equal to 497.760 MeV (the components are in a distance equal
to the Compton wavelength for the muon so we must subtract the binding energy) which is
the mass of neutral K o kaon. This kaon can emit one particle having a mass equal to
(mpion(+)mpion(o)). The particle created as a result of this is in a charged state. If we add the
radiation mass of the entire particle (the components are not at a distance equal to the
Compton wavelength of the muon because there is only one charged muon) we obtain the
mass of K + kaon that is equal to 493.728 MeV.
Due to the strong interactions the neutral kaon decays into two pions (the coupling constant
is equal to 1) or due to the weak interactions to three pions. The point mass of the proton is
about times greater than the rest mass of the neutral pion so the coupling constant of the
weak interactions of two pions is 2 times smaller than for the proton. This means that the K o L
kaons should live approximately 527 times longer than the K o S.
Earlier I calculated the lifetimes of pions.
47
The mass of W + and Z o bosons
There are in existence the W + and Z o bosons but they are not responsible for weak
interactions in the lowenergy regime.
We can calculate the mass of particles for which the ratio of their mass to the distance of
mass between the different states of known particles is equal to Xw=w(proton)/w(electronmuon)
(see formula (57)).
For the kaons we obtain
(mkaon(o) mkaon(+)Xw = 79.4 GeV. (119)
This is the mass of the W +, boson.
For the pions we have
(mpion(+) mpion(o),freeXw = 90.4 GeV. (120)
It is the mass of the Z o bosons.
For the four d states of the relativistic W pions (see Table 1) we obtain
Xw(mW(+) – mW(o))d=0 = 0.815 TeV. (121)
Xw(mW(+) – mW(o))d=1 = 140 GeV. (122)
Xw(mW(+) – mW(o))d=2 = 118 GeV. (123)
Xw(mW(+) – mW(o))d=4 = 105 GeV. (124)
The signals of existence of the masses defined by formulae (121)(124) should be very weak
because in the highenergy regime abundance of the baryons with destroyed the TitiusBode
orbits for the strong interactions is very high.
D and B mesons
The neutral kaon is a binary system of two objects. If we divide the mass of the neutral kaon
by the mass of the neutral pion, we obtain the factor Fx=3.68804 for binary systems built of
two mesonic nuclei or one mesonic nucleus and an binary system or two binary systems.
The mean mass of the binary system built up of two kaons is
D(charm, 1865) = [(π o (134.966) + π + (139.570))/2]Fx 2 = 1867 MeV, (125a)
D(strange) = m(Eta(minimal, 539.864))Fx = 1991 MeV, (125b)
K*(892) = m(244.398)Fx = 901 MeV, (125c)
B = [m(Eta(minimal, 539.864) + m(K*, 892)]Fx = 5281 MeV, (125d)
B(strange) = [m(Eta’, 953.971) + m(K o , 497.760)]Fx = 5354 MeV, (125e)
B(charm) = [m(X’, 751.522) + m(Eta’, 953.971)]Fx = 6290 MeV. (125f)
Why binary systems live longer than the lightest mesonic nuclei? It is because there changes
nature of interactions. In binary systems, the weak interaction dominates so they behave in a
similar way to a muon. Their lifetime is inversely proportional to mass to the power of four.
The mass of the B(charm) meson is Ny=6290/105.667=59.53 times greater than mass of
muon. Therefore, the lifetime of the B(charm) meson can be calculated using the following
formula (the theoretical lifetime of muon is tw(muon)=2.4·10 6 s)
tw(B(charm)) = tw(muon)/Ny 4 = 1.9·10 13 s.
Hyperons and resonances
Hyperons
The d=2 state is the ground state outside the Schwarzschild surface for the strong
interactions and is responsible for the structure of hyperons. During the transition of the W
pion from the d=2 state into d=4, in the d=2 state vector bosons occur as a result of decay of
the W pions into two large loops. Each loop has a mean energy equal to the E
E = (mW(),d=2 + mW(o),d=2  mW(),d=4  mW(o),d=4)/2 = 19.367 MeV. (126)
The vector bosons interact with the W pions in the d=2 state. The mean relativistic energy
EW of these bosons is
48
EW = E((A/(2B)) + 1) 1/2 = 25.213 MeV. (127)
Groups of the vector bosons can contain d loops. Then in the d=2 state there may occur
particles that have mass which can be calculated using the following formula
where k=0, 1, 2, 3; the k and d determine the quantum state of the particle having a mass
M(+o),k,d.
The mass of a hyperon is equal to the sum of the mass of a nucleon and of the masses
calculated from (128). We obtain extremely good conformity with the experimental data
assuming that hyperons contain the following particles (the values of the mass are in MeV)
m = mneutron + M(o),k=0,d=2 = 1115.3, (129)
m = mproton + M(o),k=2,d=2 = 1189.6, (130)
m = mneutron + M(o),k=2,d=2 = 1190.9, (131)
m = mneutron + M(),k=2,d=2 = 1196.9, (132)
m = m + M(o),k=1,d=2 = 1316.2, (133)
m = m + M(),k=1,d=2 = 1322.2, (134)
m = m + M(o),k=3,d=2 = 1674.4. (135)
Using the formulae (128)(135) we can summarise that for the given hyperon the following
selection rules are satisfied:
a) each addend in the sum in (128) contains d vectorial bosons,
b) for the d=2 state the sum of the values of the k numbers is equal to one of the d numbers,
c) the sum of the following three numbers i.e. of the sum of the values of the k numbers in
the d=2 state plus the number of particles denoted by M(+o),k,d=2 plus one nucleon is equal
to one of the d numbers,
d) there cannot be two or more objects in the nucleon or hyperon having the mass M(+o),k,d
for which the numbers k and d have the same values,
e) there cannot be vector bosons in the d=1 state because the d=1 state lies under the
Schwarzschild surface and transitions from the d=1 state to the d=2 or d=4 states are
forbidden, so in the d=1 state there can only be one W pion,
f) the mean charge of the torus of the nucleon is positive so if the relativistic pions are not
charged positively then electric repulsion does not take place  there is, however, one
exception to this rule: in the d=1 state there can be a positively charged pion because
during that time the torus of the proton is uncharged,
g) to eliminate electric repulsion between pions in the d=2 state there cannot be two or more
pions charged negatively,
h) there cannot be a negatively charged W pion which does not interact with the vector boson
in the d=2 state in the proton because this particle and the W pion in the d=1 state would
annihilate,
i) there cannot be a neutral pion in the d=2 state in the proton because the exchange of the
charged positively pion in the d=1 state and of the neutral pion in the d=2 state takes
place. This means that the proton transforms itself into the neutron. Following such an
exchange the positively charged pion in the d=2 state is removed from the neutron
because of the positively charged torus. Such a situation does not take place in the
hyperon lambda =nW(o),d=2.
Using these rules we can conclude that the structure of hyperons strongly depends on the d
numbers associated with the TitiusBode law for strong interactions (i.e. with symmetrical
decays) and on the interactions of electric charges.
49
The above selection rules lead to the conclusion that there are in existence only two
nucleons and seven hyperons.
The spins of the vector bosons are oriented in accordance with the Hund law. The angular
momentums and the spins of the objects having the mass M(+o),k,d are oriented in such a way
that the total angular momentum of the hyperon has minimal value. All of the relativistic
pions, which appear in the tunnels of nucleon, are in the S state. This means that and
hyperons have halfintegral spin, whereas has a spin equal to 3/2.
The strangeness of the hyperon is equal to the number of particles having the masses
M(+o),k,d=2 taken with the sign ‘‘.
Notice also that the percentages for the main channels of the decay of and + hyperons are
close to the x, 1x, y, 1y probabilities. This suggests that in a hyperon, before it decays, the
W(o),d=2 pion transits to the d=1 state and during its decay the pion appears which was in the
d=1 state.
Selected resonances
The distance of mass between the resonances, and between the mass of the resonances and
the hyperons or nucleons, are close to the mass of the S bosons.
The lightest resonance (1236) consists of the nucleon and the S boson in the d=2 state, i.e.
the (1236) consists of S(+o),d=2{2} and of a proton or neutron {1/2+}. The mean mass
calculated of all charge states i.e. ++, +, o, , equals 1236.8 MeV (the number before the signs
‘+’ and ‘’ denotes the approximate value of angular momentum, whereas the ‘+’ and ‘’
denotes the orientations of the angular momentum respectively ‘up’ and ‘down’).
The parity of the S(o),d pions is assumed to be negative, and the parity of the lambda hyperon
is assumed to be positive. For selected resonances we have
mN(2650) = 3mS(o),d=1{2+2+2} + 1mS(o),d=2{2+} + 1mS(o),d=4{1+} + 1mproton{1/2+}
(or 1mneutron{1/2+}) = 2688 MeV (J P =11/2  ),
m(1520) = 1mS(o),d=1{2} + m(1115){1/2+} = 1537 MeV (J P =3/2  ),
m(2100) = 2mS(o),d=1{2+2+} + 1mS(o),d=4{1} + m(1115){1/2+} = 2145 MeV (J P =7/2  ),
m(2350) = 2mS(o),d=1{2+2+} + 2mS(o),d=4{1+1} + m(1115){1/2+} = 2332 MeV (J P =9/2 + ),
m(1765) = 3mS(o),d=4{111} + m(1192.5)(mean value){1/2+} = 1753 MeV (J P =5/2  ),
m(1915) = 4mS(o),d=4{1+1+1+1} + m(1192.5){1/2+} = 1940 MeV (J P =5/2+).
The mass of tau lepton
The charged W pion in the d=1 state is responsible for the properties of the proton. What
should be the mass of a lepton in order to the mass of such pion was the radiation mass of the
lepton for the strongweak interactions in the d=1 state? From formula (63) we have
swW(+),d=1mtau,d=1/mW(+),d=1 = emmelectron/mem(electron), (136)
where swW(+),d=1=0.762594.
The calculated mass of tau lepton is
mtau = 1782.5 MeV (137)
Properties of fundamental particles
The neutrinos interact with the point mass of the electron. They are all fermions so their
physical states should be different. Neutrinos and electrons can differ by internal helicity
(which dominates inside the muon) and, if not by it, by the sign of the electric charge and the
weak charge (it is for the third neutrino inside a pion). The possible bound states are as
follows
 R e  R e(anti)L+ L,
+ L e + L eR (anti)R+,
 R e  R e(anti)L LL LLA  R (anti)R+,
where LLA denotes the large loop with the left helicity and antiparallel spin.
+ L e + L eR LR LRA.
Particle Spin
helicity 1)
50
Table 8 New symbols
Internal
helicity
Electric
charge
Weak
charge
New
symbol
e(anti) + L (left) + e(anti)L+
e  R (right)  eR
(anti)  R + (anti)R+
+ L  Le

 R  e  R
e +
+ L + e + L
p +
+ L + p + L
p 
 R  p  R
n + L 2)
+ nL
n(anti)  R 2)
 n(anti)R
  R 2)
  R
+ + L 2)
+ + L
  R 2)
 +  R
+ + L 2)
+  + L
1)
The sign ‘+’ is for the parallel senses of the velocity and spin. The
sign ‘’ is for the antiparallel senses.
2)
The resultant internal helicity is the same as the internal helicity of
the torus having greatest mass.
There are in existence the following 8 states of the carriers of the not entangled photons
L1 (eR e(anti)L+)L,
L2 (L (anti)R+)L,
L3 (eR (anti)R+)L,
L4 (L e(anti)L+)L,
R1 (eR e(anti)L+)R,
R2 (L (anti)R+)R,
R3 (eR (anti)R+)R,
R4 (L e(anti)L+)R.
These eight different states are some analogy to the eight gluons.
The kaon is a binary system and each component of this binary system consists of two large
loops (created on the circular axis of the nucleon), an electron and a neutrino
K o LL LLA e  R e(anti)L+ + LL LLA e + L eR,
K o (anti) LR LRA e  R e(anti)L+ + LR LRA e + L eR.
The mixture of K o and K o (anti) LL LLA LR LRA e  R e(anti)L+ e + L eR.
51
New electroweak theory (continuation)
Magnetic moment of the muon
The muon magnetic moment in the muon magneton should be the same as for electron
because the muon is the electrontype particle. There is a little difference due to the binding
energy emitted by muon (see the discussion below formulae (55) and (27))
Ebinding = 0.498281845 + mradiation(muon)/2 + mpion(o),free – mpion(o). (138)
This binding energy means that the mean mass of the virtual field composed of the virtual
electronpositron pairs has mass Ebinding+mbare(muon).
We can introduce the following symbol
= 1 + Ebinding/mbare(muon)
(139)
The iteration leads to =1.00540622.
The ratio of the radiation mass resulting from the interactions of the virtual pairs to the bare
mass of the muon is
= , (140)
where =0.00115963354 (see formula (66)).
The mass of muon in its bare mass is equal to the muon magnetic moment in the muon
magneton
= 1 + [1 + ’w(electronproton)/(2/3)]. (141)
From it, applying iteration, for mmuon=105.656314 MeV, we obtain
’ =  Δ = 1.00116592234 – 8.344077·10 10 (see (68)) = 1.001165921508 (142)
A greater mass of the muon leads to the smaller anomalous magnetic moment.
Frequency of the radiation emitted by the hydrogen atom under a change of the mutual
orientation of the electron and proton spin in the ground state
The parallel polarisation of two vortices increases the binding energy of a system
Epar = E + Ei, (143)
whereas the antiparallel polarisation decreases the binding energy
Eant = E  Ei. (144)
Since Ei=ich/r the change of the mutual orientation of spins causes emitted energy to be
Ei = 2ich/r = h, (145)
and therefore
= ic/r, (146)
where denotes the frequency.
In the hydrogen atom, there is the orbitorbit interaction (the n = 1 Bohr orbit with the d = 1
orbit in proton). On the first Bohr orbit (n = 1) is the mass of electron melectron whereas in the d
= 1 state in proton the mean mass is
M = (1 – y)mW(+),d=1 + ymW(o),d=1. (147)
The centre of the n = 1 Bohr orbit is inside the proton so the classical virtual electron
behaves as if it was in the d = 1 state (it is the ground state in proton). The virtual mass of the
classical electron is 4/3 times greater than the bare mass of electron (see the explanation in
Chapter “Foundations of Quantum Physics”). The total mean mass in the d = 1 state is M’ =
M + 4mbare(electron)/3. Since αi/(Mimi) = Gi/(hc) = const. and by analogy to formula (79), for the
electroweak interactions of the electron with proton we obtain
i = w(proton)αem(melectron/M’) 2 . (148)
Because the radius of the first Bohr orbit is r1=0.5291772·10 10 m, then applying formulae
(146)(148) we obtain
= 1420.4076 MHz. (149)
52
LambRetherford shift
The Lamb shift is associated with the two different states of the charged pion in the d = 1
state in proton.
We can calculate the Lamb shift using following formula
Ei = ich/r = mic 2 . (150)
The Compton wavelength of the bare particle is equal to the external radius of the torus and
is defined by the following formula
= rz(torus) = h/(mbarec). (151)
Using formulae (150) and (151) we can obtain
mi = imbare/(r/rz(torus)). (152)
Applying the aforementioned three formulae, we obtain
L = ic/(2 · 4r1). (153)
The coupling constant we can write in following form
i = w(proton)M1’m/Y 2 = 1058.05 MHz. (154)
where w(proton) = 0.0187229 denotes the coupling constant for the weak interactions of the
proton, m = 0.000591895 MeV denotes the radiation mass of the electron, Y = 424.1245 MeV
denotes the point mass of the proton whereas the M1’ is the distance of the masses between
the relativistic charged W pion in the d=1 state and the charged pion in the rest i.e. M1’ =
215.760  139.5704 = 76.1899 MeV.
We can calculate this shift by analysing the condition that the increase in the force acting on
the proton which must be equal to the increase in the force acting on the electron. The force is
directly in proportion to the energy of interaction falling to the given segment. The energy of
the interaction is directly in proportion to the coupling constant of the interaction responsible
for the change of the value of the force. The Lamb shift is caused by the weak interaction of
the mass equal to the distance of the mass between the relativistic and the rest mass of the
charged W pion in the d=1 state with the radiation mass of the electron. The increase to the
radius of the orbit of the electron is as many times smaller than the external radius of the torus
of proton hand equivalent to how many times smaller the sum of the coupling constants for
the electron is than the coupling constant of the weak interactions for the proton
dr/A = (’w(electronproton) + em)/w(proton). (155)
From this dr = 2.722496·10 16 m.
For the second shell of the atom of hydrogen the frequency associated with such a shift is
L = Rc[1/4  1/(4 + dr/r1)] = 1057.84 MHz, (156)
where R=10,973,731.6 m 1 .
Summary
Table 9 The new electroweak theory
Physical quantity Theoretical value
Electron magnetic moment in the Bohr magneton 1.0011596521735
(see formula (69))
Muon magnetic moment in the muon magneton 1.001165921508
Frequency of the radiation emitted by the hydrogen 1420.4076 MHz
atom under a change of the mutual orientation of the
electron and proton spin in the ground state
LambRetherford Shift 1057.84 MHz
1058.05 MHz
53
Table 10 Mesons
Physical quantity Theoretical value
Mass of the K +, kaon 493.728 MeV
Mass of the K o kaon 497.760 MeV
Lifetime of KL 0 /lifetime KS 0
527
Mass of K*(892) 901 MeV
Mass of Eta 549.073 MeV
Mass of Eta’ 953.971 MeV
Mass of Ypsilon 9463 MeV
Mass of Z 0
90.4 GeV
Mass of W +,
79.4 GeV
Mass of D(charm) 1867 MeV
Mass of D(strange) 1991 MeV
Mass of B 5281 MeV
Mass of B(strange) 5354 MeV
Mass of B(charm) 6290 MeV
Lifetime of B(charm) 1.9 · 10 13 s
Table 11 Hyperons and resonances
Particle Theoretical value Theoretical value
Mass J P S
Hyperon 1115.3 MeV 1/2 +1* 1
Hyperon + 1189.6 MeV 1/2 +1 1
Hyperon o 1190.9 MeV 1/2 +1 1
Hyperon  1196.9 MeV 1/2 +1 1
Hyperon o 1316.2 MeV 1/2 +1 2
Hyperon  1322.2 MeV 1/2 +1 2
Hyperon  1674.4 MeV 3/2 +1 3
Tau lepton 1782.5 MeV 1/2
Resonance (1232) 1236.8 MeV 3/2 +1
Resonance N(2650) 2688 MeV 11/2 1
Resonance (1520) 1537 MeV 3/2 1
Resonance (2100) 2145 MeV 7/2 1
Resonance (2350) 2332 MeV 9/2 +1
Resonance (1765) 1753 MeV 5/2 1
Resonance (1915)
*Assumed positive parity
1940 MeV 5/2 +1
54
Liquidlike plasma
The phase transitions of the Newtonian spacetime and the TitiusBode law for the strong
interactions lead to an atomlike structure of baryons. Such model leads to the pseudorapidity
density, NSDfraction in the pp collisions, temperature and density of the liquidlike plasma.
Pseudorapidity density in pp collisions
Electronpositron pairs that decay into photons arise close to tori/electriccharges of
colliding protons that have very low energy. The ratio X1 of the energy of particles that have a
transversemomentum to the energy of emitters (i.e. of protons having atomlike structure) is
X1 = 2melectron/mproton. (157)
When protons collide which have a higher energy, there appears, along a transverse
direction, coreanticore pairs of baryons in such way that the spins of the cores are parallel to
the transverse direction. Half of such a segment has a length equal to rT
rT = ED/(2H + ), (158)
where the E is the amount of energy of the colliding pp pair expressed in TeV, the
H + =727.44·10 6 TeV is the mass of the charged core of a baryon and D=2A/3 is the across of a
charged torus of a baryon placed inside the core (A=0.697442 fm). The segments behave in a
similar way to liquidlike plasma. The energy released during the strong interactions transits
towards the ends of the segments.
Within the CMS (the Compact Muon Solenoid) many pp collisions take place, therefore,
liquidlike plasma appears (i.e. the segments). The segments fill a prolate cylinder. Inside
such a cylinder are coreanticore pairs whereas the protons that have an atomlike structure
are only on a lateral surface of a cylinder with such a surface having a thickness equal to D.
Since the d=1, 2 and 4 states are destroyed, inside the liquidlike plasma only arise pions,
kaons and the contracted electrons having energy of approximately 4.6 MeV as particleantiparticle
pairs. The components of pions arise inside the tori whereas the kaons and
contracted electrons are produced in the d=0 state i.e. on the equators of the tori. Pairs appear
because the conserving symmetry creations and decays are characteristic for strong
interactions. All particles produced inside the liquidlike plasma have transversemomentum –
they are the nonsinglediffractive fraction (the NSD fraction). The protons that have an atomlike
structure produce hadrons that have momentum tangential to the surface of a cylinder
also – this is the singlediffractive fraction (the SD fraction). This means that the ratio X2 of
energy of the NSD hadrons that have transversemomentum to the total energy emitted by the
lateral surface of liquidlike plasma (i.e. by the protons having an atomlike structure) is (the
SD fraction is emitted through the surface whereas the NSD fraction goes through the surface)
X2 = X1πrT 2 HCMS/(2πrTHCMSD) = X1rT/(2D), (159)
where HCMS is the longitudinal length of the liquidlike plasma.
Following simple conversions we obtain
X2 = X3EN, (160)
where X3=0.37434 and EN is the number equal to the amount of energy per one pp collision
expressed in TeV.
The liquidlike plasma behaves in a similar way to a black body because the interiors of
nucleons behave like a black body. This means that the energy emitted is directly in
proportion to absolute temperature of a body to the power of four. The temperature of liquidlike
plasma is directly in proportion to the pseudorapidity density found in a central region
(pseudorapidity density=dNchargedhadrons/dη; η
55
NSDfraction = sqrt(sqrt(0.37434·EN))·100%. (161)
For energy of 0.9 TeV, we obtain the NSD fraction equal to 76.18% whereas for 2.36 TeV
we obtain 96.95%. We can see that there is an increase of 27.3% from 0.9 TeV to 2.36 TeV.
This theoretical result is consistent with experimental data [1]. There is a threshold for
EN=2.672 TeV. For energy higher than 2.672 TeV, the NSD energy becomes higher than the
energy of protons that have an atomlike structure on the lateral surface of liquidlike plasma.
This means that the external layers of liquidlike plasma can separate from it explosively.
The temperature and density of liquidlike plasma
The Compton wavelength of the bare electron is equal to the external radius of the polarized
torus (see formula (62)) so similar the characteristic wavelength for colliding nucleons,
leading to liquidlike plasma, is equal to the A=0.697442 fm. It follows from the fact that in
liquidlike plasma the TitiusBode orbits for strong interactions are destroyed. Using the
theory in Wien’s law we obtain that the lowest temperature of liquidlike plasma,
corresponding to the characteristic wavelength A, equals 4.155·10 12 K. Using the Uncertainty
Principle energy of a loop having a circumference equal to 2π·2A/3 is 67.5444 MeV,
therefore, for a length equal to A the energy is approximately 283 MeV. Following such
energy, a π + π  pair can be produced. We also know that for energy equal to the threshold
2.672 TeV per colliding pair of nucleons, the released energy is equal to the mass of a nucleon
i.e. approximately 939 MeV. This means that the 283 MeV leads to following number E0
equal to the energy per colliding pair of nucleons expressed in TeV E0=2.672·283/939=0.805.
Such energy is needed in order to create liquidlike plasma having the lowest temperature i.e.
the 4.155·10 12 K. Because the temperature is directly relative to the NSDfraction, we obtain
following formula for temperature T for liquidlike plasma
T = X4·sqrt(sqrt(0.37434·EN)), (162)
where X4=5.6·10 12 K. For example, for energy equal 9.1 TeV per colliding pair of nucleons,
we obtain the temperature of liquidlike plasma equal to approximately 7.6·10 12 K.
At the lowest temperature of liquidlike plasma, with each core of baryon, energy equal to
approximately 727+283=1010 MeV is present and such a core occupies volume equal to
approximately V=8A 3 /3. This leads to the lowest mass density of liquidlike plasma which is
2·10 18 kg/m 3 . With an increasing energy of collisions, the volume of the core of baryons is
constant whereas the released energy ER increases due to strong interactions ER=283·EN/E0
[MeV]. The density of the liquidlike plasma is ρ=(H + +ER)/V. This formula can be expressed
as follows:
ρ = X5(2.07 + EN), (163)
where X5=0.692·10 18 kg/m 3 .
References
[1] The CMS Collaboration;
Transversemomentum and pseudorapidity distribution of charged hadrons in pp
collisions at sqrt(s) = 0.9 and 2.36 TeV;
arXiv: 1002.0621v2 [hepex] 8 Feb 2010.
56
New Cosmology
Introduction
The six parameters describing the physical state of the Newtonian spacetime and the mass
density of the Einstein spacetime lead to the Protoworld. Our early Universe (the cosmic loop)
arose in a similar way to the large loop responsible for the strong interactions in baryons,
however, we must replace the binary systems of neutrinos that the large loops are composed
with the binary systems of the greatest neutron stars – which are typical neutron black holes.
The Protoworld was the big torus around the spherical mass. The surface of the torus was
composed of deuterium (i.e. of electrons and binary systems of nucleons) and appeared
similar to the Ketterle surface in a strongly interacting gas [1]. In centre of the torus there was
mass which was composed of typical neutron black holes. The calculated mass of the entire
object is M=1.961·10 52 kg. The radius of the equator of the big torus was equal to 286.7
million lightyears. Our Universe appeared on the circular axis inside the big torus as the loop
was composed of protogalaxies built out of typical neutron black holes. These protogalaxies
already assembled into larger structures, which are visible today, before the ‘soft’ big bang
due to fourneutrino symmetry resulting from the long distance interactions of the weak
charges of neutrinos i.e. due to the exchanges of the binary systems of the closed strings. The
anticlockwise internal helicity of our Universe was associated with the rotations of the
protogalaxies and the binary systems of protogalaxies and the spin speed of the cosmic loop
(the loop had spin equal to 1). Before the ‘soft’ big bang, the axes of the rotations of the
binary systems of protogalaxies were tangential to the circular axis of the big torus. The
calculated mass of the Universe (without the dark energy which is the remainder of the big
torus and the big central mass) is m=1.821·10 51 kg. The ratio of the mass of the Protoworld to
the mass of the Universe was β=10.769805. The radius of the Universe loop was equal to
191.1 million lightyears.
Because a neutrino is built out of the closed strings moving with a speed 2.4248·10 59 times
higher than the c, the energy (not mass) frozen inside a neutrino (then not measured by an
external observer) is equal to the M
M = mneutrino(2.4248·10 59 ) 2 , (164)
where mneutrino=3.33493·10 67 kg. This means that there is the possibility of the
Protoworldneutrino transition. Before such a transition, the Protoworld had a mass equal to
the M. This is because inside this object was bound energy of the Einstein spacetime equal to
E=mc 2 . During the transition, this energy appeared in the new neutrino as the lacking dark
energy. There arose regions filled with additional binary systems of neutrinos as the remnant
of the disintegrated Protoworld. It is the dark energy which had and has mass/energy equal to
the M. The structure of the Protoworld meant that there were four inflows of dark energy into
the cosmic loop.
Cosmic structures in the Universe
The fourneutrino symmetry leads to following formula which describes the number of
objects found in the structures of the Universe
D = 4 d , (165)
where d=0,1,2,4,8,16 for a flattened spheroidlike structures, and d=3,6,12 for a chainlike
structures.
The fourneutrino symmetry law concerns the neutrinos in the pions, the binary systems of
neutrinos in one component of a double helix of entangled photons, the nucleons in
protonuclei (for example, there can appear the tetraneutrons), the typical neutron black holes
in protogalaxies, the binary systems of protogalaxies (the protogalaxies I also refer to as
massive galaxies) in the Universe.
57
The cosmic structures composed of the binary systems of protogalaxies I refer to as
follows:
d = 0 is for single object (i.e. the binary system),
d = 1 is for group,
d = 2 is for supergroup,
d = 4 is for cluster,
d = 8 is for supercluster,
d = 16 is for megacluster (the early Universe was the megacluster of the binary systems of
protogalaxies),
d = 3 is for chain,
d = 6 is for superchain,
d = 12 is for megachain.
Black body spectrum
How is the black body spectrum produced? Large loops are produced from energy released
during nuclear transformations. The distance between the binary systems in the Einstein
spacetime is 554.321 times greater than on the torus of the proton. The mean distance between
the binary systems of the neutrinos on the torus is approximately 2π times greater than the
external radius of the neutrino. From these conditions, we can calculate that approximately
7.5·10 16 binary systems of neutrinos are on the large loop. This means that 512 such loops
contain approximately 3.84·10 19 binary systems of neutrinos. A superphoton consists of
2·4 32 =3.69·10 19 binary systems of neutrinos (it is the double helix loop and each helix loop is
composed of 256 megachains). This means that superphotons can appear which have energy
equal to 67.5444 MeV. An equivalent of this amount of energy transits into the equator of the
torus and each superphoton has a length equal to 2πA, where A denotes the external radius of
the torus (the equator of the torus is the trap for the photons). This length is associated with
the internal temperature of a nucleon/blackbody via the Wien’s law equation
λT[m]·T[K]=0.002898. This means that the internal temperature of nucleons is 6.6·10 11 K.
When the energy of such a set of superphotons is 208.644 MeV (the relativistic mass of the
neutral pion in the d=1 state) then such a set transits to the d=1 state and the length of each
superphoton increases to 2π(A+B). Such photons are emitted because in the d=1 state there
can only be one portion having energy equal to 208.644 MeV. This means that the measured
frequency of the photons related to the maximum of intensity is A/(A+B)=0.58154 times
lower than would result having used Wien’s law equation. Using today’s temperature of the
Universe (2.725 K) we obtain λT=1.0635 mm, λν=1.8287 mm and ν=163.94 GHz.
Why is the length of the photons increased from 2πA·2/3=2.9214·10 15 m to 1.8287·10 3 m
i.e. by approximately 6.26·10 11 times? The answer to this is for the following two reasons (see
the further explanations). The decay of each superphoton to the photon galaxies increased the
length of the early photons 2·4 16 =8.6·10 9 times. Initially, the superphotons overlapped with
the cosmic loop so it had a radius of approximately 0.1911 billion light years. Today the
elements of a superphoton interacting with the baryonic matter fill the sphere and its radius is
approximately 13.4 billion light years i.e. the radius and the length of the early photons
increased about 70 times. This means that the length of the early photons increased
approximately 6·10 11 times. We see that this theoretical result is consistent with the
observational fact discussed. Because of the broadening of the d=1 state/tunnel we observe a
black body spectrum.
In nucleons, the virtual photons appear on the circular axis and are in the d=0 and d=1 states
as well. This makes their mean length equal to 2π(2A/3 + A + A + B)/3 = 4.95 fm and such is
mean distance of interacting deuterons on the big torus. In reality, the photons arise as the
gluon loops that become the photons outside the strong field. For torus composed of the
58
binary systems of the cores of baryons the mean distance of interacting pairs is 2πA = 4.382
fm. Because the mass is directly in proportion to the area of the torus so the mass of the
Protoworld composed of deuterons is almost the same as the object composed of the binary
systems of cores of baryons {(939.54 + 938.27 – 2.22)/(2·727.44)}/(4.95/4.382) 2 = 1.012.
The anisotropy power for the CMB radiation
The electric charge of the core of a nucleon is created by the spinning loop inside the torus
of the core whereas the lines of electric forces converge on the electric charge/circle. The
direction of the magnetic vector associated with the electric charge overlaps with the axis of
the torus.
Our Universe arose and developed as the cosmic loop inside the torus of the Protoworld.
The magnetic vectors of the neutrons within the cosmic structures were tangent to the cosmic
loop. Magnetic polarisation dominated because the neutrons are electrically neutral. This
means that the cosmic loop was also the magnetic loop. The cosmic structures in the
expanding cosmic loop were mostly moving in directions perpendicular to the cosmic loop.
Due to the law of conservation of spin, the magnetic polarization of the protogalaxies should
be parallel to the direction of the relativistic motions of the protogalaxies i.e. they should be
perpendicular to the cosmic loop. This means that there were the 90 o turns of the magnetic
axes of the protogalaxies.
When the gravitational field of the big torus that squeezed the early Universe disappeared
there started an evaporation of the typical neutron black holes the baryonic loop consisted of.
The neutrons placed on the surface of the neutron stars, in respect to the weak decays, had
emitted the electrons and entangled electronantineutrinos. Due to the beta decays, protons
appeared on the surface of the neutron black hole. The electric repulsion of the protons meant
that the protons had assembled on the equator of neutron black hole. Ultimately, the electric
repulsion exceeded the gravitational attraction and what took place were separations of the
protons from the surface of the star in the plane of the equator. The proton beams carried
forward some neutrons. Rising atomic nuclei caused the nuclear explosions in the region
between the surface of the neutron star and the Schwarzschild surface. Since the neutron stars
increased their size due to inflows of the dark energy, this energy became free.
The succeeding inflows of dark energy produced during the transition of the Protoworld
caused an expansion to the neutron black holes. This meant that above the Schwarzschild
surfaces more photons, electrons and closed currents of protons recurrently appeared. Planes
of the currents were tangent to the surface of the expanding cosmic loop whereas the magnetic
axes associated with such currents were perpendicular to the surface. The photons that
appeared were moving most often in directions tangent to the surface of the exploding cosmic
loop. On the surface were also cold and hot regions. The cold regions were in the peripheries
of the exploding cosmic structures. They arose due to the redshift of the entangled binary
systems of neutrinos (i.e. the carriers of the photons) produced in the beta decays on equators
of typical neutron black holes before their expansion. The hot regions were near the magnetic
poles. They arose due to the beta decays after the expansion of the typical neutron black holes
– it was due to the lack of the redshift. There were 90 o angles between the directions of
motions of the hot photons (the radial directions) and the directions of motions of the cold
photons (directions tangential to the equators). There was also electron and proton plasma.
This means that there were adequate conditions for the electric polarization of the photons due
to the Thomson scattering. The polarized photons due to the scattering on the electric charges
were moving perpendicular to the surface of the cosmic loop. The polarized photons were
moving away from the surface i.e. were moving in cooler parts of the cosmos. Some of them
fell into the opposite part of the expanding cosmic loop. Today we should observe that the
electrically polarized early photons in the CMB and such polarization should be tangent to the
59
today celestial sphere. Enlargement of the neutron stars was easier in the peripheries of the
early cosmic structures so in these regions intensity of the Emode polarization was higher.
Because the surface of the expanding cosmic loop was the closed pipe/chain, we can assume
that on the surface were N=4 12 binary systems of protogalaxies i.e. a megachain. We can
calculate the angular size of the structures using the formula L=sqrt[(360 o ) 2 /N], where N
denotes the number of structures, whereas the multipole moment can be calculated using the
formula I=180 o /L.
On the surface of the expanding cosmic loop was one megachain (L=360 o , I=0.5). There
were 4 4 superclusters (L=22.5 o , I=8), 4 6 superchains (L=5.63 o , I=32), 4 8 clusters (L=1.41 o ,
I=128), 4 9 chains (L=0.703 o , I=256), 4 10 supergroups (L=0.352 o , I=512), 4 11 groups
(L=0.176 o , I=1024) and 4 12 single objects (L=0.088 o , I=2048).
The anisotropy power of the quadrupole is associated with the energy emitted during the
Protoworldneutrino transition. The megachain on the surface of the cosmic loop then
decayed into 16 parts each containing 16 superclusters (L=90 o , I=2). This is known as the
quadrupole. In the dark energy the electronpositron pairs had appeared. The energy of the
photons per neutron associated with the weak interactions of the radiation mass of the pairs
with dark energy can be calculated using the formula
XL = amneutronα’weak(electronproton) = 12.197 eV/neutron, (166)
where a=0.001159652, mneutron=939.54·10 6 eV, α ’ weak(electronproton)=1.11944·10 5 .
This energy is inside the sphere filled with dark energy (radius is 20.9±0.1 billion light
years – see further explanation in this paragraph and Chapter titled “Radius of the Universe
and the Hubble constant”) which meant that energy inside the sphere filled with baryons
(radius is 13.4±0.1 billion light years) is
YL = al 3 XL = 3.22 eV/neutron, (167)
where al=13.4/20.9=0.6415.
Because there are β=10.769806 less nucleons in the Universe than were in the Protoworld
released energy per nucleon in the Universe was, therefore,
60
ZL = βYL = 34.7 eV/nucleon. (168)
The released nuclear energy was L0=7.70 MeV/nucleon and today the temperature is
T=2.73 K. Therefore, the energy of ZL leads to following temperature associated with the
Protoworldneutrino transition
TL = T ZL/L0 = 1.23·10 5 K. (169)
Because the anisotropy power is equal to TL 2 the anisotropy power of the quadrupole is
equal to 1.51·10 10 K 2 =151 μK 2 .
Our early Universe was a loop composed of typical neutron black holes, therefore, due to
beta decays there appeared protons and electrons. Under the Schwarzschild surface appeared
atomic nuclei and there were the electronproton weak interactions. The circumference of the
large loop changes due to the weak electronproton interactions. The coupling constant for
strong interactions of the large loops is equal to 1 and such interactions led to the mean
temperature of the Universe today of about 2.73 K. The coupling constant for the weak
electronproton interactions is 1.11944·10 5 , therefore, the mean amplitude of temperature
fluctuations for the weak electronproton interactions is 30.56 μK on an angular scale of about
11 degrees on the sky. Today it is half an angular distance between the largest structures i.e.
the megachains of the binary systems of massive galaxies. This leads to the mean anisotropy
power equal to 934 μK 2 . When the mass density of the Einstein spacetime increases (the
additional energy is the dark energy) then additional particleantiparticle pairs appear. This
means that mass density and temperature fluctuations increase.
The largest peak/maximum is associated with the first inflow of dark energy to the cosmic
loop. The big torus before the transition from matter into dark energy consisted of binary
systems of nucleons. Afterwards the transition of the big torus consisted of two dark energy
films moving in opposite directions. In nucleons, the spin speeds are tangent to the surface of
the torus of a nucleon. The spin speeds of the binary systems of neutrinos in the torus of the
nucleon are from c/3 to c and the average speed tangent to the torus is equal to 2c/3. This
means that radial speeds are on a scale from zero to 0.94281c with the average radial speed
equal to 0.745356c. A similar theory can be acknowledged by examining the big torus after
the transition. Before the transition, inside the big torus there were also nucleons moving from
the surface of the big torus towards the cosmic loop and then, just after the transition, dark
61
energy appeared in the cosmic loop. The maximum mass density of the dark energy flow
associated with the dark energy film moving towards the cosmic loop was moving at a speed
equal to 0.745356c. This maximum approached the cosmic loop after 128 million years. This
means that the maximum approached the cosmic loop just after the decaying of the
superphotons and cosmic loop to the chains L=0.703 o , I=256 (118 million years since the
transition – see Paragraph “Acceleration of expansion of the Universe”). We can assume in
approximation the first maximum is for such a value of the multipole moment i.e. for about
I=256. The mass of the first inflow of dark energy was equal to the 1(2c/3) 2 part of half of
the mass of the big torus i.e. it was m1/m=1.3090 times greater than the mass of the cosmic
loop. Due to the law of conservation of energy, this dark energy moving with a radial speed
equal to v=0.745356c accelerated the front of the baryonic mass to a radial speed equal to
v1=0.5612c. This is because v 2 m1/m=v1 2 (1+m1/m). The second inflow was due to the
expansion of the dark energy in centre of the torus. When the front approached the
centre/circle of the expanding cosmic loop, the front of cosmic loop was at a distance of
191.1·v1/2v=71.94 million light years. The mass of the dark energy that flowed into the
cosmic loop was
m2/m=(4α/360 o )·(727.44318.2955)/67.5444=1.3885 times greater than the baryonic matter,
where tgα=v1/2v. Following the two first inflows, the mass of the dark energy inside the
cosmic loop was (m1+m2)/m=2.6975 times greater than the baryonic matter. The radial speed
of the front of the baryonic matter was equal to v2=0.6366c because
v 2 m2/m+v1 2 (1+m1/m)=v2 2 (1+(m1+m2)/m). Similar calculations for the third inflow of dark
energy shows that the ratio of the mass of dark energy that flowed into the expanding cosmic
loop to the mass of baryonic matter was equal to m3/m=(2α1/360 o )m1/m=0.1592, where
tgα1=(v1+v2)/4v. After the three first inflows, the mass of the dark energy inside the cosmic
loop was (m1+m2+m3)/m=2.8567 times greater than the baryonic matter. The radial speed of
the front of the baryonic matter was equal to v3=0.6415c because
v 2 m3/m+v2 2 (1+(m1+m2)/m)=v3 2 (1+(m1+m2+m3)/m). This means that the front of the fourth
inflow could not approach the front of the baryonic matter on the opposite site of the
expanding cosmic loop. Today v3=0.6415c is the radial speed of the front of the baryonic
matter. The fourth inflow only enlarged the cosmic structures.
The inflows produced are also protuberances composed of the dark energy and baryonic
matter. This caused some of the most distant cosmic objects to have a redshift greater than the
0.6415.
After the first inflow of dark energy, the total mass of the cosmic loop increased 2.309
times. It also increased temperature fluctuations to 70.6 μK and anisotropy power to 4980
μK 2 . The energy from the particleantiparticle annihilations tried to accelerate the surface of
the cosmic loop to a speed equal to c. After some time, the collisions of the binary systems of
neutrinos and the interactions of the dark energy with the Einstein and Newtonian spacetimes
evened the dark energy field and the front of it was and continues to move with the speed c.
The second, third and fourth maximums are also associated with the inflows of the dark
energy into the early Universe. The second was produced by the central mass in the big torus
whereas the third and fourth by the opposite part of the big torus – direct flow and the flow
after the compression in the cosmic loop was produced. The maximums of the mass density of
the dark energy flows approached the centre of the expanding Universe (initially it was the
circle) after 256 million years since the transition (multipole moment approximately I=512),
384 million years (multipole moment approximately I=768) and 740 million years (multipole
moment approximately I=1479).
62
Polarization of the CMB
Because early cosmic structures were neutron black holes, the decoupling of the photons
and electric charges from the expanding cosmic structures was possible when these particles
crossed the Schwarzschild surface. This was when angular sizes increased approximately two
times since the maximum density of the cold photons was at its highest on the surfaces of the
neutron black holes. The ionized matter, i.e. the protons, electrons and ionized atoms were
between the surfaces of the neutron stars and the Schwarzschild surface. The scenario was as
follows. The inflow of dark energy had increased the density of the Einstein spacetime inside
the neutron black holes that is what increased their angular sizes. Next, above the
Schwarzschild surface appeared ionized matter. When the radius of the neutron black holes
increased more than two times, there appeared hot and cold photons moving tangential to the
surface of the expanding cosmic loop. Due to the Thomson polarization theory, there
appeared E photons. We can see that at first there appears anisotropy power maximum (i.e.
maximum for density fluctuation of the dark energy and temperature fluctuation), followed by
the maximum for density of ionized matter and then the maximum for the E polarization. The
CMB polarization was highest when the produced velocity gradient was at its highest (i.e. the
neutron black holes swelled). The velocity gradient, i.e. the polarization spectrum, is out of
phase with the density spectrum, i.e. with the temperature anisotropy. For the maximums of
the E polarization, we should observe multipole moments equal to approximately I≈128, 256,
384, and 740.
The most energetic early photons had energy of about 8.8 MeV – which is the binding
energy of the nucleons inside iron. The characteristic energy for the beta decays is 0.754
MeV. Furthermore, the maximum temperature fluctuations for the scalar Emode polarization
should be approximately 8.8/0.754=11.7 times lower than the maximum temperature
fluctuations for the densest matter i.e. 70.6/11.7=6.1 μK. The maximum anisotropy power
associated with the scalar Emode polarization should be approximately 37 μK 2 . This was for
the multipole moment I=384 because the density of ionized matter was at its lowest then, and
the ranges of the photons was greatest and the E polarization were strongest. The last
maximum of the Emode is lower than the last but one because there was also an inflow of
baryonic matter that increased the mass density of the ionized matter. The obtained value is
only a rough estimate.
The peak for I=256 for the E polarization is partially masked due to the similar conditions
leading to this peak and the peak for I=384. The peak for I=128 for the E polarization is lower
than the peak I=384 due to a higher mass density of the electric charges. The peak for I=740
is lower than the peak I=384 because some part of the energy of the dark energy was absorbed
by the baryonic matter in the opposite part of the cosmic loop.
We can see that the CMB strongly depends on the atomlike structure of baryons, on the
new interpretation of the uncertainty principle (the decays of entangled photons) and on the
new cosmology i.e. on the evolution of the Protoworld and on the initial distribution of the
binary systems of protogalaxies associated with the fourneutrino symmetry.
Radius of the Universe and the Hubble constant
During the era of neutron stars and big stars 80% of free neutrons were transformed into
iron (about 92%) with impurity of nickel (about 8%) and 5.81% into helium  this means that
approximately 40% of neutrons were transformed into protons (see Paragraph titled
“Abundance of the chemical elements…”). During the decay of a neutron energy equal to
approximately 0.76 MeV is released – about 0.30 MeV per each nucleon in the Universe.
Nuclear binding energy was also released. Because the binding energy per nucleon inside iron
is 8.79 MeV, whereas inside helium it is 7.06 MeV energy of 7.4 MeV per each nucleon was
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released into our Universe. This sum is equal to L0=7.7 MeV per each nucleon. This means
that energy of the CMB (without the ripples) is
Ebackground = mL0c 2 /mneutron = 1.32 . 10 66 J. (170)
We know that today the density of the energy of the microwave background radiation is
equal to background=4.17 . 10 14 J/m 3 . The formula is therefore
4RCMB 3 /3 = Ebackgroundbackground , (171)
which results that the mean radius of the sphere filled with CMB is
RCMB=1.96·10 26 m, i.e. 20.7 billion lightyears (precisely 20.7±0.1). Such a radius, in
approximation, also has a sphere filled with dark energy (approximately 20.9±0.1 billion
lightyears).
The Hubble constant H is defined as H=c/Rsphere, with its dimension km . s 1. Mps 1 today
which is H=47.
Today the radius of the sphere filled with the baryonic matter is 0.6415c·20.9=13.4 billion
light years (precisely 13.4±0.1). Outside this sphere but in distance smaller than 20.8 billion
lightyears, due to the protuberances in the thickened Einstein spacetime, there can be only
not numerous cosmic objects.
Acceleration in the expansion of the Universe
Using the formula tlifetime=λ/c, we can calculate the lifetime of a vortex/photon which has a
circumference equal to the λ. At the beginning of the ‘soft’ big bang, the length of the photons
coupling the structures inside a binary system of protogalaxies was equal to the circumference
of circle drawn by the typical peripheral neutron black holes in rotating the binary system of
protogalaxies. It was 2π times longer than the mean distance between the binary systems of
protogalaxies in the cosmic loop because the planes of rotation of the binary systems were
perpendicular to the cosmic loop. This means that the size of protogalaxy was equal to the
radius of the circle drawn by the peripheral black holes. Because in the cosmic loop there
were 4 16 binary systems of protogalaxies then mean distance between the planes of rotation of
the binary systems of protogalaxies was 0.28 light years. The circumference was 1.76 light
years so the lifetime of such a photon galaxy would be 1.76 years. A superphoton (the
entangled photons coupled the cosmic structures) consisted of 2·4 16 photon galaxies so it
decayed into photon galaxies after 15.09 billion years. The lifetime of a photon galaxy is
considerably longer than the age of the Universe today – photon galaxies will live
approximately 3.9·10 12 years (and will decay into 256 fragments). The photon galaxies
coupling the cosmic structures in a galaxy lead to an illusion of present of a dark matter – the
illusion follows from the fact that the photon galaxies are the massless particles.
The cosmic loop was the lefthanded double helix loop that was composed of protogalaxies.
Electromagnetic interactions of electrons are responsible for the structure of the DNA.
Moreover, electrons are righthanded so the DNA always winds to the right.
Due to the succeeding decays of the superphotons, the cosmic loop also decayed. The free
binary systems of massive galaxies appeared 7.54 billion years after the transition of the
Protoworld into a neutrino. The free groups appeared 1.89 billion years after the transition,
supergroups after 472 million years, chains after 118 million years, clusters after 1.84 million
years, superclusters after 115 thousand years and the free megachains after 1.76 years.
Due to the inflows of dark energy into matter a few billion years after the transition of the
Protoworld into a neutrino, the percentage of the matter and dark energy changed. Just after
the first inflow of dark energy into loop of matter, there was approximately 43% of the matter
and 57% of the dark energy whereas today there is approximately 26% of matter and 74% of
dark energy (see Paragraph titled “Matter and dark energy”). This means that over time the
rate of the expansion of the Universe changed – it was the period two billion years after the
transition. Due to the turbulence in the compressed dark energy inside the cosmic loop, finite
64
regions of the dark energy moving in the Einstein spacetime appeared. Since there are cosmic
structures, the upper limit for a redshift for quasar having a mass equal to a group of galaxies
is 7, for a massive protogalaxy 8, whereas for a supercluster of typical black holes 10. The
maximum observed redshift should not exceed 16. Due to spacetimes, the finite regions
quickly disappeared (in a cosmic scale).
To calculate the distance to a cosmic object, we can calculate the redshift z using the
formula whilst calculating the General Relativity z=[(1+zob) 2 1]/[(1+zob) 2 +1], where zob is the
observed redshift. Why are Type Ia supernovae fainter than when they result from the z? This
is because the last formula was derived using incorrect initial conditions i.e. the dynamics of
the ‘soft’ big bang is different. This means that we cannot say for certain whether the General
Relativity is incorrect. Previous calculations show that for zob=0.6415 the massive spiral
galaxies are on the surface of the sphere filled with baryons whereas using the above formula
the results are that they appear at a distance approximately 3.8 billion light years from the
surface. This means that supernovae Ia are in reality at a greater distance from us than from
the result using the above formula. We can see (see Fig. titled “Discrepancy for the
formula….”) that the discrepancy for z
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quasars about 7.5 billion years before the decays of the photons. The quasars with low redshift
arose in the collisions of galaxies. Due to the fourneutrino symmetry the emission lines of
hydrogen, helium, oxygen and iron (of carbon and magnesium also) are the brightest lines – it
suggests also that the new cosmology is correct. The second flare up of the Universe leads to
the illusion of acceleration of expansion of the Universe about 5.7 billion years ago.
The constant and number of photons in cubic meter
Using the Einsteinde Sitter model the critical density is
ES = 1.9·10 26 h 2 kg/m 3 , (172)
where h is associated with the Hubble constant H by relation
H = h·100 (km/s)/Mps. (173)
We know that the Hubble constant has a value equal to H=47 therefore, the critical density
is ES = 4.2·10 27 kg/m 3 .
The ratio of the radius of a sphere filled with baryons to the radius of a sphere filled with
dark energy is equal to approximately al=13.4/20.9=0.6415. The mass density inside the
sphere filled with baryons is (baryonic matter plus dark energy)
= m(1 + βal 3 )/(Val 3 ) = 8.28·10 28 kg/m 3 , (174)
where V=3.2·10 79 m 3 .
The ratio of the mass density inside a sphere filled with baryons to the critical density is
= /ES = 0.02.
How many photons are present in a cubic meter? Initially, the number of superphotons was
equal to the number of neutrons in the cosmic loop and was associated with the transitions of
the electronpositron pairs into neutrons in the region of the Einstein spacetime having an
anticlockwise internal helicity and a sufficiently high mass density.
About 15.09 billion years following the transition, 2·4 16 photon galaxies per each initial
superphoton appeared. By knowing the mass of our Universe and by knowing the mass of a
nucleon, we can calculate the total number of nucleons in existence. This is equal to 1.09·10 78
so the total number of photons inside a sphere filled with CMB radiation is today equal to
1.09·10 78 ·2·4 16 =0.94·10 88 . The volume of a sphere filled with CMB radiation is 3.2·10 79 m 3
therefore, in one cubic meter there should be approximately 300 million photons.
Abundance of chemical elements before the era of the big stars
Due to the fourneutrino symmetry and the weight equilibrium before the era of big stars,
per each free 256 nucleons there were 64 groups each containing 4 nucleons, 16 supergroups
each containing 16 nucleons, 4 chains each containing 64 nucleons, and 1 cluster containing
256 nucleons. As a result, the abundance was as follows (total number of the nuclei is 341)
Free nucleons 75.07 % (hydrogen was created from them)
Groups 18.77 % (helium was created from them)
Supergroups 4.69 % (oxygen was created from them)
Chains 1.17 % (iron was created from them first of all)
Clusters 0.29 % (First Pu244 and then lead was created from them first of all)
Abundance of chemical elements immediately after the era of big stars
The observed ‘oscillations’ of neutrinos are the only exchanges of free neutrinos for which
the neutrinos in the nonrotatingspin binary systems of neutrinos that the Einstein spacetime
is composed of. This means that on the basis of such ‘oscillations’ we cannot calculate the
mass of neutrinos. To explain the solar neutrino problem without the neutrino ‘oscillations’
(impossible because of the tremendous energy frozen inside them) we must assume that inside
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the sun and other stars, on the surfaces separating the layers of chemical elements, the
GASER (Gamma Amplification by Stimulated Emission of Radiation) works.
The energy of emitted quanta in the nucleonhelium transformation is 7.06 MeV. These are
quanta group because of the fourneutrino symmetry. This means that their associations
contain 1, 4, 16, 64, 256…. quanta. The total energies of the possible associations are
approximately 7 MeV, 28 MeV, 113 MeV, 452 MeV…. The association having energy of
approximately 28 MeV disturbs the 4 nucleons and causes these nucleons to transform into
helium (in such a transformation the next association having energy about 28 MeV is
emitted). The association having energy equal to approximately 113 MeV disturbs the 14
nuclei of helium and causes these nuclei to transform into iron or nickel (in such a
transformation the next association having energy equal to approximately 97 MeV is emitted).
The other associations are useless. This means that in the core of a star the associations
containing 4 and 16 quanta are amplified. We see that there are two basic channels of nuclear
transformations in the core of star: hydrogen into helium, and helium into iron (with an
impurity of nickel).
The GASER and the fourneutrino symmetry leads to the conclusion that the abundance of
chemical elements (in the Universe) should have higher 'peaks' for 1, 4, (16), 56, (208)
nucleons. This is consistent with observational facts.
Assume that the released energy in the centre of the sun takes place only as a result of
neutronshelium transformations. For example, the transformation of 112 neutrons into 28
nuclei of helium releases energy equal to 791 MeV. Moreover, 56 electronantineutrinos are
emitted.
Assume that now the GASER is implemented. To release energy of approximately 791
MeV 4 nuclei of iron56 should arrear as a result of heliumiron transformations (about 388
MeV) and 14 nuclei of helium as a result of neutronshelium transformations (about 395
MeV). During these two main channels of nuclear transformations, the same amount of
energy should be released. In the first channel 8 electronantineutrinos are absorbed (because
of the 8 processes inverse to the beta decay), whereas in the second 28 electronantineutrinos
are emitted (because of the 28 beta decays). Therefore, during these two transformations 20
electronantineutrinos are emitted. The concluding result depends on abundance of protons
and neutrons in the centre of the sun. In the centre, the density of the nucleons is sufficiently
the formula (196) would be valid (there is approximately 3/8 protons). When the GASER acts
such abundance leads to emission of 22 electron neutrinos  it is about 39% of the expected
number of the electron neutrinos. When the GASER does not act and when the abundance of
protons is 100% 56 electron neutrinos are emitted.
We can also assume that in stable stars there is energy equilibrium for the dominant
processes of nuclear transformations. Because the nuclear binding energy per nucleon has the
value 8.79 MeV for the iron56, for the helium4 it has 7.06 MeV. There should, therefore, be
approximately 100%·(8.797.06)/7.06=24.5% of helium and 75.5% of hydrogen if we do not
take into account the more massive nuclei. Immediately after the era of the big stars, the
abundance of helium and hydrogen differed. We can calculate the binding energy per nucleon
in iron in cores of the big stars. The simplest large loop consists of two binary systems of
neutrinos and has energy 67.5444 MeV. This means that energy of binary system of neutrinos
(its spin is 1) is approximately 33.77 MeV. When the ratio of mass density of the thickened
Einstein spacetime inside core of a big star to its mean mass density outside star is higher than
approximately (939+33.77)/939=1.036 the thickened Einstein spacetime intensively emits
energetic photons. Since binding energy per nucleon is directly proportional to mass density
of the Einstein spacetime then binding energy per nucleon in iron in the cores of a big star
was 8.79·1.036=9.11 MeV. This result leads to conclusion that immediately after the era of
big stars was approximately 29% of helium and 71% of hydrogen. What were the causes of
67
the creation of such a composition of matter? The first reason is the initial abundance of
chemical elements. The second cause is associated with the values of the nuclear binding
energy per nucleon. Finally, the third reason is the law that says that the released binding
energy for the dominant types of nuclear transformations should have the same value. We
assume that the big stars exploded when all the heaviest nuclei were transformed into iron
(with an impurity of nickel) and that the heaviest nuclei contained 256 nucleons (i.e. Nobel
256 and Lorens256) they have a binding energy equal to 7.06 MeV per nucleon (they are
extremely unstable so we can treat them as a set of almost free alphaparticles).
We know that luminosity is almost directly proportional to mass of a star to the power of
four. My theory, however, leads to the conclusion that the lifetime of a star is inversely
proportional to its mass to the power of four. This means that the lifetime of a star is inversely
proportional to its luminosity. In brief, a history of the solar system is as follows. First, there
was a big star  the Oort’s cloud is remnant of the era of big stars. Next, there followed the
supernova of an Ia type  the Kuiper’s belt is remnant of the supernova. Now, there is the sun.
The dark matter is composed most of all of Fe+Ni lumps which were produced during the era
of big stars. The temperature of these lumps is equal to the CMB radiation so detecting them
is extremely difficult. The dark matter is also composed of stone+iron lumps that were
produced by the supernovae.
Table 12 Big stars just after the beginning of the ‘soft’ big bang
Composition Composition at the end Released binding
at the beginning
energy per nucleon
20% H1 71% H; 100%·2.05/7.06=29% He 7.06 MeV
20% He4 20% Fe56 2.05 MeV
20% 016 20% Fe56 1.11 MeV
20% 64 X 20% Fe56 0.00 MeV
20% 256 Y 20% Fe56 2.05 MeV
From the results shown in Table 12 we can see that just after the era of the big stars, there
was 4 times as much dark matter than visible matter. During the explosions of the supernovae
the first thing produced is protonneutron symmetrical nickel followed by Fe56, Si28, N14,
Li7. This is because in extremely high temperature the decays should be symmetrical – for
example, we can see the series: 56, 28=56/2, 14=28/2=56/4, 7=56/8; similarly also for Ni64,
S32, O16.
Table 13 Stars of second generation with working the GASER
Composition at Nuclear transformations Released binding
the beginning
energy per nucleon
71% H1 H1 He4 7.06 MeV
29% He4 He4 Fe
For 1 part of the H1 He4 is
7.06/1.73=4.081 parts of the He Fe
Over time, the amount of He decreases
8.797.06=1.73 MeV
About 0% Fe56 Over time, the amount of Fe increases
After the era of big stars, i.e. about 20 billion years ago, there was 71% of hydrogen and
29% of helium. Today is 75.5% of hydrogen and 24.5% of helium. Such composition we
obtain on assumption that during the 20 billion years 3.1% of hydrogen transformed into
helium 71%·0.031 = 2.2% i.e. there is 71% – 2.2% = 68.8% of hydrogen. From Table 13
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follows that simultaneously, due to the GASER, 31% of helium transformed into dark matter
i.e. 29%·0.31 = 9% whereas abundance of helium is 29% + 2.2% – 9% = 22.2%. When we
omit the dark matter we obtain 100%·68.8/(68.8 + 22.2) = 75.6% of hydrogen and
100%·22.2/(68.8 + 22.2) = 24.4% of helium. We should notice also that 9%/2.2% ≈ 4.081
(see Table 13).
Matter and dark energy
The ratio of the radius of spheres filled with baryonic matter (visible and dark) to the radius
of spheres filled with dark energy is bl=13.4/20.9=0.6415. Due to the fact that dark energy is
the β times greater than the baryonic matter inside the sphere filled with baryons, we should
observe 1 part of baryonic matter (visible and dark) per βbl 3 =2.843 parts of dark energy. This
leads to the conclusion that inside a sphere filled with baryons there is approximately 26%
matter and 74% dark energy. After the era of big stars, about 9% of visible matter transformed
into dark matter. This means that today the matter consists of approximately 80% +
26%·0.2·0.09 = 80.47% of dark matter and 19.53% of visible matter i.e. there is around 21%
dark matter and 5% visible matter. It is very difficult to detect dark matter (the illusory and
real parts) because the real part has a temperature equal to the CMB.
The curvature of Space and Cosmological Constant
We know that ρ(matter plus dark energy inside and between matter) = 8.28·10 28 kg/m 3 . The
mean density of the Einstein spacetime is ρ(background) = 1.1·10 28 kg/m 3 , then
ρ(background)/ρ(matter plus dark energy inside and between matter) = 1.3·10 55 .
This means that the Universe is extremely flat (k=0) because it is only a very small ripple on
the background. Furthermore, there is more of the spreading of dark energy than of matter. Λ
denotes the cosmological constant associated with dark energy. Dark energy also only
insignificantly increases the density of the background, therefore, Λ is also practically equal
to zero (Λ=0). Today we see that the Universe describes the flat Friedman model (k=Λ=p=0)
which is also known as the Einsteinde Sitter model.
Ω denotes the ratio of the mass density of a component to the total mass density (matter plus
dark energy) without the background.
Today visible baryonic matter is
Ωb = 0.05,
visible and dark matter is
Ωm = ρm/ρ = 0.26,
and dark energy is
ΩΛ = 0.74.
Today the mean local radial speed of baryonic matter is the same as dark energy. Some time
in the future, collisions of matter with antimatter will take place within the partner of our
Universe i.e. in the antiuniverse. This will signal the beginning of an end to our Universe.
Cosmogony of the Solar System and Massive Spiral Galaxies
By studying the fourneutrino symmetry, we can see that a virtual pion can interact at
maximum with 2·4 32 neutrinos (this is because of the longdistance interactions of the weak
charges of neutrinos) each placed in another typical neutron black hole (the TNBH). Firstly,
we can say that our early Universe contained 2·4 32 the TNBH and secondly that smaller
structures were the binary systems of protogalaxies which were composed of 2·4 16 the TNBH
and having two cores (because of the virtual pairs) – of which each core contained 4 16 the
TNBH (for example M31 was created in such manner) or one core which contained 4 16 the
TNBH. The succeeding smaller structure i.e. the binary protosupercluster contained 2·4 8 the
TNBH and had two cores (note that some globular clusters are ovalshaped)  such structures
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have a mass approximately 3.3 million times greater than the sun or had one core (some
globular clusters are sphericalshaped)  such structures have a mass approximately 1.6
million times greater than the sun. The next smaller structures were binary protoclusters
which each contained 2·4 4 the TNBH and had two cores, and so on. Such binary protoclusters
I refer to as solar clusters. The cores of the solar clusters evaporated intensively and as a result
the following chemical elements arose: H, He, O, X64 (which first transformed into iron), Y
256 (which first transformed into plutonium Pu244 and then into lead). From these gaseous
rings arose. The TitiusBode law defines the radii of the rings. The A/B for strong
gravitational field has almost the same value as for strong interactions. If we assume that at
the beginning of the evaporation of the solar cluster the constituents of this binary system
were at a distance equal to the radius of the Pluto ring then the centre of the mass was the
point of tangency between Uranus and the Uranustwin rings. This means that the Saturntwin
ring was tangent to the Neptune ring as well (precisely the Saturntwin ring split into two
rings tangential in one place). The Dogon myth identifies that the Sun and the star Potolo was
binary system, and notes that human life arose on the planet revolving around Potolo. In the
distant past the star Sirius, covered an area near the Potolo and the binary system of these
two stars then arose. The probability of such an event occurring is very low, therefore, the
solar system is unique. The separation of the Sun and Potolo should occur when there were
rings, not planets. This means that it was almost a miracle that the creation of the solar system
took place.
The Solar System
The megachain of binary systems of neutrinos is the first stage in the evolution of photons
that are emitted during nuclear transformations. The mass of it is
mphotonmegachain = 4·4 32 ·mneutrino/(4·4 4 ) = 2.403·10 50 kg. (175)
The megachain composed of the binary systems of neutrinos has the unitary angular
momentum on orbit having a radius equal to r(megachain)=1.464·10 7 m. The protonuclei Y
256 accumulate on this orbit. They then they quickly decay into Pu244 because these nuclei
have a long halflife period. The angular momentum of the nuclei must also be conserved,
therefore, the plutonium collected on the orbit has the following radius (from mvr=const., for
nuclei we obtain r~1/m 2 )
Aconstituentbeginning + Bconstituentbeginning = r(plutonium) = 1.611·10 7 m. (176)
The next, the protonuclei Y256 emitted by the surface of the solar cluster which reached the
plutonium orbit and then symmetrically fell into pieces analogically in a similar way to the
group of four remainders inside the baryons. This occurrence leads to establishing the Titius
Bode law for a strong gravitational field.
To calculate the radii of the orbits of the planets from the initial conditions we can use the
following analogy.
Using the formula for angular momentum we know that if the mass of the rings have
changed very slowly over time then the evaporation of the solar cluster caused the radii of
rings to increase inversely in proportion to the mass of the constituent of the binary system:
mringvringrring=const., since mring=const. and vring=(GMconstituent/rring) 1/2 then Mconstituentrring=const.
Mconstituentbeginning = 4 4 ·4.935·10 31 kg = 1.263·10 34 kg, (177)
whereas
Mconstituentnow = Msun = 1.99·10 30 kg. (178)
The radii of the rings increased
Mconstituentbeginning/Msun = 6348 times. (179)
At the beginning, the radius of the Earthring was equal to
rEarthringbeginning = Aconstituentbeginning + 2Bconstituentbeginning, (180)
where Aconstituentbeginning=GMconstituentbeginning/c 2 .
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From this for G=6.674·10 11 m 3 kg 1 s 2 we obtain Aconstituentbeginning=0.9382·10 7 m.
This means that for a strong gravitational field is
Aconstituentbeginning/Bconstituentbeginning = 1.394. (181)
Since the orbits have a certain width we can see that the A/B has almost the same value for a
strong gravitational field (A/B=1.394) as for strong interactions (A/B=1.3898).
The initial radius of the Earthring was
rEarthringbeginning = 2.284·10 7 m.
The present radius of the orbit of the Earth should be
rEarthringnow = rEarthringbeginningMconstituentbeginning/Msun = 1.45·10 11 m. (182)
This result accurately corresponds with the established interval (1.47·10 11 , 1.52·10 11 ) m.
Kuiper’s belt is remnant of a supernova.
The Oort’s cloud is remnant of the era of the big stars.
Following the era of the big stars, a star arose in the centre of the solar system with a mass
approximately 1.44 times greater than the mass of the Sun. After the explosion of this Ia
supernova about 5 billion years ago, the Sun was created. During the explosion of the
supernova, the following transformations took place
Ni56 Co56 Fe56.
Firstly, nickel56 appeared because this nucleus is the protonneutron symmetrical nucleus.
Such symmetry is always preferred during a very high temperature.
Because symmetrical decays prefer very high temperatures then the following elements
should be produced
Fe56 Si28 N14 or C14 Li7.
The acting GASER produced nuclei that contained 64 nucleons so their symmetrical decay
lead to the development of the following nuclei
Ni64 S32 O16 Li8 He4 D2 H1.
Because the halfperiod for C14 is approximately six thousand years, today we should
detect many C12 atoms.
In regions having a high density of muons symmetrical fusion of three nuclei was possible.
This is possible because the weak mass of a muon consists of three identical weak energies
i.e. there are two neutrinos and the point mass of the contracted electron that have the same
energies. Because nucleons and He4 were (and are) the most abundant of all, the probability
of the production of T3 and C12 was very high.
Symmetrical fusion of two nuclei was also preferred because the simplest neutral pions
consist of two carriers of the not entangled photons that have the same energy. This leads, for
example, to the following fusions
C12 + C12 Mg24.
We can say that muons and neutral pions are the catalysts for symmetrical fusions.
The length of arms of the massive spiral galaxy
If we assume that the core of a protogalaxy, composed of big neutron stars, emits
protonuclei containing 1, 2, 4, 8, 16, 32, 64, 128, and 256 the neutrons, we can use the
following analogy. The number 256 refers to the d=0 unit found in the TitiusBode law.
Consequently, the number 128 is for d=1, 64 for d=2, 32 for d=4, 16 for d=8, 8 for d=16, 4 for
d=32, 2 for d=64, and 1 for d=128. The ranges of the protonuclei were inversely proportional
to their mass and to the mass of the emitter i.e. to the mass of the protogalaxy core. We can
see that the last number d has a value of 128. For a protogalaxy which contained two cores,
for example M31  Andromeda, contained 2·4 16 times the amount of typical neutron black
holes then the initial radius of the ring rinitial, for which d=128, and had value (Ainitial=3.15·10 14
m, and Binitial=Ainitial/1.394)
rinitial=2.92·10 16 m i.e. 3.1 lightyears (3.1 ly).
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If we assume that today, in the centre, the binary system of globular protoclusters exist
(containing 2·4 8 the typical neutron black holes) then up through to the present day the radius
rinitial increased 4 8 times i.e. the length of the spiral arm should be approximately 203 thousand
lightyears (62 thousand parsec).
Size of globular cluster
Using a similar method for calculating globular clusters containing one core, means we can
establish that their diameter is equal to 79 lightyears (this is if we assume that today there is a
star in the centre which has a mass equal to the Sun). Using this formula on globular clusters
containing two cores means we can calculate their diameter to be equal to 158 lightyears (this
is if we assume that today there is a binary system of sunlike stars in the centre).
Summary
Table 14 Structures of the Universe
Structures of the Universe Mass
Largest neutron star/blackhole 4.9·10 31 kg
Massive galaxy 2.1·10 41 kg
Group of binary systems of galaxies 1.7·10 42 kg
Supergroup of binary systems of galaxies 6.8·10 42 kg
Cluster of binary systems of galaxies 1.1·10 44 kg
Supercluster of binary systems of galaxies 2.8·10 46 kg
Chain of binary systems of galaxies 2.7·10 43 kg
Superchain of binary systems of galaxies 1.7·10 45 kg
Megachain of binary systems of galaxies 7.1·10 48 kg
Table 15 Theoretical results
Physical quantity Theoretical value
Radius of the sphere filled with CMB and dark energy 20.8 billion ly
Radius of the sphere filled with baryons 13.4 billion ly
Mass of the Protoworld 1.961·10 52 kg
Mass of visible and dark matter of the Universe 1.821·10 51 kg
Hubble constant 47 km·s 1 ·Mps 1
Radius of the Protoworld 286.7 million ly
Radius of the loop of the early Universe 191.1 million ly
Number of binary systems of massive galaxies 4.295·10 9
Number of massive galaxies together with dwarf
galaxies assuming there are twenty dwarf galaxies per
86 billion
one massive galaxy
Abundance of H1 and He4 following the era of big
stars when we do not take into account the heavier
elements
Abundance of H1 and He4 in the present day when
we do not take into account the heavier elements
Abundance of visible and dark matter and dark energy
inside the sphere filled with baryons
71% H and 29% He
75.5% H and 24.5% He
Visible matter: approx.
5%
Dark matter: approx. 21%
Dark energy: approx. 74%
72
Table 16 Theoretical results
Physical quantity Theoretical value
λν/λT for black body 1.7195
Ω 0.02
Number of photons in a cubic meter 300 million
Anisotropy power for a quadrupole 151 μK 2
Anisotropy power for megachains 934 μK 2
Maximum anisotropy power for mass density fluctuations 4980 μK 2
Multipole moments for maximums of the anisotropy power
associated with inflows of dark energy
256, 512, 768, 1479
Multipole moments for maximums of the E polarization
spectrum
128, 256, 384, 740
Maximum anisotropy power for scalar Emode polarisation 37 μK 2
Amplitude of the temperature fluctuations for the CMBR on 1.11944·10 5
angular scale of 11 degrees
A/B for strong gravitational field 1.394
Radius of orbit of the Earth 1.45·10 11 m
Length of arms of the M31 203,000 ly
Size of globular clusters 79 ly or 158 ly
References
[1] M W Zwierlein, J R AboShaeer, A Schirotzek, C H Schunck, and W Ketterle; Vortices
and superfluidity in a strongly interacting Fermi gas; Nature 435, 10471051 (2005).
73
Fourshell Model of an Atomic Nucleus
On the basis of the four phase transition of the Newtonian spacetime and the TitiusBode
law for strong interactions, in this section I shall analyse the interior structure of atomic
nuclei.
Volumetric binding energy of a nucleus per nucleon
The sum of the mass of the free relativistic charged and neutral W(d=1) pions is 424.403
MeV. The nucleons that an alpha particle is composed of, occupies the vertices of the square
with the diagonal of the square equal to A+4B. The exchanged pions are most frequently
located in the centre of this square. As A/r=v 2 /c 2 , mW(+o),d=mpion(+o)/(1(v 2 /c 2 )) 1/2 , and the
nucleonpion distance is (A+4B)/2, the sum of the mass of the charged and neutral W pions is
394.499 MeV. The distance between the mass of the unbound and bound states is 29.904
MeV per two nucleons. When side of the square is
Side = (A + 4B)/2 1/2 , (183)
then the volumetric binding energy per nucleon is 14.952 MeV.
Radius of a nucleus
Each nucleon occupies a cube which has a side equal to ac=(A+4B)/2 1/2 =1.91258·10 15 m.
We can assume that the nucleons inside a nucleus are placed on the concentric spheres where
the distances between them equal ac. This means that the radius of the first sphere is equal to
ac/2. This, therefore, leads to the following formula for the radii of the spheres (they are not
the radii of the nuclei because the spheres have a thickness)
rsn = (n  0.5)ac where n=1, 2, 3, 4. (184)
The maximum number of nucleons placed on a sphere is
An = 4(n  0.5) 2 , (185)
followed by, A1=3.14, A2=28.27, A3=78.54 and A4=153.94.
If we round these figures to the nearest even number (nuclei containing an even number of
nucleons are more stable), we obtain the following series: 4, 28, 78, and 154. This means that
on the first four wholly filled spheres there are 264 nucleons. As we see by the first two
numbers, the sum of the first and third and the result of subtracting the third and second, and
the fourth and second numbers, we can see that the result is the wellknown magic numbers of
4, 28, 82, 50, 126. This cannot be a coincidence which confirms that we are on the right path
in order to build the correct theory of an atomic nucleus. When the number of neutrons
becomes equal to one of the magic numbers then transitions of the protons between higher
and lower spheres occurs. This increases the binding energy of a nucleus.
To calculate the electric radius of a nucleus (i.e. the radius of a nucleus obtained in
experiments based on the bombardment of a nucleus by electrons) we have to add the electric
radius of the nucleon to the radius of the last sphere. Since the charged pions in the nucleons
are placed in the d=1 state the electric radius is, therefore, equal to A+B=1.19927·10 15 m.
Furthermore, the electric radius of the nucleus An=110 is
rje(An=110) = 2.5ac + (A + B) = 5.98·10 15 m. (186)
If we define the electric radius by using the formula
rje = roeAn 1/3 , (187)
then for a nucleus containing An=110 nucleons we obtain roe=1.25 fm. The value roe changes
from 1.28 fm for An=32 to 1.23 fm for An=264.
Since the range of strong interactions of a nucleon is A+4B the radius of a nucleus for strong
interactions (i.e. the radius of a nucleus obtained during experiments based on the
bombardment of a nucleus by nucleons having energy of approximately 20 MeV) is greater
than the electric radius
74
rjj(An=110) = 2.5ac + (A + 4B) = 7.49·10 15 m. (188)
If we define such a radius by using the formula
rjj = rojAn 1/3 , (189)
then for a nucleus containing An=110 nucleons we obtain roj=1.56 fm. The value roj changes
from 1.76 fm for An=32 to 1.47 fm for An=264.
Model of dynamic supersymmetry for nuclei
From [1] results we can see that the nucleons in a nuclei are grouped in following way
a = 2 protons and 2 neutrons,
b = 3 protons and 5 neutrons,
c = 3 protons and 4 neutrons,
d = 1 proton and 1 neutron.
The new theory explains the above as follows
a) A proton exists in two states with the probabilities:
y=0.50838 and 1y=0.49162.
If we multiply these probabilities by two (for a deuteron) or by four (for an alpha particle),
we obtain the integers (approximately) because the probabilities are that y and 1y have
almost the same values.
b) A neutron exists in two states with the probabilities:
x=62554 and 1x=0.37446.
If we multiply these probabilities by eight, we obtain in the integers (5.004 i.e.
approximately 5, and 2.996 i.e. approximately 3). The 8 is the smallest integer which leads to
integers (in approximation).
c) For a system containing 50% of a) and 50% of b), we obtain the following probabilities
(x+y)/2=0.56696 and (1x+1y)/2=0.43304.
This factor is equal to 7 (3.969 i.e. approximately 4, and 3.031 i.e. approximately 3).
A nucleus chooses a mixture of the a), b), c), d) and states in such a manner which binding
energy was the greatest. The 2p2n groups appear when the interactions of protons dominate
whereas the 3p5n groups appear when the interactions of neutrons dominate.
The energy of the Coulomb repulsion of protons
To calculate the Coulomb energy of the repulsion of protons for wholly filled spheres we
can use the following analysis. Since wholly filled spheres have a spherical symmetry, the
Coulomb energy of the repulsion of a proton placed on the surface of the last wholly filled
sphere per one nucleon equals
Ecn/An = (kZe 2 /rsn)(Z/An), where k=c 2 /10 7 . (190)
If we express the energy in MeV then we obtain
Ecn/An[MeV] = 0.753Z 2 /(An(n  0.5)). (191)
If Z=2, An=4 we would obtain 1.5 MeV, if Z=16, An=32 we would obtain 4.0 MeV, if Z=46,
An=110 we would obtain 5.8 MeV, and for Z=104, An=264 we would obtain 8.8 MeV.
Theory of the deuteron
The magnetic moment of a deuteron is only slightly lower than the sum of the magnetic
moments of a proton and a neutron. This suggests that the pn binary system is bound for
short times in a region having a high negative pressure. We can assume that negative pressure
appears due to the exchanges of the free neutral pions. The free neutral pions appear due to
the weak interactions because then pions can run out from the strong field. Since in neutron is
the resting neutral pion in the H o Z o π o state then emissions and absorptions of neutral pions do
not change magnetic moment of neutron. We can calculate probability of emission of the
neutral pion by a proton. Due to the W o Z o π o transitions, the emission of neutral pion by
75
proton changes its magnetic moment. In such transition, the angular momentum of the
relativistic W o cannot change. This condition causes that during the emission of the pion π o
the electromagnetic loop Z o (spin speed of this loop is equal to the speed c) is in the d=4
tunnel, i.e. in the last tunnel for strong interactions, because then the angular momentum of
W o d=1 is close to the angular momentum of Z o . The ratio of these two angular momentums is
u=0.9575329. Since probability of the H + W o state is y=0.5083856 and the ratio of the
coupling constants for the weak and strong interactions is αw(proton)=0.0187228615 then
probability of emissions of the free neutral pions by a proton is z=yαw(proton)u=0.009114214.
The probability of the H + W o and H + Z o π o states of proton in the neutronproton bound state is
w=y+z whereas of the H o W + state is 1w. This leads to following the deuteronnuclear
magnetic moment ratio 0.85230.
The scattering length is
atrip = 2(A + 4B)(1  z) + 3(A + 4B)z = (2 + z)(A + 4B) = 5.4343 fm. (192)
In nucleons, the relativistic pions are in the d=1 state. Since pions consist of the large loops
that have radius equal to 2A/3 the effective range for this state is A+B+2A/3. The effective
range of deuteron is
rtrip = (A + B + 2A/3)(1z) + 2(A+4B)z = 1.6984 fm. (193)
To obtain the binding energy for a deuteron we must take into account the electric
interactions in the triplet states (spin=1).
The W  W + interact from distance equal to 2πA/3 for a period equal to 1w.
The H + protonW  interact from L for a period equal to x(1y), where
L = [(2πA/3) 2 + (A + B  2A/3) 2 ] 1/2 = 1.63491 fm. (194)
The H + protonH + neutron interact from 2πA/3 for a period equal to x(1y).
The H + neutronW + proton interact from L for a period equal to (1w).
This leads to the protonneutron electric attraction in a deuteron equal to
ΔEem = e 2 (x + y + w 2)(1/L – 1/(2πA/3))/(10 7 ·Z8) = 0.0366111 MeV,
where Z8=1.78266168115·10 30 kg/MeV.
Therefore, the binding energy of deuteron emitting two free neutral pions and bound due to
the volumetric binding energy equal to ΔEvolumetric=29.903738 MeV is
ΔEnp = (2mpion(o)  ΔEvolumetric)z + ΔEem = 2.22428 MeV.
Binding energy of a nucleus and the path of stability
In the alpha particle, there are two possible states that I refer to as the square and deuteron
states. The square state leads to the volumetric binding energy per nucleon (i.e. 14.95 MeV)
and the electric repulsive force equal to 1.5 MeV per nucleon (see formula (191)). In the
deuteron state, all linear axes of the tori of nucleons overlap so one deuteron and two free
nucleons or two deuterons arise. If we assume that the probability of both states is equal then
for the deuteron state we obtain the total binding energy to be equal to 3.33 MeV. If we also
assume that the probability of the square and deuteron states to be equal then the binding
energy per nucleon in the alpha particle is
E(He4) = (4·14.95 – 6 + 3.33)/8 = 7.1 MeV. (195)
When the electric repulsive force per nucleon is lower than the total binding energy for two
separated deuterons (E
76
When the electric repulsive force per nucleon is higher than the total binding energy for two
separated deuterons then the neutrons dominate i.e. the groups containing five neutrons and
three protons. This is because the following formula is satisfied
x/(1  x) = 5/3. (196)
Table 17 Main path of stability of nuclei
ZXA a b c d ZXA a b c d ZXA a b c d
1H1 36Kr84 9 6 71Lu175 10 16 1
2He4m 1 37Rb85 9 5 1 1 72Hf180 9 18
3Li7 1 38Sr88m 10 6 73Ta181 9 17 1 1
4Be9 1 1 39Y89 10 5 1 1 74W184 10 18
5B11 1 1 40Zr90m 12 5 1 75Re187 9 18 1
6C12 3 41Nb93 11 5 1 1 76Os192 8 20
7N14 3 1 42Mo98 10 7 1 77Ir193 8 19 1 1
8O16m 4 43Tc97 12 5 1 1 78Pt194? 10 19 1
9F19 3 1 44Ru102 11 7 1 79Au197 9 19 1 1
10Ne20 5 45Rh103 12 6 1 80Hg202 8 21 1
11Na23 4 1 46Pd106 12 7 1 81Tl205 7 21 1 1
12Mg24 6 47Ag107 13 6 1 82Pb208m 8 22
13Al27 5 1 48Cd114 10 9 1 83Bi209 8 21 1 1
14Si28 7 49In115 11 8 1 84Po209 10 20 1 1
15P31 6 1 50Sn120m 10 10 85At210 12 20 1
16S32 8 51Sb121 10 9 1 1 86Rn222 5 25 1
17Cl35 7 1 52Te130 6 13 1 87Fr223 6 24 1
18Ar40 6 2 53I127 10 10 1 88Ra226 6 25 1
19K39 8 1 54Xe132 9 12 89Ac227 7 24 1
20Ca40m 10 55Cs133 9 11 1 1 90 Th 232 6 26
21Sc45 7 1 1 1 56Ba138 8 13 1 91Pa231 8 24 1
22Ti48 8 2 57La139 9 12 1 92U238 5 27 1
23V51m 7 2 1 58Ce140 11 12 93Np237 7 25 1 1
24Cr52m 9 2 59Pr141 11 11 1 1 94Pu244 5 28
25Mn55 8 2 1 60Nd142 13 11 1 95Am243 7 26 1
26Fe56 10 2 61Pm147 11 12 1 96Cm247 6 27 1
27Co59 9 2 1 62Sm152 10 14 97Bk247 8 26 1
28Ni58m 12 1 1 63Eu153 10 13 1 1 98Cf251 7 27 1
29Cu63 10 2 1 64Gd158 9 15 1 99Es254 7 28 1
30Zn64 10 2 1 1 65Tb159 10 14 1 100Fm253 9 26 1 1
31Ga69 9 3 1 1 66Dy164 9 16 101Md258 8 28 1
32Ge74 8 5 1 67Ho165 9 15 1 1 102No256 12 26
33As75 9 4 1 68Er166 11 15 1 103Lr256 14 25
34Se80 8 6 69Tm169 10 15 1 1 104Ku260 13 26
35Br79 10 4 1 70Yb174 9 17 1
ZXA – denotes the atomicnumber/symbolofelement/massnumber
a=2p+2n=2He4; b=3p+5n; c=3p+4n=3Li7; d=p+n=1D2
?  denotes the discrepancy with the results in the periodic table of elements
m – denotes magicnumber nucleus
This principle, in particular, satisfies nuclei which contain 2k(3p+5n) more nucleons than
the Ca40 10(2p+2n): Fe56 [(Ca40)+2(3p+5n)], Ge72, Sr88, Ru104, Sn120, Ba136, Sm
152, Er168, W184, Hg200 [(Ca40)+20(3p+5n)].
Comments relating to the table titled ‘Main path of stability of nuclei’:
77
The consistency with the experimental data is very high – only one result is inconsistent
with experimental data. The abundance of the 78Pt194 should be slightly higher than the
78Pt195 with needs revising.
The mean number of the ‘a’ groups for nuclei greater than the 17Cl35 is nine – this is
consistent with the theoretical value An=36. Deviation from the mean value is significant ±4a.
Within light nuclei the a groups dominate whereas in heavy nuclei the b groups dominate.
This is because the binary system of the 2p2n can create the 4 deuteron bonds (which leads to
additional binding energy of approximately 1.1 MeV per nucleon) whereas within the 3p5n
only 3 deuteron bonds are created (which leads to additional binding energy of approximately
0.8 MeV per nucleon). The difference between the binding energy is approximately 0.3 MeV
per nucleon. Notice that in comparison with the 2p2n groups, the 3p5n groups significantly
reduce electric repulsion in heavy nuclei. At maximum, there can be only one intermediate c
state and only one d state having a low binding energy per nucleon.
The smallest magic numbers (2 and 8) are associated with the fourneutrino symmetry D=4 d
where d=1, 2 whereas the D denotes the mass numbers of the smallest magic nuclei D=4, 16.
The magic number 20 is associated with the transition from proton domination to neutron
domination. The 20Ca40 is the greatest nucleus only composed of the 2p2n groups.
The other magic numbers (28, 50, 82, and 126) are associated with the transitions of the
protons between the higher shell of nucleus and the lower shell(s). This reduces the mean
electric repulsive force (see formula 191). We should take into account that on the filled inner
shells of the nuclei the numbers of protons and neutrons have approximately the same value.
Detailed calculations leads to the binding energy associated with the transitions to be equal to
approximately 0.230.25 MeV per nucleon.
Among the most abundant isotopes collected in the table titled “Main path of stability of
nuclei”, are only 10 elements with an odd number of neutrons. Two are the very light
elements 4Be9 and 7N14 and eight are the radioactive elements. This suggests that there is a
pairing of neutrons for strictly determined distances between them. In the light elements,
neutrons are too close whereas on the surfaces of the radioactive elements they are too far
away. Neutrons have electromagnetic structures and when they are very close to one another,
electrostatic repulsion appears. When the distance between neutrons is sufficiently high we
can neglect the electrostatic repulsion whereas the attraction of neutrons as result of the
exchange of photons cannot be neglected. Electromagnetic attractions of neutrons have
maximum distances equal to A+8B and 2πA where the A denotes the radius of the equator of
the core of baryons. These two distances are respectively about 4.7 fm and 4.4 fm. The
diameter of the nuclei 4Be9 and 7N14 are approximately equal to these distances, however, in
light nuclei the neutrons are most often found in the centre of a nucleus. This means that the
pairing of neutrons is sometimes impossible in these nuclei.
We can also calculate the lower limit for the number of nucleons for the radioactive nuclei.
This is when the electric repulsive force per nucleon is higher than the binding energy per
nucleon in the alpha particle. Using formula (191) for the Bi209, we obtain that the electric
repulsive force equals 7.09 MeV, therefore, the An>209 defines the lower limit.
On the basis of formulae (191), (195) and (196) we can calculate the binding energy per
nucleon for select nuclei
E(O16) = (7.1 + 3.33/4) = 8.0 MeV, (197)
E(Fe56) = (26·8.0 + 6(14.95  4) + 24·(14.95  5.8))/56 = 8.8 MeV. (198)
When we neglect the proton transitions for Pb208, we obtain
E(Pb208) = (26·8.0 + 6(14.95  4) + 78(14.95  5.8) + 98(14.95  8.8))/208 = 7.65 MeV.(199)
The proton transitions increase the binding energy by approximately 0.25 MeV.
We can see that the approximate positive obtained results reflect the experimental curve.
The binding energy per nucleon depends on the internal structure of the nucleons, the
78
volumetric binding energy, the Coulomb energy of repulsion and the transitions of protons
associated with the magic numbers.
Summary
We obtain very positive theoretical results in only taking into account the internal structure
of nucleons, volumetric binding energy, electric repulsion of nucleons, and the transitions of
protons between the shells.
Table 18 Theoretical results
Physical quantity Theoretical value
Volumetric binding energy per nucleon 14.952 MeV
Magic numbers 4, 28, 50, 82, 126
Coefficient roe for radii of nuclei for An=32: 1.28 fm
electromagnetic interactions
An=264: 1.23 fm
Coefficient roj for radii of nuclei for An=32: 1.76 fm
strong interactions
An=264: 1.47 fm
Groups of nucleons in nuclei dominants: 2p+2n; 3p+5n
accessory: 1p+1n; 3p+4n
Binding energy of a deuteron 2.22428 MeV
Electric pn attraction in a deuteron 0.0366111 MeV
Deuteronnuclear magnetic moment ratio 0.85230
np(triplet) scattering length 5.4343 fm
np(triplet) effective range 1.6984 fm
Upper limit for the domination of protons Mean value: An=36
Lower limit for radioactive nuclei
(experimental result is >209)
An>209
Binding energy per nucleon for He4 7.1 MeV
Binding energy per nucleon for O16 8.0 MeV
Binding energy per nucleon for Fe56 8.8 MeV
Binding energy per nucleon for Pb208 7.9 MeV
References
[1] P. Van Isacker, J. Jolie, K. Heyde and A.Frank; Extension of supersymmetry in nuclear
structure; Phys. Rev. Lett. 54 (1985) 653.
79
Mathematical Constants
In this chapter, I will show that the everlasting theory leads to the mathematical constants
applied in physics.
Theories that describe the same but contain more parameters are the worse theories.
Mathematical constants applied in physics if they have not a physical meaning are the
parameters as well.
To formulate the ultimate theory, we should first define a fundamental spacetime and
identify that the physical properties of such a spacetime leads to the mathematical constants
associated with physics (i.e. to the number e=2.718…, the π=3.1415…. and the imaginary
unit equal to the sqrt(1)). The properties of such a fundamental spacetime should also lead to
physical constants (i.e. to the G, h, c, e, rest mass of electrons and pions – the other physical
quantities we can calculate once we know these seven parameters).
I derived the mentioned above physical constants and a few hundred other physical
quantities from the properties of the fundamental Newtonian spacetime (the six parameters)
and the Einstein spacetime (the one additional parameter because the Einstein spacetime arose
due to spontaneous phase transitions of the Newtonian spacetime).
The physicomathematical relations are very important in order to decipher the structure of
nature.
In physics the mathematical constants e=2.7182…, the number π=3.1415… and the
imaginary unit equal to the sqrt(1) appear almost everywhere. This must have a very deep
meaning.
Ground state of nature leads to the e=2.718....
In the proceeding section, I will prove that the ground state for the whole of nature leads to
the Newton definition of the mathematical constant e=2.718….
e=2.718….=1/0!+1/1!+1/2!+1/3!+1/4!+1/5!+….=1+1+1/2+1/6+1/24+1/120+….
P.Plichta [1] described how the number e1=1.718… is associated with a random sampling
and theory of combinations. My interpretation of the expression 1/0!=1 is as follows. When
there is no ball in a box, there is also a possibility that we will draw nothing i.e. the nothing
(i.e. 0!) leads to one possibility (i.e. 1). This means that there is a natural explanation for the
0!=1 i.e. a natural explanation as to why the number 1 appears twice.
What is the physical meaning of the number e=2.718… i.e. how does this number lead to
my scheme of nature i.e. what are the relationships between the e=2.718… and the succeeding
levels of nature following from the phase transitions of the Newtonian spacetime?
I established that the phase transitions of the Newtonian spacetime composed of tachyons
that lead to stable objects i.e. to the closed strings, neutrinos, cores of baryons and
protoworlds. In order to describe the position, shape and motions of these objects with a
rotating spin we need phase spaces containing the following numbers of coordinates and
quantities N (see the formula below Table 4)
N = (d  1) · 8 + 2.
When spin does not rotate then the number 2 in this formula disappears. This means that for
each stable object there are two possibilities i.e. the ground state when spin does not rotate
and the excited state when spin rotates. The d=0 is for tachyons, d=1 is for rotating spin, d=2
is for closed strings, d=4 is for neutrinos, d=8 is for cores of baryons and d=16 is for
protoworlds.
Now we can interpret the numbers 1, 1, 2, 6, 24, 120, which appear in the definition of the
number e=2.718…..These are the numbers which characterize the phase spaces of objects
appearing in the ground state of nature. I will also show that the numbersfactorials define
80
spatial and time dimensions in new way. The above series of numbers can be written as
follows: 1, 6, 24, 1, 2 and 120.
1.
The 1=0!=0D at the beginning of the series means that there is one ideally empty volume
i.e. the 0D volume.
The phase space of the Newtonian spacetime contains six elements (precisely the 6
suggesting that it is the imaginary spacetime).
The 6=3!=3D means that the 0D volume is filled with 3D objects described by the six coordinates
and quantities. There are the three coordinates (the x, y, and z), one mean radius of
the tachyons, one mean angular speed associated with the spin of tachyons and one mean
linear speed of tachyons associated with time in the fundamental/Newtonian spacetime. We
can note that 3+1+1+1=6. The spin of tachyons is very small in comparison to the halfintegral
spin of the closed string.
We can also see that the 0!=0D and the 3!=3D, describes the phase space of the
fundamental/Newtonian spacetime/idealgas. This is the 0D volume filled with the free 3D
tachyons.
2.
The number 24 describes the phase space of a nonrotatingspin neutrino. The 24=4!=4D
shows that the spacetime composed of free nonrotatingspin neutrinos which is the 4D
spacetime.
The ground state of the Einstein spacetime consists of the nonrotatingspin binary systems
of neutrinos. There are also in the ground state of it opened threads which are composed of
the binary systems of neutrinos i.e. there are the 1=1!=1D objects. These opened threads lead
to fractal structures (among other things also to the mental world). There are also surfaces
which appear similar to the Ketterle surface for strongly interacting gas i.e. the 2=2!=2D
objects leading to the tori of electrons and the cores of baryons. We see that the 4D, 2D and
1D objects are the constituents of the ground state of the Einstein spacetime. In such a
spacetime, there are possible quantum effects. The known particles are the excited states of
the Einstein spacetime. Time in the Einstein spacetime is associated with the speed of light c
and this quantity is among the 24 coordinates and quantities.
For rotatingspin neutrinos and binary systems of neutrinos, the number 26 is characteristic
of appearing in the string/M theory. This number does not appear within the definition of
e=2.718…. as its definition only reflects the ground state of nature as a whole.
3.
The phase space of the ground state of the Protoworld contains 120 coordinates and
quantities. What is the meaning of the equation 120=5!=5D? This means that inside a 4D
object a loop having a one dimension appears. Similarly, a large loop appears inside the cores
of the baryons responsible for the strong interactions. We can say that the 4D Protoworld
produced a 1D loop i.e. the early Universe. The evolution (i.e. cosmology) of the Protoworld
and the early Universe, I described earlier in Chapter titled “New Cosmology”. This
description leads to the today Universe.
We can see that in this scheme the phase spaces of the closed strings (i.e. the 8 or 10) and of
the cores of baryons (i.e. the 56 or 58) do not appear. The almost all closed strings are the
components of the neutrinos so they are not a part of the ground state of nature. Due to the
internal structure of the cores of baryons, they are always ‘dressed’ into the pions. This means
that the cores of the baryons also are not the ground state of the Einstein spacetime. All of the
observed particles are the excited states of the ground state of the Einstein spacetime. This
means that phase spaces of these particles should not appear in the Newton definition of
e=2.718…. There are only two spacetimes: the Newtonian spacetime (which leads to Einstein
81
gravity) and the Einstein spacetime (which leads to electromagnetism and quantum effects but
also to the weak and strong interactions having finite ranges of interactions).
The two basic elements of the Everlasting Theory lead to the mathematical constant
e=2.718… i.e. the phase transitions of the fundamental/Newtonian spacetime and the Titius
Bode law for the strong and gravitational interactions.
What can be found in the TitiusBode law for the strong interactions is (see the formulae
(10) and (31))
A = 0.6974425 fm,
B = 0.5018395 fm.
If we change these values, we obtain incorrect values for, for example, the mass of nucleons
and the magnetic moments of nucleons. The theory is very sensitive for each change in value
of the parameters associated with the properties of the Newtonian and Einstein spacetimes.
We can see that the following expression is close to the e=2.718…
x = 1 + (A + B)/A = 2.71954.
On other hand, the phase spaces of the objects in the ground state of nature leads to the
following number
y = 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 = 2.71667.
The mean value is then very close to e=2.7182…
z = (x + y)/2 = 2.7181.
There cannot exist a stable cosmic object greater than the Protoworld (120=5!=5D) leading
to the 720=6!=6D. This is because the time it takes to create such object surpasses the lifetime
of it. When we add the 1/720, the z then differs far more from the e=2.7182…. – we,
therefore, obtain z’ = 2.71880. It is evident that my theory is extremely sensitive to any
changes.
The free tachyons have broken contact with the rest of nature. This leads to conclusion that
in the ground state of nature the nonrotatingspin neutrinoantineutrino pairs are the most
important particles i.e. most important is the phase space containing 24 numbers. The
grouping of the natural numbers in 24 sets leads to the prime number cross and to many
physicomathematical relations (see Chapter titled “Fractal Field”).
π=3.1415… also proves that the Everlasting Theory is correct
Similarly to the number e=2.718…, the number π is also extremely common in physics.
This means that the number π should have very significant physical meaning. The constancy
of π=3.1415… suggests that the smallest stable objects (i.e. an object appearing during the
first phase transition of the Newtonian spacetime) should be inflexible circles (for a circle in a
curved spacetime or for a flexible closed string, the ratio of the circumference to the size is
not equal to π). Because 1 1 =1 2 =1 3 =1, then the mass of a closed string is directly in proportion
to its circumference but to its area and volume as well. Mass are directly proportional to
number of the closed strings they consist of – these strings are inside the neutrinos in the
neutrinoantineutrino pairs that the Einstein spacetime consists of. The closed strings are
inflexible (i.e. they are always an ideal circles) and consists of spinning tachyons. Only the
inflexible closed strings lead to the constancy of the gravitational constant. There also appear
other coincidences associated with the number π. For example, the mass that is responsible for
the weak interactions in the centre of the cores of baryons (approximately 424.1 MeV) is π
times greater than the mass of the neutral pion (approximately 135.0 MeV).
What is the physical meaning of the imaginary unit ‘i’?
The Everlasting Theory leads to an imaginary unit.
The Newtonian spacetime on the circle inside the closed string has entirely broken contact
with the points lying on the plane that the closed string lies, outside of. It looks as if the closed
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string cut the circle out from the Newtonian spacetime. We are able to call such a circle the
imaginary/absent circle. Furthermore, due to the infinitesimal spin of the tachyons, the closed
string has internal helicity – i.e. it produces a real jet (real axis) within the Newtonian
spacetime in a direction perpendicular to the imaginary circle. If we assume that the area of
such an imaginary/absent circle is π (the sign “” relates to the word “absent”) then the radius
of such a circle can be defined by i = sqrt(1).
Summary
The phase spaces of the objects in the ground state of nature (i.e. in the ground states of the
Newtonian and Einstein spacetimes and in the ground state of the field composed of the
protoworlds) and the TitiusBode laws for strong and gravitational interactions lead to the
mathematical constant e=2.718….
The inflexible closed string leads to the π=3.1415… and to the imaginary unit.
Furthermore, we can see that the theory which started from the phase transitions of the
Newtonian spacetime (1997) and the TitiusBode law for strong interactions (1985) is the
lacking part of the ultimate theory of nature because the mathematical constants e=2.718…,
π=3.1415…, and the imaginary unit i=sqrt(1) and the physical constants there are coded.
Such theory must be correct because this theory shows that values of the mathematical and
physical constants depend on properties of the fundamental/Newtonian and Einstein
spacetimes. I proved that the origin of mathematics and physics is associated with the
properties of the Newtonian spacetime that is composed of internally structureless tachyons
that have a positive inertial mass. Such physicomathematical theory needs only 7 parameters.
References
[1] P Plichta; God's Secret Formula: Deciphering the Riddle of the Universe and the Prime
Number Code.
83
Fractal Field
It is very important to unite particle physics with the theory of chaos via a single field.
In the following section, I will attempt to show which properties should have a physical
field and that the creation of fractals was possible.
The physical meaning of the complex number
The formula i(imaginary unit)=exp(iπ/2) shows that the imaginary plane is perpendicular to
the real axis. Let us cut out the circle that has a radius equal to i from the imaginary plane.
The area of the nonexistent circle equals –π. Let us assume that the axis x is the real axis
whereas the plane defined by the axes iy and iz is the imaginary plane. Let as also assume also
that such a mathematical object is moving along the axis iy and that the real axis x rotates
around the axis iy. Using those assumptions the arising wave along the axis iy, associated
with the interval on the real axis x and the interval on the axis iz, describes the
frequently applied Euler formula exp(iφ)=cosφ+isinφ. Are we able to define a physical object
for such a moving mathematical object? Assume that there is a moving and spinning closed
string in existence which has internal helicity and which is placed in the Newtonian gaslike
spacetime. Due to the sufficiently high internal helicity and shape of the closed string, the
winds created around the closed string separate from it on the internal equator of the closed
string because in the pressure of the Newtonian spacetime/gas these points are lowest. The
winds that are separated are the jets perpendicular to the plane defined by the closed string.
The internal equator of the closed string is equivalent to the boundary/edge of the nonexistent/cutout
imaginary circle whereas the jet is equal to the real axis x and the cut out
circle is equal to the imaginary surface. If the jet of such a closed string rotates around the
direction of the motion then the aforementioned Euler formula describes the arising wave.
The cut out imaginary circle has broken contact with closed string i.e. such circle is ideally
flat. The gravitational field and the jets in the Newtonian spacetime are the real parts in this
spacetime. Gravitational field consists of the flat imaginary part (i.e. the Newtonian
spacetime) and the part having a gradient so the gravitational field is the complex volume.
Fractal field
We can describe the behaviour of the binary system of neutrinos in a similar way to the
closed string. I call a fractal field a field that consists of threads that are composed of nonrotatingspin
binary systems of neutrinos where the spins are tangential to the threads.
The divergent or convergent arrangements of the spins of the binary systems of neutrinos
(i.e. of the real axes x) lead to the particle physics whereas the single file arrangement of the
spins (i.e. the single file arrangement of the complex planes) leads to fractal geometry.
The TitiusBode law and bifurcation
The chaos game method [2] leads to the Sierpinski triangle associated with the Pascal
triangle [3]. The sum of the numbers in the succeeding lines of the Pascal triangle are equal to
d=1, 2, 4, 8, 16, 32, 64, 128, 256, and are characteristic for the TitiusBode law
Rd = A + dB, (200)
where A/B=1.39. This means that the TitiusBode law is somehow associated with fractal
geometry i.e. travelling halfdistances, distribution of sources of interactions, and the creation
of consecutively smaller selfsimilar physical objects due to symmetrical decay (bifurcation).
How would the fractal field associated with the TitiusBode law appear?
Assume that the origin of the orbits defined by the TitiusBode law is associated with the
creation of physical rings around the neutron black hole. The temperature was sufficiently
84
high enough to realize the symmetrical decays of the atomic nuclei. When we begin with a
nucleus that is composed of 256 nucleons, then 8 symmetrical decays are possible. On other
hand, however, in following the Uncertainty Principle, this leads to the conclusion that the
ranges of the objects are inversely proportional to their mass. Assume the following model is
possible: The nuclei that contain 256 nucleons appear on a circle (the distribution of the
sources) and have the radius r=A. The range of such nuclei would be B. At distance from B to
the circle are the first symmetrical decays – there appear two nuclei that each contain 128
nucleons. One part of the decay is moving towards the circle whereas the other is moving in
the opposite direction. When the first part reaches the circle, the other stops (at a distance 2B
from the circle) and subsequently the second symmetrical decay is realized, and so on – it is
the mechanism associated with travelling half of the distance between a circle and the place of
the next symmetrical decays. Moreover, within the symmetrical decays smaller and smaller
selfsimilar physical objects appear i.e. smaller and smaller atomic nuclei. As a result, we can
conclude that fractal geometry may be possible due to phenomena similar to the phenomena
that lead to the TitiusBode law.
Creations of fractals in the fractal field
How is the fractal field associated with the fractal geometry?
Assume that in the fractal field all circular electric currents and those inside atoms and
brains as well, create concentric quantized circles. The dipoles in a circle are oriented in such
a way that the spins of the dipoles are tangential to the circle. Such circles are very stable
objects for radii greater than a lower limit. The tangle of the closed threads composed of weak
dipoles and produced by a tangle of circular electric currents leads to a stable ‘soliton’ in the
fractal field. Due to the current decays and circuit breakers (for example neurons can also do
this), smaller and smaller selfsimilar ‘solitons’ are produced. The smaller and smaller selfsimilar
‘solitons’ tangle themselves because they have identical fragments which causes an
attractive force to appear – and subsequently there appears a fractal. Due to the exclusion
principle, the ‘solitons’ in a fractal, should be angled differently, however, the fractals must
always be symmetrical because the binding energy is at its highest then. The attractive force
also acts on fractals that contain identical fragments. We can see that consequently a conflict
for the domination of identical fragments takes place. Such processes are possibly responsible
for the free will.
We see that the theory of chaos is associated with the fractal field composed of moving
threads that are composed of nonrotatingspin dipoles. There is a possibility that the fractals
that appear in such a field can very slowly modify the genetic codes.
How to group natural numbers to obtain a special number theory consistent
with the Everlasting Theory
The Everlasting Theory begins from the four possible phase transitions of a gaslike
Newtonian spacetime and the TitiusBode law for strong interactions. The Newtonian
spacetime consists of the internally structureless tachyons i.e. the mass of tachyons packed to
the maximum is directly in proportion to the size to the power of three. Because of the
dynamic viscosity of the liquid that is composed of maximum packed tachyons, there appear
closed strings that have identical mass. In such closed strings, the tachyons arrange
themselves in an Indian file. For such a string, the mass is directly in proportion to the length
(one dimension) of the closed string but also to its surface (two dimensions) and volume
(three dimensions). Because 1 1 =1 2 =1 3 =1, we can assume that the number 1 represents the
mass of the fundamental closed string. Due to the phase transitions of such closed strings, tori
arise i.e. objects arise that have a mass directly in proportion to their surface i.e. to its size to
the power of two.
85
The transition from the maximum packed tachyons (3D; its mass is directly proportional to
the size to the power of three) to closed strings (1D; its mass is directly proportional to the
length), suggests the production of finite number of sets containing the natural numbers in
such a way that a set containing a prime number should contain also the number equal to this
prime number to the power of three. Following such split, we obtain a grouping of the natural
numbers in 24 infinite sets. If each concentric circle contains 24 succeeding natural numbers
then on first circle there would be 10 prime numbers (the number 1 is the special prime
number, 2, 3, 5, 7, 11, 13, 17, 19, and 23). There also appear 8 radii that contain many prime
numbers that have at the beginning the following prime numbers: 1, 5, 7, 11, 13, 17, 19, and
23 (we can see that nature behaves as if the number 1 was a prime number). For example, the
radius starting from the prime number 13 also contains the following prime numbers: 37, 61,
109, 157, and so on. On this radius also lies the numbers 13 3 , 37 3 , and so on. P. Plichta [4]
referred to the taking place of such a division of the natural numbers for the first time as the
prime number cross. Plichta obtained such a division from the requirement that a radius
starting from number 1 also contained numbers equal to the prime numbers to the power of 2.
I obtained an identical division on using the Everlasting Theory i.e. on the basis of the gaslikeNewtonianspacetimeclosedstrings
transitions. The radius starting from number 1,
containing squares of prime numbers, represents the closedstringstori transitions.
The Everlasting Theory identifies that there is far more physicomathematical analogy than
P. Plichta described. For example, the ten prime numbers on the first circle suggest that the
Everlasting Theory should contain ten parameters. We can reduce the number of parameters
to seven because we can ignore the mass density of three fields. The ten prime numbers also
suggest that the phase space of a closed string should contain ten elements. The radii starting
with the prime numbers 2 and 3 do not contain other prime numbers. This suggests that two
parameters from the seven parameters cannot change with time (in a cosmic scale). Such two
parameters are absolute parameters. They are the mass density of the structureless tachyons
and the dynamic viscosity that leads to the closed strings always having halfintegral spin and
an identical radius. The prime numbers 2 and 3 are also associated with the internal structure
of each microquasar and with the tori arising in the phase transitions of the Newtonian
spacetime. Each microquasar emits two tones and the ratio of their frequencies is 2:3. This is
associated with the ratio of the lengths of the circular axis and the equator in a dense cosmic
object – it is 2:3. Also in existence are only one series of prime numbers (prime numbers =
5+d·6, where d=0, 1, 2, 4, 8, 16, 32, 64, and 128) which leads to the TitiusBode law. We
obtain the TitiusBode law by applying the following gauge symmetry
R(AU) = A + d·B = (5·2/3 + 5 + d·6)/20.34 = 0.41 + d·0.295 i.e. A/B = 1.39.
We know that the numbers 8 (eight rays containing prime numbers) and 24 (each circle of
the prime numbers cross contains twentyfour succeeding natural numbers) are characteristic
for the Ramanujan modular equations. The TitiusBode laws for strong gravitational
interactions and strong interactions respectively lead to three symmetrical decays (there are
the three succeeding prime numbers: 1, 2, 3) and eight symmetrical decays (there are 8 rays).
This suggests that these laws are indirectly associated with the prime numbers. There are also
eight different binary systems of neutrinos with rotating spin.
It is possible that prime numbers are associated with probable exclusion principles because
the states that result from selection rules are as unique as the prime numbers.
Summary
In this chapter, I have described how to unify particle physics with the theory of chaos via a
single field. In the Einstein spacetime theory, carrying electromagnetic interactions are
possible in different arrangements of the dipoles. The divergent or convergent Ketterle type
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arrangements of the spins of the weak dipoles lead to particle physics whereas the single file
arrangement of the spins of the dipoles leads to the fractal geometry.
I have also explained the physical meaning of the complex number. Complex numbers lead
to physical reality, the Pascal triangle leads to the TitiusBode law and the TitiusBode law is
associated with fractal geometry i.e. with travelling halfdistances, with the distribution of the
sources of interactions and with the creation of smaller and smaller selfsimilar physical
objects due to symmetrical decays (the bifurcation).
Fractals appearing in the fractal field can most probably modify genetic codes very slowly.
The grouping of the natural numbers in the twentyfour infinite sets leads to many physicomathematical
relations. Most important are the numbers 2, 8 and 24. The number 2 represents
the rotation of spin, 8 represents the carriers of gluons and photons whereas the phase space of
the nonrotatingspin neutrino or binary system of neutrinos contains 24 elements. We can see
that these three numbers are associated with the ground state of the Einstein spacetime and its
excitations.
References
[1] M W Zwierlein, J R AboShaeer, A Schirotzek, C H Schunck and W Ketterle; Vortices
and superfluidity in a strongly interacting Fermi gas; Nature 435, 10471051 (2005).
[2] E W Weisstein; Chaos Game; MathWorld.
[3] E W Weisstein; Pascal’s triangle; MathWorld.
[4] P Plichta; God's Secret Formula: Deciphering the Riddle of the Universe and the Prime
Number Code.
87
New Big Bang Theory
Theory of tachyons
The Special Theory of Relativity leads to conclusion that no particle can accelerate from
subluminal speed to superluminal speed but symmetry that is characteristic of the energymomentum
relation
E = p 2 c 2 + m 2 c 4
(201)
applied in this theory permits to exist particles all the time moving with superluminal speed
(which I refer to as tachyons) and which have a real (i.e. positive) inertial mass. My
interpretation of this solution of this Einstein equation is as follows. The superluminal speeds
cause that denominator in the energy equation
E = mc 2 /sqrt(1  v 2 /c 2 ) (202)
is imaginary so we can multiply the mass and speeds by the imaginary unit i, where i 2 = 1.
The solution shows that energy of a tachyon decreases when linear speed increases
E = mc 2 /sqrt(v 2 /c 2  1). (203)
Because the mean speed of tachyons is 8·10 88 times higher than the speed of light in
‘vacuum’ (such value leads to the physical constants) then in approximation the energy of
tachyon is inversely proportional to its speed
E(v >> c) = mc 3 /v. (204)
Such phenomenon is possible only if with increasing speed of a tachyon its mass decreases.
This is possible due to the direct collisions of the tachyons. But when size of a tachyon
decreases then area of contact in the direct collisions is smaller and smaller and for some
strictly determined size the grinding of a tachyon ends. The mass of a tachyon does not
increase when it accelerates because the tachyons are moving in the truly empty volume. This
leads to the conclusion that the fasterthanlight particles cannot move through a
field/spacetime but rather with field/spacetime. So wee can assume that the fundamental
spacetime consists of the tachyons placed in truly empty volume.
Supertachyon
Speed of a tachyon should be zero for infinite crosssection of it whereas should be infinite
for sizeless tachyon so we obtain
v = a/r 2 , (205)
where a=0.540031·10 31 m 3 /s for mean tachyon in the Newtonian spacetime.
Mass is directly proportional to volume of tachyon
m = b1·4πr 3 /3 = br 3 , (206)
where b=3.485879·10 86 kg/m 3 for mean tachyon in the Newtonian spacetime.
Due to the flows (in cosmic scale) of finite regions of the Newtonian spacetime, their
condensation is possible. Formulae (204)(206) lead to following formula for a condensation
E = dr 5 , (207)
where d=1.739225·10 143 J/m 5 .
Because the free tachyons have broken contact with the rest of nature and because
practically all binary systems of closed strings are bound inside neutrinos so the Newtonian
spacetime does not act similarly as the Einstein spacetime i.e. the spin energy of the tachyons,
closed strings and neutrinos cannot be converted into mass. This causes that the Planck
critical density and the critical mass are not associated with a condensate in the Newtonian
spacetime. We can calculate radius and mass of a hypothetical supertachyon which mass
density is equal to the Planck critical density c 5 /(hG 2 )=5.1553·10 96 kg/m 3 . This definition is
for a cubic meter so we obtain
c 5 /(hG 2 ) = E/(c 2 L 3 ) = dL 5 /(c 2 L 3 ) = dL 2 /c 2 , (208)
88
where L is the side of the cube. The linear speed of such supertachyon is almost equal to zero
so the definition M/L 3 for the mass density is obligatory. From formula (208) we obtain
L = sqrt(c 7 /(dhG 2 )) = 1.632189·10 15 m. (209)
Radius R of the supertachyon is
R = L/(4π/3) 1/3 = 1.012529·10 15 m. (210)
Mass M of the supertachyon is
M = 4πc 5 R 3 /(3hG 2 ) = 2.2415·10 52 kg. (211)
In reality, because the tachyons have the maximum mass density then a condensate of
tachyons having mass equal to M should have radius about 4·10 12 m.
Of course, the Planck density should have a physical meaning. We can calculate the mean
energy density (not the mean mass density) frozen inside the binary systems of neutrinos a
protoworld consists of. The virtual particles most of all arise on the circular axis of the big
torus and their speeds are equal to the speed of light in the Einstein spacetime. This leads to
conclusion that a hypothetical radius of the Schwarzschild surface for such particles RS is two
times greater than radius of the circular axis and is RS=3.616·10 24 m. Mass of the object is
Mo=1.961·10 52
kg. Energy frozen inside the binary systems of neutrinos is
v 2 /c 2 =(2.4248·10 59 ) 2 times greater than the M. This leads to the mean energy density inside
the sphere which has the radius equal to the hypothetical Schwarzschildsurface radius (for
the virtual particles produced on the circular axis of the big torus) equal to
3Mov 2 /(4πRS 3 c 2 )=5.8·10 96 kg/m 3 . In approximation, we obtained the Planck density. We can
say that in approximation the evolution of the protoworlds begin from the Planck critical
energy density. The same mass density we obtain for the geometric mean of the Einstein mass
of a neutrino (mneutrino) and Newtonian energy of a neutrino (i.e. the energy of the fasterthanlight
closed strings a neutrino consists of mneutrinov 2 /c 2 ) inside sphere that has radius two times
greater than the circular axis of the weak charge of neutrino. The geometric mean
mass/energy is mneutrinov/c=8.1·10 8 kg whereas the geometric mean density 5.8·10 96 kg/m 3 .
The definition of the mass density shows that we obtain the same mass density dividing the
mass and volume by the same factor. To obtain the Planck mass and length, the factor must be
approximately Fx=3.7. It is the ratio of the masses of neutral kaon and neutral pion). I must
emphasize that most important to create particles or cosmic objects (such as, for example,
stars) is mass density, not mass or volume. This means that first of all the Planck density
should have a physical meaning.
Due to the inflation of a supertachyon there appear the binary systems of the closed strings
and next the binary systems of the neutrinos. Due to the spin of a supertachyon as a whole and
the infinitesimally small spin of the tachyons, the supertachyons have internal helicity. It is
also uncharged. This means that finally there only neutrons or only antineutrons appear.
The mass needed to create the Protoworld (i.e. after the period of inflation) and the cosmic
loop (i.e. the early universe) is 2.1431·10 52 kg plus the emitted binding energy (about 2.06 %
of this mass). The needed total mass is 2.1835·10 52 kg. We can see that the surplus mass of
the supertachyon is only 2.7 %.
Eras in the New Big Bang Theory
During a collapse of a region of the Newtonian spacetime pressure increases so also speed
of tachyons. This means that mean radius of tachyons decreases. When such supertachyon
expands in the surrounding Newtonian spacetime composed of slower tachyons, there arises
shock wave that can create a cosmic bulb composed of pieces of space packed to maximum.
Inside such cosmic bulb, the initial parameters cannot change unless there can arise new
supertachyons. In different cosmic bulbs, the initial four of six parameters can have different
values.
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The maximum mass density of a condensate of tachyons is about 8.3·10 85 kg/m 3 . In the
Newtonian spacetime can appear condensates that have different sizes. To create the
Protoworld and the cosmic loop, the minimum radius of a condensate of tachyons should be
about 4·10 12 m. The eras for such hypothetical condensate are as follows. In reality, besides
the Protoworld and the cosmic loop there must be created the two spacetimes so the mass of
the tachyonic condensate must be much, much greater than the hypothetical supertachyon.
The era of the binary systems of the closed strings production: The binary systems of
closed strings arise on the surface of the condensate. Due to the size of the condensate and
the speed of tachyons this era lasted about 10 109 s.
The era of the binary systems of the neutrinos production: From the new theory of the
weak interactions, we know that minimum distance between neutrinos is 2π times (sometimes
2π/3) greater than the radius of the equator of a neutrino. This leads to following maximum
mass density of a volume filled with neutrinos 10 36 kg/m 3 . This means that volume of the
condensate increases about 10 50 times so radius about 6·10 16 times i.e. to about 200 km (it is
approximately a size of a tropical cyclone). Due to the superluminal speeds of the binary
systems of the closed strings this era lasted about 3·10 63 s. Because the neutrinos produce
gradients in the Newtonian spacetime, so their production stops the inflation.
The era of the neutrons production: Minimum distance between neutrons in the neutron
stars is about 2 fm. This leads to following maximum mass density of a volume filled with
neutrons 2·10 17 kg/m 3 . This means that volume of the condensate increases about 4·10 68 times
so radius about 5·10 22 times to about 2·10 11 m (it is approximately the radius of the Earth
orbit). Due to the speeds of the binary systems of the neutrinos, this era lasted about 600 s.
Next the biggest neutron stars appeared.
The era of the protoworlds and the early universes formation lasted at least about 300
million years.
The era of the cosmic loop (i.e. the early Universe) evolution began about 21 billion
years ago. Due to the Protoworldneutrino transition, there appeared the dark energy and the
four inflows of it into the cosmic loop, i.e. into the early Universe, what started the expansion
of the early Universe.
The rotary vortices composed of the binary systems of neutrinos can arise directly in the
Einstein spacetime. Their evolution I described in Paragraph titled “Broken symmetry” in
Chapter “Interactions”.
We can ask following question. Are in the Newtonian spacetime some regions defined by
different initial parameters? In different regions, values of five between the seven parameters
could be different. There are only two absolute parameters i.e. the inertial mass density of the
tachyons (which ties mass with radius) and dynamic viscosity. In overlapping parts of
different regions grinding of the tachyons takes place. We can calculate the lower limit for
size of our region in absence of cosmic bulb. The Universe exists about 21 billion years (i.e.
about 7·10 17 seconds) and tachyons are moving with mean linear speed 2.4·10 97 meters per
second. This leads to the lower limit of the size equal to 3·10 115 meters. This is a vast volume
but we know that the truly empty volume is infinite. The second solution leads to a cosmic
bulb. Then, size of the cosmic bulb can be smaller.
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Reformulated Quantum Chromodynamics
The QCD is the theory of interactions then in this theory appear the distances of mass
characteristic for the atomlike structure of baryons such as the mass of the up quark 2.23
MeV, down quark 4.89 MeV or strange quark 106 MeV. Moreover, due to the strong
interactions described within the atomlike structure of baryons there appear particles carrying
masses the same as the three heaviest quarks i.e. 1267 MeV, 4190 MeV and 171.8 GeV. The
QCD does not lead to the very stable atomlike structure of the baryons. Within the
reformulated QCD, we can derive the masses characteristic for the QCD from the atomlike
structure of baryons.
Experimental data lead to the atomlike structure of baryons. The phase transitions of the
Newtonian spacetime and symmetrical decays of virtual bosons also lead to the atomlike
structure of baryons. In the core is torus which shape leads to the gluon loops which radii are
1A/3 and 2A/3, where A denotes the radius of the equator of the torus. The elementary
electric charge carried by the torus arises from gluon loop which radius is A. The quarks in
the QCD carry the fractional electric charges equal to ±1Q/3 and ±2Q/3 (in the reformulated
QCD the signs of the charges depend on the spin polarization of the surfaces of the torielectriccharges).
Then, assume that the sham quarkantiquark pairs arise from binary systems
of the gluon loops when they overlap with the characteristic orbits in baryons. Assume also
that the linear mass densities of all gluon loops are the same. Then, mass and electric charge
of the sham quarks are in proportion to radii of the gluon loops. There are six different basic
sham quarks. Two of them are associated with the shape of the torus inside core whereas the
next four are associated with the four TitiusBode orbits for the strong interactions. Due to the
value of the sum of mass of the core of baryons and the relativistic pion under the
Schwarzschild surface for the strong interactions, there are only four orbits. There are in
existence the six basic sham quarks for which the gluon loops have following radii: 1A/3,
2A/3, A, A+B, A+2B and A+4B. But there are many other sham quarks when particles
interact. The charges and mass of the six basic sham quarks are as follows.
First: ±1Q/3 and 242.5 MeV
Second: ±2Q/3 and 485 MeV
Third: ±1Q and 727.4 MeV
Fourth: ±1.72Q and 1251 MeV
Fifth: ±2.43Q and 1767 MeV
Sixth: ±3.9Q and 2821 MeV
We can see that the first and second sham quarks have the expected electric charges
whereas the fourth has expected mass. The sham quarks are not a point particles but they
consist of the almost point binary systems of neutrinos which are the Feynman partons. The
sham quarks have only one colour, not three as the quarks. The colour of sham quarks is
associated with their internal helicity. The sham quarkantiquark pairs are colourless. This
shows that it is not enough to call the sham quarks the quarks. In reality, due to the gluon
condensates produced in collisions there arise other gluon loops and next the sham quarkantiquark
pairs.
The ground state of the Einstein spacetime consists of the nonrotatingspin binary systems
of neutrinos. They can carry the rotational energies, i.e. the photons and gluons, so photons
and gluons are the massless particles (they are the rotational energies i.e. the excitations of the
Einstein spacetime). Each rotating binary system of neutrinos has three internal helicities so
the carriers of gluons and photons are the 3coloured particles. The number of different
neutrinos and the three internal helicities lead to 8 different carriers of the photons and gluons.
Outside strong fields, the internal helicity of the Einstein spacetime is equal to zero so to
describe electromagnetism we can neglect the internal structure of the carriers. Due to the
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internal helicity of the core of baryons, the strong fields have internal helicities not equal to
zero so there are the 8 different gluons.
The relativistic W pion in the d=2 state (its relativistic mass is 175.709 MeV) is responsible
for the strangeness of particles.
Due to the four TitiusBode orbits for the strong interactions, the length of the large loops
(their radius is 2A/3) and due to the helicity of the core of baryons and the strong field, there
is the illusion of the confinement of gluons and sham quarks for low and high energies.
The essential part of the curve R(s) = f(sqrt(s)) for electronpositron collisions
The sham quarks appear as gluon loops which linear mass density is the same as the loop
from which the torus inside the core of the baryons arises. Next, they transform into the
baryoniccorelike sham quarkantiquark pairs. This means that mass and electric charge of a
sham quark is in proportion to radius of gluon loop (mshamquark ~ Qshamquark ~ Rgluonloop). For
R=A we have Qshamquark = ±1Q, where 1Q is the electric charge of antiproton. Describe
following curve [1]:
R(s) = σ(e + e  hadrons,s)/σ(e + e  μ + μ  ,s) = ΣQi 2 , (212)
where summation concerns the electric charge of the core of proton (+1Q) and electric
charges of all different sham quarkantiquark pairs produced in the collisions. For low
energies, due to the shape of the torus and the ternary symmetry for the electric/strong charges
(see Chapter “General Relativity in Reformulated Quantum Chromodynamics and New
Cosmology”), inside the core of baryons, there are following electric charges: ±2Q/3, ±1Q/3
and +1Q so we obtain R(s) = 2.1. For production of the coreanticore pairs too, i.e. there are
following charges: ±2Q/3, +1Q and ±1Q, is R(s) = 3.9. The gluon loop overlapping with the
d=1 TitiusBode orbit for the strong interactions leads to the charges of sham quarks ±1.72Q
and to their mass 1251 MeV (is it the charm sham quark?). When in the collisions appear the
charm sham quarkantiquark pairs too we obtain R(s) = 8.9 (+1Q, ±1Q, ±1.72Q). Particles
production (i.e. the numerous different loops production when state is broadening) increases
value of the R. The essential part of the curve R(s) = f(sqrt(s)) is associated with the atomlike
structure of baryons and the sham quarkantiquark pairs production. How to define the
essential part for the sham quarkantiquark pairs production? The Everlasting Theory shows
that the numbers 10 and 26, which appear in the string/M theory, do not define higher
dimensions but the numbers of elements in the phase spaces of a loop (10) and neutrino (26,
fermion) or binary system of neutrinos (26, boson). Such is origin of the fermionboson
symmetry. We can treat the elements in the phase space of a loop (the 10 elements) as the
degrees of freedom. This means that the hypervolume of the phase space and its total mass
(the mass is in proportion to the hypervolume), i.e. the mass of the sham quarkantiquark pairs
created in electronpositron collisions, must be in proportion to the radius of gluon loop to the
power of 10 so also to the ratio R(s) to the power of 5. In the electronpositron collisions, the
gluon loops arise as the binary systems of the binary systems of the gluon loops i.e. as the
quadrupoles. Lightest binarysystem meson, which consists of four gluon loops, is the kaon
K. The electronpositronpairfourgluonloops(quadrupole) transition looks as an analog to
the decay of neutral kaon (there are two opposite electric charges) to charged kaon (there is
quadrupole of gluon loops). In each neutralkaonpositivekaon decay, is emitted energy
approximately 4.032 MeV. Calculate the thresholds for sqrt(s) [GeV] from following formula
sqrt(s)[GeV] = (mkaon(o)  mkaon(+))[MeV]R(s) 5 /1000 (213)
For R(s) = 2.1 we obtain sqrt(s) = 0.16 GeV. Baryons arise as the baryonantibaryon pairs.
This means that to create two the lightest sham quarkantiquark pairs, the minimum value for
the essential part should be sqrt(s)minimum = 0.97 GeV ≈ 1 GeV.
For R(s) = 3.9 we obtain sqrt(s) = 3.6 GeV.
For R(s) = 8.9 we obtain sqrt(s) = 227 GeV.
92
But there is the broadening of the central mass (see the explanations below formula (216))
starting from 3 GeV for R(s) = 3.9 and 191 GeV for R(s) = 8.9.
The additional part of the curve R(s) = f(sqrt(s))
Mass of created particles M we can calculate from formula similar to (213):
M[GeV] = sqrt(s)[GeV] = a(rrange[fm] + A[fm]) 10 , (214)
where rrange denotes range of particle/gluoncondensate created on equator of the torus in core
of baryons whereas A = 0.6974425 fm is the radius of the equator of the torus in the core.
What is physical meaning of this formula? On the equator of the torus, arise the gluon
condensates which masses are the same as the calculated within the atomlike structure of
baryons. Knowing that range of mass equal to mS(+,),d=4 = 187.573 MeV is 4B = 2.00736 fm,
we can calculate range for a gluon condensate from formula
rrange[fm] = mS(+,),d=4[MeV]4B[fm]/mcondensate[MeV], (215)
where mcondensate is the mass of gluon condensate. Since for M = 0.72744 GeV we should
obtain rloop = rrange + A = A, then a = 1/2αw(proton), where αw(proton) = 0.0187229 is the coupling
constant for the weak interactions of baryons. We can rewrite the formula (214) as follows
M[GeV] = sqrt(s)[GeV] = (rloop[fm]) 10 /(2αw(proton)) (216)
The gluon condensates are the regions with thickened Einstein spacetime so they are the
carriers of the weak interactions.
In generally, the particles arise when total length of the loops is equal to the length of the
two electron loops (there collide the electron and positron) or two muon loops. The electron
loop has length 554.3A whereas the muon loop has length 2.68A.
We can see that gluon condensates carrying greater mass (due to higher energy of collisions)
produce lighter particles. This is the reason why in the last LHC experiments for very high
energies the number of produced pions and kaons was greater than expected [2]. This means
also that for higher and higher energies of collisions, there are weaker and weaker signals that
there is in existence the atomlike structure of baryons. Just for higher and higher energies,
more and more baryons have destroyed the TitiusBode orbits for the strong interactions. To
‘see’ the atomlike structure we should analyse the weak signals for the medium energies of
collisions i.e. close but below about 1 TeV. Gluon condensates carrying mass following from
the atomlike structure of baryons can create new particles. There should be a weak signals of
existence of the type Z o particles for the d states. There arise gluon balls which have mass
equal to the mass distance between the charged and neutral relativistic pions in the d states
multiplied by the Xw = 19,685.3 (see formula (57)). Their mass should be 105 GeV for the
last state for the strongweak interactions, 118 GeV for the ground state above the
Schwarzschild surface for the strong interactions and 140 GeV for the ground state (see
formula (219)). These mass follow from the atomlike structure of baryons. Such gluon balls
arise in centre of the baryons and decays between the equator of the torus (radius = A) and the
sphere between the strong and electromagnetic fields (radius of the last d=4 orbit is 2.7 fm
whereas the range of the strong field is 2.9 fm so the mean value is 2.8 fm). The mean value
for the lifetime or mass we obtain for the Schwarzschild surface for the strong interactions
(radius = 1.4 fm). We know that lifetime is inversely proportional to range. This means that
maximum lifetime to the central value is 2. On the other hand, lifetime is inversely
proportional to four powers of mass (see formula (89)). This means that to calculate the
broadening of the central mass, we must multiply and divide the central mass by 2 1/4 =
1.1892. Respectively, the broadenings of mass are as follows: the (88, 125) GeV for the 105
GeV, (99, 140) for 118 GeV and (118, 166) for 140 GeV. For the mean central mass (105 +
118 + 140)/3 = 121 GeV, the final broadening is (88, 166) GeV. Similar data experimentalists
obtained in the SLD (SLAC Large Detector) experiment [3]. In the highenergy regime, the
TitiusBode orbits are in great part destroyed so there dominate the phenomena on the
93
Schwarzschild surface. For this surface (radius is 2A) we obtain 128 GeV and it is in
approximation the mean value for the interval (88, 166) GeV i.e. (88 + 166)/2 = 127 GeV.
The values 105 GeV, 118 GeV, 140 GeV and especially the 127128 GeV are most important
in the latest LHCexperiment data [4].
Due to the interactions of the core of baryons with bosons, we observe the mass broadening
for the Z o boson. Calculate mass of particle produced by gluon condensate carrying mass
equal to the sum of mass of the core of baryons (727.44 MeV) and charged pion (139.57
MeV). The total mass is 867 MeV. Calculated mass of the particle is 92.0 GeV and it is the Z o
boson. The broadening is from 77 GeV to 109 GeV but the ends of this interval are
broadening by the virtual mass of the core i.e. 727.44 MeV and virtual mass of nucleon i.e. in
approximation 939 MeV. For such condensates R(s) = 3.9 whereas the sqrt(s) respectively are
188 GeV and 68 GeV. The broadening of the 188 GeV is (158, 223) whereas of the 68 GeV is
(57, 81). These two signals should be weak, i.e. the R(s) should be much lower than for the Z
boson. The three intervals overlap partially or are tangent. The sum of the three intervals is
(57, 223) GeV what is consistent with experimental data.
For the maximum of the R(s), there arise about 683 gluon loops and each sham quark has
electric charge equal to ±1.623Q. This means that the maximum for the R(s) should be in
approximation 1800. For collision of two electronpositron pairs (the quadrupole), we obtain
R(s) ≈ 3600. The mass of the Z o boson we can calculate also from following formula
(mpion(+) mpion(o),freeXw = 90.4 GeV, (217)
where Xw = w(proton)/w(electronmuon) = 19,685.3. This boson can decay into hadron jets.
Comparing the formulae (213) and (217) shows that the Z o is not a part of the essential part of
the curve R(s) = f(sqrt(s)) whereas the W + boson could be
(mkaon(0) mkaon(+)Xw = 79.4 GeV, (218)
but it is only an illusion.
We should observe a weak peak in the data for mass equal to the distance of the relativistic
masses between the relativistic pions in the d = 1 state (it is 7.11 MeV) multiplied by the Xw
(mW(+),d=1 mW(o),d=1Xw = 140 GeV. (219)
Particle carrying such mass I will refer to as Zrel. The obtained theoretical result is consistent
with the last data [5]. We can see that the Zrel particle is the type Z o particle so it decays into
hadron jets. The Zrel particles arise also due to the transition of gluon balls or loops carrying
mass equal to 780 MeV – in approximation, it is mass of the ω meson (its mass is 782 MeV).
Calculate mass of a particle produced by gluon condensate carrying mass equal to the mass
of the Φ3(1850) meson (m = 1854 ± 7 MeV [6]). Calculated mass for mass equal to 1847
MeV is 9.45 GeV. This mass is close to the mass of the Y(1S, 9460 [6]). There are 863 loops
and each sham quark carries electric charge equal to ±1.289Q. This leads to R(s) ≈ 1440. For
collision of two electronpositron pairs (the quadrupole) is R(s) ≈ 2880. The mass of the
π(1800) meson (m = 1816 ± 14 MeV [6]), i.e. the value 1813 MeV, leads to the χb0(1P)
meson (m = 9859 MeV [6]).
Masses of quarks applied in the QCD
Masses of quarks applied in the QCD we can calculate within the reformulated QCD that
follows from the atomlike structure of baryons.
Mass of the up quark (it is the up sham quark because its electric charge is different) is
equal to the half of the distance of masses between the two states of proton (2.23 MeV).
Mass of the down sham quark is equal to the half of the distance of masses between the two
states of neutron (4.89 MeV).
Mass of the strange sham quark (106 MeV) is equal to the distance of masses between the
point mass in the core of baryons (in approximation Y = 424 MeV = 4·106 MeV) and the
torus in the core of baryons (in approximation X = 318 MeV = 3·106 MeV). Moreover, the
94
mean relativistic mass of the relativistic pions in the d = 2 state is in approximation R = 212
MeV = 2·106 MeV. Ratio of (X + Y)/R and X/Y is in approximation 14/3 = 4.667. The exact
calculations lead to 4.66913…. Obtained result is close to the Feigenbaum constant δ =
4.66920… We can see that the mass of the strange sham quark is indirectly associated with
the Feigenbaum universality. The point mass Y is responsible for the weak interactions of
baryons so the Y = 4·106 MeV leads to the quadrupole symmetry for the weak interactions so
also to the bidipoles of neutrinos (spin = 2) responsible for emission and absorption of
gravitational energy/mass. The internal structure of torus and the mass R are responsible for
the strong interactions. This means that the X = 3·106 MeV leads to the ternary symmetry for
the strong interactions of the torus (i.e. the core of baryons plus a particleantiparticle pair)
whereas the R = 2·106 MeV leads to the binary symmetry for the strong interactions (i.e. to
particleantiparticle pairs so to some mesons as well). There are also the 3 different electric
charges associated with the torus in the core of baryons: 1Q/3, 2Q/3 and Q. This is the ternary
symmetry for the electromagnetic interactions.
Applying formulae (215) and (216), we can calculate the masses of the three heaviest
quarks. Mass of gluon condensate equal to mass of the Υ(1S, 9460 MeV) leads to the mass of
the charm sham quark M = 1267 MeV. Mass of the bare electronpositron pair is 4 times
greater than the circular mass of electron, i.e. than the mass of electric charge of electron.
Some analog composed of the strong charges/masses (its mass is 4X) has mass close to the
mass of the charm quark as well and is 1273 MeV. Mass of gluon condensate equal to mass of
the sixth basic sham quark, i.e. mcondensate = 2821 MeV, leads to the mass of the bottom sham
quark M = 4190 MeV. The sixth basic sham quark is the valence quark so we can treat the
bottom sham quark as the valence quark also. It is the reason why the calculations of the
running coupling for the strong interactions via the bottom sham quark are simplest [7]. Mass
of gluon condensate equal to sum of masses of the torus inside the core of baryons
(X=318.2955 MeV) and the point mass (Y=424.1245 MeV), i.e. mcondensate = 742.42 MeV,
leads to the mass of the top sham quark M = 171.8 GeV.
When there appear the charm sham quarkantiquark pairs (m = 2·1267 ≈ 2.5 GeV) that carry
the electric charges ±1.72 Q, then there is forced the quadrupole symmetry for the electric
charges (±1Q/3, ±2Q/3, ±1Q and ±1.72Q i.e. four different charge states) characteristic for the
weak interactions. Strong mass of virtual particles produced by a pair is 2αSm so weak mass is
2αWαSm. This means that the running coupling for the strongweak interactions is αSW =
2αWαS (see formula (79)). For example, the weak mass of virtual particles produced by the
strong mass of the K kaon is in approximation equal to the mass of pion. This means that for
energy about 7.1 GeV there appear the ‘horns’. This is consistent with the experimental data.
We can see also how the mass of a charm sham quarkantiquark mass defines the energy E1
for the transition from the strong to the strongweak interactions. The energy E1 is about 2/3
times lower than the mass 2.5 GeV. To see the transition, the collision energy must be higher
than the 2.5 GeV.
Similarity of interactions of different sham quarks follows from the fact that their masses
and electric charges are in proportion to radii of their equators.
We see that mass of particles follow from the atomlike structure of baryons. Particles can
arise also due to the decays of the gluon condensates.
Origin of limitations in nonreformulated QCD
Here I explain the origin of the limitations in the asymptotic freedom described within the
mainstream perturbative QCD. The limitations follow from the fact that we neglected the
atomlike structure of baryons. The perturbative QCD does not lead to correct results for the
asymptotic freedom in the low energy regime, there appears the mass scale 5 GeV and the
95
free parameter about 217 MeV. The nonperturbative Everlasting Theory is valid in whole
spectrum of energy.
At first, I will point the important things concerning the asymptotic freedom in the
mainstream QCD.
1.
In the Lagrangian appear the dimensionless coupling constants. We can change one of them
(i.e. the integration constant) on the free dimensional parameter i.e. the QCD scale i.e. the
lambda parameter. Its central value is 217 MeV. The lambda parameter sets the scale at which
the alpha_strong becomes large i.e. below this mass/energy we cannot apply the perturbative
QCD. We must apply some nonperturbative theory.
2.
In the perturbative QCD appears the mass scale which is chosen arbitrary. The asymptotic
freedom is for mass scale about 5 GeV i.e. greater than the mass of the bottom quark and
much smaller than the mass of the top quark i.e. about 172 GeV.
3.
The QCD is asymptotically free thus for large energy we can use perturbative theory safely.
4.
In perturbative QCD absolute value of alpha_strong has to be obtained from experiment.
Today the fundamental parameter is the alpha_strong for the mass of the Z boson (91.19
GeV). The experimental data for the mass of the Z boson are as follows (see hepex/0407021,
(2004)):
Alpha_strong(mass of Z boson) = 0.1182 ± 0.0027.
The nonreformulated perturbative QCD gives 0.118 ± 0.006 (see S. Weinberg book
“Quantum Theory of Fields”, Volume II, (1996)).
What says the Everlasting Theory about origin of the limitations concerning the asymptotic
freedom described within the nonreformulated QCD?
1.
The reformulated QCD shows (see formulae (214)(216)) that there appears the energy 3.3
GeV which is the lowest limit of energy of collision above which produced gluonballs, which
are responsible for the strongweak interactions in the perturbative regime (i.e. in the nonreformulated
QCD), have mass lower than the lowest limit. We can see that in the nonreformulated
QCD must appear the mass scale but why the applied mass scale 5 GeV (this
mass is greater than the mass of the bottom quark about 4.2 GeV) is higher than the 3.3 GeV
(this mass is greater than the mass of the charm quark)? It is because for mass scale 3.3 GeV
we cannot neglect the mass of the bottom quark (4.2 GeV>3.3 GeV) and then we obtain
incorrect theoretical results. We can see also that the law of conservation of energy is
obligatory for energies higher than 3.3 GeV i.e., then, mass/energy of produced gluonball(s)
is lower than energy of collision. In this point, we should add that from the formula (216)
follows that when energy of collision increases then masses of the created gluonballs are
smaller and smaller i.e. the alpha_strong decreases. It leads to the asymptotic freedom in the
perturbative QCD. It is also the reason that we detect much more the pions and kaons than it
was expected in the highenergy regime.
In the perturbative QCD the mass scale 5 GeV is above the threshold 3.3 GeV so we should
obtain correct results but there is needed one additional free parameter which will eliminate
the great values of the alpha_strong.
2.
The asymptotic freedom within the Everlasting Theory follows from the law of conservation
of spin, atomlike structure of baryons and Uncertainty Principle. When energy increases then
mass of the carriers of the strong interactions decreases. This follows from the coupling of the
core of baryons with the Einstein spacetime. It is obligatory for the whole spectrum of
96
energies and for the mass of the Z boson we obtain from formulae (81), (83) and (86)
following result:
Alpha_strong(mass of Z boson) = 0.1176 ± 0.0005.
This value is consistent with experimental result.
3.
What is physical meaning of the lambda parameter 217 MeV (+25, 23)?
The atomlike structure of baryons shows that in the d = 1 state, which lies under the
Schwarzschild surface for the strong interactions, there can be the relativistic neutral pion
which mass is about 209 MeV or relativistic charged pion which mass is about 216 MeV (see
Table 1, page 18). Both masses are consistent with value of the lambda parameter. This shows
that for energies below the lambda parameter, we must apply the nonperturbative Everlasting
Theory because we cannot neglect the relativistic masses of the pions which are the carriers of
the strong interactions as well.
4.
There should be differences for the alpha_strong for very high energies. For example, for
energy 2.76 TeV, I obtained alpha_strong = 0.114.
Recapitulation
I showed the close relations between the perturbative QCD and the Everlasting Theory. The
Everlasting Theory, especially the atomlike structure of baryons, shows the origin of the
limitations in the perturbative QCD. The described limitations follow from the fact that the
perturbative asymptotic freedom fully neglects the internal structure of the core of baryons.
The Everlasting Theory, which is the more fundamental theory than the perturbative QCD,
leads to origin of the limitations in the perturbative QCD. Due to the mass scale, the law of
conservation of energy is valid and we can neglect the masses of the quarks bottom, charm,
strange, down and up. The free lambda parameter appears to eliminate the great values of the
alpha_strong. The lambda parameter is associated with the d = 1 state which appears in the
atomlike structure of baryons.
The last data (2011) lead indirectly to the core of baryons as well. The Everlasting Theory
leads to the charged core. Its mass is 727.44 MeV. Such core produces virtual gluons which
masses are ±727.44 MeV. On the other hand, in following paper: J. Phys. G: Nucl. Part. Phys.
38 (2011) 045003 (17pp), O. Oliveira and P. Bicudo find that “the infrared data (low energy)
can be associated with a constant gluon mass of 723(11) MeV, if one excludes the zero
momentum gluon propagator from the analysis.” This means that the infrared data lead
indirectly to the core of baryons.
Summary
Due to the atomlike structure of baryons, we should reformulate the QCD. There appear the
6 basic sham quarks and 8 gluons. The gluonloopsbasicshamquarks transitions lead to
the essential part of the curve R(s) = f(sqrt(s)). The particlesgluoncondensatesnewparticles
transitions cause the particles transform into new particles. The new particles are the
additional part of the curve R(s) = f(sqrt(s)). The atomlike structure of baryons, internal
structure of the kaons K and their decays in strong fields are most important to understand the
phenomena associated with the highenergy collisions of particles. The reformulated QCD
contains six parameters only.
The calculated mass of the top quark (171.8 GeV) is associated with the edge of the core of
baryons whereas the calculated mass of the bottom quark (4190 MeV) is associated with the
edge of the strong field. There should be in existence the next two flavours of the quarks
associated with the state d = 1 (26.3 GeV) and state d = 2 (10.46 GeV) but probably the
“edges” concerning these orbits/tunnels are too small to detect distinct signals.
98
References
[1] http://pdg.lbl.gov/current/xsect; K. Nakamura et al. (Particle Data Group), J. Phys. G 37,
075021 (2010)
[2] The CMS Collaboration; Transversemomentum and pseudorapidity distribution of
charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV;
arXiv: 1002.0621v2 [hepex] 8 Feb 2010
[3] http://vixra.files.wordpress.com/2011/08/gfitvars.jpg
[4] http://www.atlas.ch/news/2011/figurecombo2.html
[5] http://blois.in2p3.fr/2011/transparencies/punzi.pdf
[6] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)
[7] D.J. Gross, F. Wilczek (1973). "Ultraviolet behavior of nonabelian gauge theories".
Physical Review Letters 30 (26): 1343–1346. Bibcode 1973PhRvL..30.1343G.
doi: 10.1103/PhysRevLett.30.1343
99
Proton and Loops as Foundations of Theory of Chaos
This theory leads to the atomlike structure of proton. There is the core and outside it is in
force the TitiusBode law for the strong interactions. The binary systems of neutrinos, i.e. the
Einstein spacetime components, carry the massless gluons and photons. Strong field has
internal helicity – this causes that properties of gluons depend on internal structure of binary
systems of neutrinos because each such system has three different internal helicities. There
are eight different gluons. We can neglect the internal helicities outside strong fields. This
means that outside strong fields the gluons behave as photons. Proton consists of additional
Einstein spacetime components. In collisions of baryons, there arise gluon loops that outside
the strong field behave as photon loops or photons. Some ratio of the masses of the proton
components leads to the Feigenbaum constant. The internal structure of proton, via some
structures built up of the Einstein spacetime components, leaks outside it. This leads to the
Feigenbaum universality. The atomlike structure of proton leads to bifurcation also.
Concentric loops composed of the Einstein spacetime components arise due to the weak
interactions and lead to the Mandelbrotlike sets. The structure of bare particles and binding
energies associated with this structure cause that elimination of renormalization is possible.
This is possible because the internal structure of proton codes the Feigenbaum constant
applied in the renormalization group theory. Properties of the two spacetimes show that
trajectories of the quantum particles in the Einstein spacetime have no sense.
New particle theory has much more the ‘tangent points’ with the theory of chaos than the
SM. Theory of chaos leads to the correct structure of baryons.
The Everlasting Theory and some experimental data lead to the atomlike structure of
baryons, six basic sham quarks and eight gluons. The phase transitions of the fundamental
spacetime lead to the core of baryons that consists of the torus and point mass in its centre.
The point mass (Y = 424.1245 MeV) is responsible for the weak interactions of baryons
whereas on the circular axis inside the torus arise the large loops (mass = 67.5444 MeV)
responsible for the strong interactions. Symmetrical decays of virtual bosons cause that
outside the core of baryons is obligatory the TitiusBode law for the strong interactions. The
equator of the sixth basic sham quark overlaps with the last orbit for the strong interactions. I
will try to show that the logistic map [1] and the Feigenbaum constant and bifurcation [2] are
associated with the internal structure of proton.
Due to the two spacetimes, we should change interpretation of the quantum mechanics. New
interpretation leads to nonlinearity and shows how we can eliminate it.
The logistic map and structure of baryons
The logistic map we can write as follows [1]
xn+1 = kxn(1  xn). (220)
Assume that the control parameter k is 1 for radius of the gluon loop from which the lightest
sham quark arises i.e. for A/3 is k = 1 (A = 0.6974425 fm is the radius of the equator of the
torus inside the core of baryons). Then, for the gluon loop from which the third basic sham
quark arises, i.e. the core of baryons, is k = 3. Assume also that the xn is the distance r from
the centre of the point mass in the centre of the core of baryons and for A is xn = 1. After the
gluonloopthirdbasicshamquark transition, the energy released in collisions of baryons
appears first of all as the large loops on the circular axis of the torus in the core of baryons.
The large loops are responsible for the strong interactions of mesons whereas the binary
systems of the large loops (i.e. the pions) are responsible for the strong interactions of
baryons. For the circular axis is xn = 2/3. We can see that the xn = 2/3 is the attractor for k = 3.
For k < 1, the point mass attracts the surplus energy/mass so the xn = 0 is the attractor for the
k < 1.
100
To conserve the spin of the core, the large loops cross the equator of the core of baryons as
the binary systems of the large loops with antiparallel spins i.e. as the pions or are open. To
conserve in strong fields the symmetrical fusions/decays, the bosons appear as the groups
containing 2 d bosons, where d = 0, 1, 2 and 4.
The Feigenbaum constant and bifurcation code the structure of proton
Outside the core of baryons is obligatory the TitiusBode law for the strong interactions
xn = A + dB, (221)
where d = 0, 1, 2, 4 whereas B = 0.50184 fm. In the d = 4 state, the carrier of the strong
interactions (it is group of eight loops) decays to 16 gluons. Calculate the range of a gluon
ball which mass is equal to the mass of the gluon loop from which arises the most heavy basic
sham quark i.e. the sixth basic sham quark (mass = 2821 MeV). Mass of the gluon ball is (X +
Y)/mH(+) = 1.020593 times greater than the mass of a sham quark because during the sham
quark creation is emitted the weak binding energy. In the last formula the X = 318.2955 MeV
is the mass of the torus inside the core of baryons whereas mH(+) = 727.440 MeV is the mass
of the core of baryons. This means that the mass of the gluon ball is 2879 MeV. Since range
of mass equal to mS(+,),d=4 = 187.573 MeV is 4B = 2.00736 fm then range of the gluon ball is
Δr = 0.13078 fm. If such gluon ball arises on the equator of the torus in the core of baryons
and its motion is radial then it transforms into the sham quark in distance r from centre of the
point mass where r = A + Δr i.e. r = 0.82822 fm. Since k = 1 for A/3 then for the r = 0.82822
fm we obtain k = 3.5625 whereas the Feigenbaum bifurcation, for the cycle 2 n = 16 leads to k
= 3.5644. Because the equator of the sixth sham quark overlaps with the last orbit for the
strong interactions then we can say that the k = 3.5625 is some analog to the upper limit for
the strong interactions. I should emphasize also that the set of numbers d = 0, 1, 2 and 4 for
strong field is characteristic for a perioddoubling cascade. In the strong fields most important
are facts that the symmetrical decays are the preferential decays and that range is in inverse
proportion to mass of a particle. This leads to the perioddoubling cascade. The fourneutrino
symmetry leads also to n = 3, 6, 12 perioddoubling cascade whereas for the neutron black
holes is d = 1, 2, 4, 8, 16, 32, 64, (for binary system is 96 too) and 128. In the d = 4 state is the
gluonphoton transition (more precisely, in distance 4πA/3). The carriers of the photons and
gluons interact weakly. Due to the ratio of the coupling constants for the weak interactions of
proton and electron Xw = w(proton)/w(electronmuon) = 19,685.3, the radius of the Bohr orbit is in
approximation Xw times greater than the last orbit for the strong interactions A + 4B ≈ 2.7 fm.
In biology and chemistry most important are the electromagnetic interactions so to solve
some problems which appear in these two fields of knowledge we must know the internal
structure of protons, electrons and fields. Nonlinearity appears when we do not take into
account the local binding energies. Can the internal structure of proton lead to the
Feigenbaum constant δ = 4.669201609? The core of proton consists of the point mass, torus
and by analogy to the source of the radiation mass of an electron, of an electronpositron pair
and its electromagnetic mass that appears in interactions. When we neglect the binding
energies then mass of the core of proton (all baryons) is mcore,chaos = Y + X + 2melectron(1 + αem)
= 743.4498 MeV. Mean mass of the relativistic pions in the d = 1 state we can calculate from
following formula
MW,d=1,mean = mW(o),d=1y + mW(+),d=1(1  y) = 212.1417 MeV. (222)
In interactions, in the d=1 state, there appears additional electromagnetic energy, not
associated with a binding energy, equal to
Δmem = (mW(+),d=1  mW(o),d=1)(1  y)αem = 0.025535 MeV. (223)
The mean energy in the d = 1 state not associated with the core is
Z = MW,d=1,mean + Δmem = 212.1673 MeV. (224)
Calculate following ratio
101
(mcore,chaos/Z)/(X/Y) = 4.66913 MeV. (225)
In the numerator is the ratio of the mass of the two parts of the proton as a whole (core and
relativistic pion) whereas in the denominator is the ratio of the mass of the two parts of the
core of proton (torus and point mass). We can see also that the nominators in both nominator
and denominator contain the mass of torus associated with the electric charge. Due to the two
spacetimes, the internal structure of proton ‘leaks’ outside the strong field of proton – this is
due to the carriers of the gluons and photons i.e. due to the binary systems of the neutrinos the
Einstein spacetime consists of. We can see that the calculated ratio is close to the Feigenbaum
constant. The ‘leaking’ structure of proton (the leaking information concerning the internal
structure of proton) causes that different systems behave identically (qualitatively/structurally
and quantitatively/metrically) – this leads to the Feigenbaum universality. We should notice
also that the ratio of the mass of the torus X, i.e. the mass of the source of the strong
interactions, to the mass of the carrier of the strong interactions for mesons, i.e. the mass of
the large loop (67.5444 MeV), is close to the Feigenbaum constant and is 4.71.
Notice also that 3 + Y/mcore,chaos = 3.5705 whereas Y/(mcore,chaos + Z) = 0.4438. For real
proton is Y/mproton = 0.4502. The last two results are close to the exponent β = log2/logδ =
0.4498 applied in the renormalization group theory.
Mandelbrot set
Impulses of electric current create concentric loops composed of the Einstein spacetime
components i.e. the binary systems of neutrinos (the weak dipoles). A loop is stable when
spins of the weak dipoles are tangent to the loop. Weak mass of virtual particles produced by
a loop we can calculate from formula mw = αwm, where m is the mass of a loop whereas αw is
the coupling constant for the weak interactions. For example, the weak mass of virtual
particles produced by the large loop is equal to the distance of mass between the neutron and
proton. Due to following formula, a larger loop creates smaller loop, and so on
αw,n+1 = Gw(αw,nm) 2 /(ch) + C1, (226)
where Gw is the weak constant whereas C1 is a constant which follows from entanglement of
the components of the loops – they exchange the binary systems of the closed strings the
neutrinos consist of. Field composed of groups of such sets composed of the concentric stable
loops is the fractal field. Physical properties of such field we can describe applying the
imaginary unit i = sqrt(1). There appear the polar form of complex numbers, i.e. the
imaginary unit and the sine and cosine, and second power of moduli of the complex numbers
i.e. the quadratic functions. We can rewrite formula (226) as follows
αw,n+1 = C2(αw,n) 2 + C1. (227)
This relation is an analog to the Mandelbrot map
zn+1 = zn 2 + C. (228)
It is iteration on the complex plane of following type: take a complex number z, calculate its
second power and add an initial number C, and so on.
The 3spacedimensional fractals produced, for example, by brains I refer to as the
‘solitons’. Creative thinking leads to phase transitions of smaller ‘solitons’ to greater
‘solitons’. Next, there is period of rebuilding of the ‘solitons’ containing false fragments.
Such period can last for very long time.
Types of mechanics, elimination of nonlinearity
We know that mechanics of chaos is the nonlinear mechanics. There is the very good
description of the transition from the classical mechanics (we know all trajectories) to statistic
mechanics (the phase spaces contain averaging parameters also). Whereas due to the lack of
the correct description of the internal structure of spacetime(s), the description of the
transition from the statistic mechanics to quantum mechanics is not good. The Everlasting
102
Theory leads to two spacetimes. The fundamental spacetime, i.e. the Newtonian spacetime, is
practically the scalar spacetime and is statistical whereas the Einstein spacetime composed of
the weak dipoles, i.e. of the binary systems of neutrinos, is the quantum spacetime. Due to the
scalar/statistic spacetime, particles, which arise in the quantum spacetime, disappear in one
place and appear in another and so on. Sometimes the quantum particles arise in places very
distant from the places of disappearing. This means that trajectories of quantum particles have
no sense in the quantum mechanics. To describe ‘motions’ of the quantum particles such as,
for example, electrons and photons we need the wave functions and probabilities.
What is the origin of the linearnonlinear transition? The Newtonian gravity is linear
because is associated only with the scalar spacetime. In such spacetime quantum particles
cannot appear. Nonlinearity is associated with the spacetime composed of the weak dipoles.
Properties of this spacetime cause that superposition is not characteristic for the Einstein
gravity. This is due to the internal structure of the virtual bare particles and local binding
energies that locally change mass density of the spacetime composed of the weak dipoles. We
can see that the locally changing mass density leads to the nonlinearity of the metric tensor in
the Einstein equations. Since the metric tensor defines geometry of spacetime then geometry
of spacetime depends nonlinearly on mass density. Similarly is for the weak, strong and
electromagnetic interactions because they are associated with the quantum spacetime. The
changing local mass densities lead to the mechanics of chaos. When we take into account the
internal structure of bare particles and appropriate binding energies, sometimes we can reject
the perturbation theory. Applying such mechanism, I formulated new theory of interactions.
Summary
The atomlike structure of baryons described within the Everlasting Theory leads to the
logistic map and Feigenbaum constant and bifurcation applied in the theory of chaos. The
internal structure of proton ‘leaks’ outside it due to the carriers of the gluons and photons i.e.
due to the binary systems of neutrinos the Einstein spacetime consists of. The ‘leaking’
structure of proton causes that different systems behave identically – this leads to the
Feigenbaum universality i.e. the Feigenbaum scaling is the same for many functions (for
example, xn+1 = kxn(1  xn) and xn+1 = rsinπxn) and processes. We can say that nature
‘chooses’ such functions some phenomena were in resonance with the internal structure of
proton. Information of the structure of proton leaks due to the virtual structures composed of
the entangled Einstein spacetime components. They are the ghosts of protons and they carry
the negative degrees of freedom i.e. due to the entanglement, the virtual structures absorb
surplus energy. This causes that we can apply the renormalization group theory so the
Feigenbaum scaling also. We can eliminate the renormalization group theory via the correct
internal structure of the bare particles and local binding energies.
Impulses of electric current create concentric loops composed of nonrotatingspin binary
systems of neutrinos with spins tangent to the loops. Entanglement of groups of such sets
composed of the particular loops leads to the Mandelbrotlike set.
Chaos is due to the lack of the initial synchronization with the internal structure of protons
and the fourneutrino symmetry. The attractors appear because a system wants to synchronize
its behaviour with the Universe/nature.
Due to the two spacetimes, trajectories of quantum particles have no sense. The more
fundamental spacetime, i.e. the Newtonian spacetime, is statistical/deterministic whereas the
second, i.e. the Einstein spacetime, is quantum/nondeterministic and leads to the free will.
Due to the interactions of the deterministic and nondeterministic fields, the
quantum/nondeterministic fields try to behave in deterministic way. Nondeterministic
behaviour appears sporadically only when deterministic behaviour is broken.
103
Nonlinearity follows from the locally changing binding energy. We can eliminate
nonlinearity when we take into account internal structure of bare particles and appropriate
binding energies. For example, we can calculate the emitted binding energy by electron or
muon due to the electroweak interactions of the virtual electronpositron pair(s) with the bare
electron or muon. There are two methods to calculate the magnetic moment of electron: via
the Feynman diagrams or via internal structure of bare electron and local binding energies.
The first method is nonlinear whereas the second is linear and very simple. Due to the local
phenomena that follow from nonlinearity, the nature drifts towards linearity. When we neglect
the local phenomena then geometry of spacetime and other fields depends nonlinearly on
mass density.
We cannot eliminate the nonlinearity from mathematical description of a system in which
local binding energies behave in unforeseeable manner and the system cannot emit them at
least partially. But even then, detected noise carries some information about mean values of
the local binding energies. Sometimes the mean values change over time in unforeseeable
manner. Then, prediction of behaviour of such system is impossible. When a system cannot
eliminate the nonlinearity via emission of the local binding energies turbulence appears.
Turbulence is a disorder without rules. Chaos is an ordered disorder via simple
processes/rules. Attractors appear due to convergent lines of forces, perioddoubling cascades
appear due to symmetrical decays of particles whereas 3D fractals due to cascades of smaller
and smaller loops.
The purposeful causes are typical only for free will. The matrices of the DNA arose before
the ‘soft’ big bang and are composed of many of the four different weak dipoles (they are the
carriers of the photons and gluons). Some ‘purposeful behaviour’ of many systems follows
from the ‘leaking’ internal structure of proton and the coded information in the DNA
matrices.
References
[1] Weisstein Eric W., ”Logistic Equation” from MathWorld
[2] Feigenbaum Mitchell, Universal Behaviour in Nonlinear Systems, “Los Alamos
Science” 1 (1981)
[3] Mandelbrot Benoit, Fractals and the Rebirth Iteration Theory in: Peitgen HeinzOtto,
Richter Peter H., The Beauty of Fractals, p. 151160, (Berlin: SpringerVerlag, 1986)
104
Theoretical Curve for the KaontoPion Ratio
Some experimental data leads to the atomlike structure of baryons. This theory leads to
following conclusions. There is core composed of the torus with point mass in its centre. The
structure of the torus leads to the laws of conservation of the electric charge and spin. There
appears internal helicity of the torus. Positive electric charges as, for example, of proton,
positron and positive pion, have the left internal helicity (this concerns the core of neutron
also) whereas the negative electric charges and antineutron have the right internal helicity.
The gluon loops or pions or other bosons carry the strong interactions. Pions are the binary
systems of gluon loops whereas the kaons are the binary systems of binary systems of gluon
loops so they are the quadrupoles. Strong field has internal helicity the same as the torus in
the core. Since the kaons are the binary systems, so the produced kaons always have the
resultant internal helicity the same as the torus in the core i.e. the helicity does not depend on
electric charge of kaons. The kaontopion ratio mostly depends on internal helicity of the
electric charge inside pions. Experimental data that concern the kaontopion ratio are
collected on following website [1].
Characteristic values for the kaontopion ratio
Number of produced particles is inversely proportional to their mass. For the K/π ratio is
K/π = mi/mkaon(+) , (229)
where mi is the mass of loops composed of gluons or structures composed of gluon loops
whereas mkaon(+) is the mass of the charged kaon. When energy of collisions increases then
there are produced more and more of more energetic gluons, loops and structures. Pions are
the binary systems of gluon loops and mass of each loop for resting pion is 67.54 MeV and
consists of two gluons. Each such gluon carries energy equal to 33.77 MeV. Mass of charged
pion is 139.57 MeV. The mass of pion leads to the coupling constant for the strong
interactions of the nonrelativistic nucleons αs NN = 14.4. For a very short period of the K and π
production in the nucleonnucleon collisions, the produced nucleonantinucleon pairs are in
the rest. The strong masses of the charged pion and kaon we can calculate multiplying their
masses by the coupling constant. For the charged pion, we obtain about sqrt(s) = 2 GeV and it
is the started point of the curve for the K/π ratio. For the charged kaon we obtain sqrt(s) = 7.1
GeV. A kaon is the binary system of binary systems of loops so it is quadrupole of loops.
Masses of the gluon loops the resting kaons consist of are greater than in the resting pions.
There is obligatory the fourneutrino symmetry for the gluons so there arise particles
containing following numbers of gluons x
x = 2·4 d , (230)
where d = 0, 1, 2, 4, 8… We can see that for energies lower than 7.1 GeV the pions and kaons
arise from the single loops (x = 2 for d = 0). When the energy of collisions increases then
there arise more and more the more energetic gluons from which the kaon loops arise. For
energies higher than 7.1 GeV pions are produced from single loops (mi = 67.54 MeV)
whereas kaons are produced at once as the quadrupoles (x = 8 for d = 1; there are eight
different gluons carrying appropriate energies to produce the kaon loops). This leads to K/π =
67.54/493.7 ≈ 0.14 and it is the asymptote for positive and negative particles (the black basic
curve on the figure). To obtain the real curve we must take into account also the helicity of
electric charge inside pions. The helicity of charge of the negative pions are opposite to the
colliding nucleons so for the threshold energy for kaons, i.e. 7.1 GeV, they are produced from
the gluons which carry energy equal to mi = 33.77 MeV. This means that for energy sqrt(s) =
7.1 GeV for the negative particles should be K/π = 33.77/493.7 ≈ 0.07. We can see that the
curve K/π = f(sqrt(s)) is lowered in relation to the basic (black) curve and has small maximum
for the threshold energy. The helicity of charge of the positive pions is the same as of the
105
colliding nucleons so they arise at once as the positive pions. This means that for the threshold
energy for the positive particles should be K/π = 139.57/493.7 ≈ 0.28. We can see that the
curve K/π = f(sqrt(s)) is elevated and there appears the big ‘horn’.
Summary
The atomlike structure of baryons leads to the two curves K/π = f(sqrt(s)) consistent with
experimental data. On the figure are collected the obtained theoretical results. The division of
the basic (black) curve follows from the different helicities of electric charges of pions (left
helicity for positive pions and right for negative pion) in relation to the helicities of the
colliding nucleons (left helicity). We can neglect the helicities of charges of the kaons because
they are the binary systems. In such systems appears additional spin speed that causes that the
total helicity is always the same as of the colliding nucleons.
References
[1] http://en.wikipedia.org/wiki/File:Strange_production_7.gif
106
The Cross Section for Production of the W Boson
Here I will show how from the atomlike structure of baryons follows the cross section for
production of the W boson as a function of collision energy.
We know that cross section is inversely in proportion to square of mass of created particle.
For the mass of proton in the rest, the cross section for the weak interactions is the equatorial
cross section of the point mass of the proton. Then, for the W boson, for collision energy
equal to the mass of the W boson (this theory leads to 79.4 GeV – see formula (119) or 80.38
GeV – see discussion below formula (246)), is
σW(mW = 80.38 GeV) = πrp(proton) 2 /(mW/mproton) 2 = 0.3248 nb, (231)
where rp(proton) = 0.8711·10 17 m is the radius of the point mass of proton (see formula (49))
whereas mW is the mass of the W boson.
When energy of collision increases then increases the radius of the point mass so the cross
section also. Cross section is in proportion to the equatorial cross section of the point mass
whereas the volume of the point mass is in proportion to collision energy E. This means that
there appears following factor f
f = (E/mW) 2/3 . (232)
We can see that the formula for the mean cross section for production of the W + and W 
bosons as a function of collision energy looks as follows
σW,mean(E[TeV]) = πrp(proton) 2 (E/(mW/1000)) 2/3 /(mW/mproton) 2 = 1.744·E 2/3 nb. (233)
This is the mean value for the W + and W  bosons.
Inside the core of baryons appear the sham quarkantiquark pairs which carry following
electric charges: ±1/3 and ±2/3 (see Chapter “Reformulated Quantum Chromodynamics”).
The electric charge of the core of proton is +1. The charge helicities of the W + boson and
proton are the same so the W + boson is associated with the greatest positive electric charge
i.e. the +1. The charge helicities of the W  boson and proton are opposite so the W  boson is
associated with the absolute value of the 2/3. We know that involved energy is in proportion
to the absolute value of the electric charge. This leads to following formula
(σW+ + σW)/2 = σW,mean , (234)
where σW = (2/3) 2/3 σW+. This leads to conclusion that in the formula for the cross section for
the W + boson appears the factor g1(+) = 1.13434 whereas for the W  boson the factor g2() =
0.865662. For the total cross section for the protonproton collisions appears the factor g3(±) =
g1(+) + g2() = 2 whereas for the protonantiproton collisions the factor g4(±) = 2g1(±) =
2.26868. Now, the formula for the cross section looks as follows
σW[nb] = giσW,mean(E[TeV]) = 1.744·giE 2/3 , (235)
where i = 1, 2, 3 or 4. The formula (235) is not a final formula.
For mesons carrying mass close to the proton (for example, ω(782)) or for nuclei composed
of such mesons (for example, Υ(9460 MeV)), the cross section should be close to the
equatorial cross section of the point mass of the proton in the rest i.e. about 2.4·10 3 mb.
When energy of proton increases then emitted energy also increases and for energy in
approximation 18 TeV is 100 % (see Chapter “Interactions”). Then, the radius of the point
mass of proton is equal to A/3 and it is the radius of the gluon loop from which the first basic
sham quark is produced. Masses of the sham quarks are in proportion to their radii so energy
emitted by relativistic proton is in proportion to radius of the point mass of proton. This
means that ability to production of the W bosons increases with energy of collision and is
equal to one for 18 TeV. To obtain correct value for the cross section, we must multiply the
formula (235) by following function
Br = rpointmass/(A/3) = (E[TeV]/Eo[TeV]) 1/3 , (236)
where Eo = 18 TeV.
The final formula for the cross section looks as follows
107
σW[nb]×Br = giσW,mean(E[TeV])Br = 0.6655·giE , (237)
This is the linear function. We can see that the cross section for 7 TeV is 3.5 times greater
than for 2 TeV. For 7 TeV, for the W + boson we obtain 5.3 nb whereas for W  boson 4.0 nb
and it is consistent with experimental data.
Summary
The figure entitled “The cross section for production of the W boson as a function of
collision energy” contains the obtained theoretical results.
108
Neutrino Speed
The data in this paper [1] lead to the atomlike structure of nucleons. The Schwarzschild
radius for the strong interactions is 1.4 fm. From the Uncertainty Principle follows, that such
is the range of the neutral pions produced in centre of the baryons. Assume that the muons,
pions and W bosons (denote their mass by m) arise in the centre of the core of nucleons as the
entangled gluonball quadrupoles. Such a quadrupole can be entangled with a neutrino
(denote its mass by mneutrino) on, for example, the Schwarzschild surface. This means that the
centrifugal force is directly proportional to the product 4m·mneutrino, where mneutrino
109
so we can apply to them the Newton’s second law. The Newton’s second law we can write for
neutrinos as follows
mneutrinoΔvneutrino = Fneutrino · tint. (239)
The strange quarkantiquark pairs and next the muonantimuon pairs arise in the centre of
the core of baryons as the gluonball quadrupoles i.e. as the quadrupoles of pure energy. This
means that such objects are also the nonrelativistic objects so we can apply to them the
Newton’s second law. The force acts on the carriers of gluons i.e. on the Einstein spacetime
components. They are the neutrinoantineutrino pairs i.e. the weak dipoles carrying spin equal
to 1 so they are the nonrelativistic particles also. Speed of entangled weak dipoles is equal to
the c. From the formulae (238) and (239) we obtain that the increase in the radial speed of
neutrinos that appear in the beta decays is
vneutrino – c = Δvneutrino ~ 4{mneutron – (mproton + melectron)} 2 = 4M 2 . (240a)
The increase in the radial speed of the neutrinos appearing in the weak decays of the
exchanged gluonball pairs is
vneutrino – 0 = Δvneutrino ~ 4m 2 , (240b)
where m is mass of gluon ball which decays due to the weak interactions. Energy of such
gluon balls can be equal to the mass of muons or to the one fourth of the mass of the core of
baryons or to the mass of the W bosons. Due to the weak interactions of the neutrinos with the
gluon balls, the neutrinos appearing in the beta decays and the neutrinos appearing in the
decays of the gluon balls must have the same resultant speed. From formulae (240a) and
(240b) we obtain
(vneutrino – c)/vneutrino = (M/m) 2 . (241)
Since vneutrino ≈ c then in approximation is
(vneutrino – c)/c = (M/m) 2 , (242)
or
vneutrino = {1 + (M/m) 2 }c. (243)
To the gluon balls we can apply the theory of stars. The theory of stars leads to conclusion
that lifetime T is inversely proportional to four powers of mass, i.e. T ~ 1/m 4 , so we can
rewrite the formula (242) as follows
sqrt(Tlifetimeof particle/Tlifetimeofneutron) = (vneutrino – c)/c. (244)
We can see that we can calculate the neutrino superluminal speeds both from masses of
particles (formula (242)) or from their lifetimes (formula (244)). Both methods lead to the
experimental data.
From the Uncertainty Principle and the invariance of the neutrino mass follows that the
square of the change in neutrino speed is inversely proportional to the time of exchange t. On
the other hand, from formula (240a) and the relation T ~ 1/M 4 follows that similar relation is
for the lifetime T. This means that the interval for the broadening of the time of exchange t,
i.e. the (t/2, 2t) leads to following conclusions. To obtain the maximum neutrino speed, we
must multiply the central value for an increase in neutrino speed in relation to the c, i.e. the
Δv/c = (v – c)/c, by sqrt(2) i.e. vmaximum = (1 + Δv·sqrt(2)/c)c. For the minimum speed we
obtain vminimum = (1 + Δv/(sqrt(2)c))c. The theoretical results are the central values whereas in
the round brackets we will write the increases in speed for the maximum neutrino speed.
For lower energies, such as in the MINOS experiment [4], there are mostly the neutrinos
from the decays of neutrons and gluonball pairs carrying energy equal to the mass of the
muonantimuon pairs. The ratio of the lifetime of neutron to lifetime of muon is smallest
(882/2.20·10 6 = 4·10 8 [2]) so the obtained neutrino speed is the upper limit. From formula
(243) follows that for the more precise MINOS experiment, for the neutrino speed we should
obtain 1.000050(21)c i.e. the maximum neutrino speed should be 1.000071c.
For higher energies, such as in the OPERA experiment [5], there are mostly the neutrinos
from the weak decays of the neutrons and gluonball pairs carrying energy equal to the half of
110
the mass of the core of baryons. Mass of one gluon ball is 181.7 MeV. This means that
lifetime of such gluon ball which decays due to the weak interactions at once into 3 neutrinos
and electron, is 8.74 times shorter than lifetime of muon. This leads to conclusion that the
neutrino speed is 1.0000169(70)c i.e. the maximum speed is 1.0000239c so the timedistance
between the fronts of the neutrino and photon beams is 58.4 ns.
For highest energies, such as in the explosions of the neutron cores of supernovae, dominate
the neutrinos from the decays of the neutrons and gluonball pairs carrying energy equal to the
mass of the W bosonantiboson pairs. The distance of mass between the point mass and the
torus in the core of baryons is equal to the mass of muon whereas the mass of the point mass,
which is responsible for the weak interactions of baryons, is 4 times greater than the muon.
The quadrupole symmetry shows that creation of systems containing 4 elements is preferred.
This means that the lifetime of the muon is characteristic also for the point mass (i.e. 424
MeV = 4·105.7 MeV – each one of the four muons lives 2.2·10 6 s [2]). This leads to
conclusion that lifetime of the W bosons (mass = 80,400 MeV [2]) which decay due to the
weak interactions is TlifetimeWboson = 2.2·10 6 s/(80,400/424) 4 = 1.7·10 15 s.
This leads to following neutrino speed 1.0000000014(6)c i.e. maximum speed is
1.000000002c (i.e. (1 + 2·10 9 )c). This result is consistent with the observational facts [6]. The
timedistance Δt between the fronts of the neutrino and photon beams, measured on the Earth
for the SN 1987A, should be
Δt = 168,000 ly · 365 days · 24 hours · 2·10 9 = 3 hours.
If before the explosion, the mass of the SN 1987A was close but greater than four masses of
the Type Ia supernovae, i.e. greater than 5.6 times the mass of the sun, then due to the
quadrupole symmetry, during the gravitational collapse, there could arise the system
containing 4 the Type Ia supernovae. After simultaneous explosion of the 4 supernovae, we
should not observe there a remnant i.e. neutron core. Due to gravitational collapse, a
supernova transforms into neutron star. The collapse decreases pressure inside the neutron star
that forces the inflow of the dark energy into the star. Next, there are the beta decays of the
neutrons and nuclear fusions of the nucleons. These two processes appear simultaneously.
The additional dark energy and released binding energy cause the explosion of the neutron
star. This means that neutrinos and photons appear on surface and inside neutron star
simultaneously. When mass of a neutron star is equal to mass of the Type Ia supernova then
neutrinos and photons appear simultaneously in whole volume of the star. We can see that a
supernova that has mass in approximation 5.6 times the mass of the sun practically should not
have some plasma layer around the four neutron stars. This means that during the explosion of
such quadrupole of neutron stars there should not be a timedistance between the fronts of the
neutrino and photon beams. The observed on the Earth the 3hours delay must be due to the
superluminal speed of neutrinos.
Limitations in detection of superluminal neutrinos
The speed of light c depends on the inertial mass density of the fundamental/Newtonian
spacetime. Lower density means higher speed of light. The pressure inside the fundamental
spacetime is tremendous about 10 180 Pa. This causes that the fundamental spacetime is exactly
flat so the c is constant. The density is lower than the mean only for distances smaller than
about 10 32 m from the neutrinos. Due to this negative pressure, i.e. due to the weak
interactions in the lowenergy regime, there arise the regions in the Einstein spacetime in
which the binary systems of neutrinos are confined. When such regions are sufficiently large,
the neutrinos from weak decays of particles in such regions can be superluminal.
The Everlasting Theory says that the carriers of the massless photons, i.e. the entangled
binary systems of neutrinos the Einstein spacetime consists of, so the photons as well (the
entanglement causes that photons, i.e. the rotational energies of the binary systems, are the
111
wave packets), are moving in the Newtonian spacetime with the speed c. The neutrinos in the
binary systems of neutrinos interact weakly so the neutrinos are moving almost
independently. This means that generally the neutrinos are moving with the same speed as the
binary systems of neutrinos. This means that the neutrinos, which have mass, mostly are
moving with the speed c. We will never see neutrinos which are moving with speeds lower
than the c. Just the General Theory of Relativity is incomplete. The Everlasting Theory shows
that we must introduce new term “dominating gravitational gradient” because accelerated
particles, besides neutrinos, change their internal structure. The ratio of mass of source of the
strong interactions to mass of the carriers of the strong interactions changes as 1/(1 – v 2 /c 2 )
i.e. there appears the running coupling for the strong interactions which value depends on the
speed v in the dominating gravitational gradient. The accelerated baryons behave as if with
each interacting strongly baryon were associated two different reference frames. This means
that an observer in a falling lift in a dominant gravitational field can measure the speed of the
lift in relation to the dominating gravitational gradient. We can see that the Principle of
General Covariance is strictly correct only for resting masses or moving with the same speed
in dominating gravitational gradient. Without a reformulation we cannot unify the General
Theory of Relativity with the strong interactions. The Everlasting Theory shows how the
unification of gravity with strong interactions looks. For example, the Kasner solution for the
flat anisotropic model is correct because it concerns the part of the GR when the Principle of
General Covariance is obligatory i.e. the exact solution (0, 0, 1) is for the resting structure in
the dominating gravitational gradient. The approximate solution, i.e. (1/3, 2/3, 2/3), concerns
the sham quarks. The exact Kasner solution leads to the core of baryons. The ground state of
the Einstein spacetime is invisible for detectors because the Lagrangian for this state cannot
change. For this state, the total energy and speed c are constant. This means that the ground
state behaves as an empty spacetime, with no matter. These properties cause that the Kasner
solution describes the real phenomena.
The Everlasting Theory shows that the neutrinos are the nonrelativistic particles (i.e. their
mass does not depend on their speed) so sometimes in the special conditions they can be the
superluminal particles. Such neutrinos appear when the weak decays take place inside the
strong fields inside baryons containing regions in which the Einstein spacetime components
are confined. Total volume of the regions containing the confined components increases when
energy of baryons per collision increases. Due to the atomlike structure of baryons, there is
the natural broadening in the spectrum of the superluminal speeds of neutrinos. In the
neutrinospeed spectrum for the neutrinos obtained due to the collisions of nucleons there
should be the “luminal” peak associated with the speed equal to the c and there should be the
naturally broadened superluminal peak separated from the luminal peak. The Everlasting
Theory shows why neutrinos have such “strange” properties.
For the “stairs” presented in the Fig. titled “Dependence of speed of neutrinos on their
energies for collisions of nucleons”, for the lower superluminal speeds the y is greater
whereas the x smaller. This is because mean distances between the strong fields of the
nucleons are smaller for higher energies so probability of weak decays inside the strong fields
increases. The w is quantized (see Fig. titled Dependence of speed of neutrinos on their
energies for collisions of nucleons).
In the collisions of the superluminal neutrinos with the Einstein spacetime components the
momentum of the components mc cannot change. There can change the rotational energies.
This means that the superluminal speeds are conserved. The superluminal speeds can change
in the exchanges of the superluminal neutrinos on the neutrinos in the binary systems of
neutrinos the Einstein spacetime consists of but such “oscillations” are the very rare
processes.
112
Summary
The calculated neutrino speed for the MINOS experiment is 1.000050(21)c. The maximum
neutrino speed is 1.000071c. The calculated timedistance between the fronts of the neutrino
and photon beams for the OPERA experiment is 58.4 ns whereas the neutrino speed is
1.0000169(70)c i.e. maximum neutrino speed is 1.0000239c. The calculated timedistance
between the fronts of the neutrino and photon beams, observed on the Earth, for the supernova
SN 1987A is 3 hours whereas the neutrino speed is 1.0000000014(6)c.
Neutrino speed depends on internal structure of baryons and phenomena responsible for
creation of particles that decay due to the weak interactions. The MINOS and OPERA
experiments and the data concerning the supernova SN 1987A suggest that there is in
existence an atomlike structure of baryons. In MINOS dominated neutrinos from decays
caused by gluonball pairs which energy is two times greater than the mass of muon. In
OPERA dominated neutrinos from decays caused by gluonball pairs which energy is two
times smaller than the mass of the core of baryons whereas in the supernova SN 1987A
113
explosion by gluonball pairs which energy is two times smaller than the mass of the W
bosons.
We can calculate the neutrino speed for the MINOS experiment also in different third way.
Neutrons and muons decay due to the weak interactions. From formula (51) follows that
coupling constant for weak interactions is in proportion to square of exchanged mass whereas
theory of stars leads to T ~ 1/M 4 . This means that square root from lifetime is inversely
proportional to coupling constant so applying also formula (57) we can rewrite formula (244)
as follows
Xw = αw(betadecay)/αw(decayofmuon) = c/(vneutrino – c) = 19,685.3. (245)
From this formula we obtain
vneutrino = c(Xw + 1)/Xw = 1.0000508c. (246)
Due to the weak interactions, the mass of the electronpositron pair can increase the Xw
times whereas the resultant mass due to the quadrupole symmetry can increase the four times.
The final mass is 80,473 MeV and it is the mass of the W boson.
We can see that due to the quadrupole symmetry there are the 4 basic quadrupoles leading
to the superluminal neutrinos. Their masses are as follows. The 4{mneutron – (mproton +
melectron)}, in approximation the mass of the point mass in the centre of the core of baryons
424 MeV and mass of the core of baryons 727 MeV, and the mass of the W boson 80,473
MeV. For the bare mass of the pair we obtain 2·0.510407 MeV·19,685.3·4 = 80.380 GeV.
This theoretical result is consistent with the experimental data [2].
There is the relativity of lifetimes for entangled particles. To free a neutron from an atomic
nucleus is needed the mean energy equal to the volumetric binding energy 14.952 MeV (see
the description concerning formula (183)). On the other hand, we know that the binding
energy of the mass X and Y is 14.98 MeV. This energy is close to the volumetric binding
energy so the free neutrons can be entangled with the volumetric binding energy i.e. the
bound neutrons can simultaneously interact with energy two times higher than the volumetric
binding energy. From relation T ~ 1/m 4 and formula (95) follows that lifetime of neutron
entangled with the volumetric binding energy 14.97 MeV is 888 s. Similarly, the distance of
mass between the two charged states of the core of baryons is 2.67 MeV. When a muon is
entangled with such energy then its lifetime is 2.21·10 6 s.
References
[1] https://www.worldscientific.com/etextbook/5500/5500_chap0.1.pdf.
[2] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)
[3] Feigenbaum Mitchell, Universal Behaviour in Nonlinear Systems, “Los Alamos
Science” 1 (1981)
[4] P. Adamson et al. (MINOS Collaboration) (2007). "Measurement of neutrino velocity
with the MINOS detectors and NuMI neutrino beam". Physical Review D 76 (7).
arXiv:0706.0437.
[5] OPERA Collaboration, T. Adam et al. (2011), “Measurement of the neutrino velocity
with the OPERA detector in the CNGS beam”, arXiv:1109.4897 [hepex].
[6] K. Hirata et al., Phys. Rev. Lett. 58 (1987) 1490;
R. M. Bionta et al., Phys. Rev. Lett. 58 (1987) 1494;
M. J. Longo, Phys. Rev. D 36 (1987) 3276.
114
Mtheory
We cannot formulate an useful Mtheory without the phase transitions of the fundamental
Newtonian spacetime which lead to the closed strings (their radius is about 10 45 m),
neutrinos, cores of baryons and the protoworlds after the period of inflation.
Mtheory: My Everlasting Theory is some extension of the useful Mtheory. Within the
nonperturbative Everlasting Theory, I described internal structure and behaviour of all types
of closed and open loops/strings. There are the bosonic and fermion loops/strings. There is
something beyond the useful Mtheory i.e. the TitiusBode law for the strong and strong
gravitational interactions.
Fundamental bosonic string theory: All particles consist of the binary systems of my
closed strings. The phase space of such systems contains 11 elements but we can reduce it to
10 elements because the distance between the closed strings follows from the internal
structure of the closed string. The distance is π times greater than the thickness of the string.
We can see that the binary system of closed strings (spin=1) and the bidipole of the closed
strings (spin=2) are the bosons so the fundamental string theory is not the superstring theory.
But it consists of the fermions. There arise at once the binary systems because the internal
helicity of the created systems must be equal to zero. Then, the quantum fluctuations in the
fundamental spacetime are reduced to minimum. The superstring theories, i.e. theories that
describe simultaneously the fermions and bosons appear on higher level of nature. I showed
how to derive the superstring theories from the fundamental string theory i.e. from the
Bosonic String Theory. Due to the phase transitions, there appear the three superstring
theories. There are the three stable tori/fermions carrying the halfintegral spin i.e. the torus of
neutrinos, the torus in the core of baryons and the cosmic torus i.e. the Protoworld after the
period of inflation (they are the k‘dimensional’ tori in the Mtheory). The tori look as closed
fermion strings. Inside them, there arise the bosonic loops. We can see that there appears the
supersymmetry i.e. the fermionboson symmetry. The bosonic loops inside the neutrinos and
the cosmic loops cannot be open whereas the large loops produced inside the torus in the core
of baryons can be closed or open. The tori of neutrinos and the cosmic object cannot be open
whereas the electric charges/tori come open in the annihilations of the pairs.
Type I superstring theory is the theory of baryons (typical size is about 10 15 m) and
electrons (~10 13 m).
Type IIA superstring theory is the theory of neutrinos (typical size is about 10 35 m). In
this theory, the closed strings in the binary systems of the closed strings the neutrinos consist
of have different internal helicities. This looks the same as in the fundamental bosonic string
theory.
Type IIB superstring theory is the theory of the protoworlds after the period of inflation
(typical size is about 10 24 m). In this theory, the nucleons in the binary systems and in the
alpha particles the cosmic objects consist of have the same internal helicities.
Tduality: We can see that in approximation the inverse of the geometric mean of the
typical sizes for the Type I and IIA superstring theories is equal to the typical size for the
Type IIB superstring theory. Moreover, the transition from the Type IIB superstring theory to
the Type IIA superstring theory was the cause of the ‘soft’ big bang.
Heterotic E8×E8 theory: The ground state of the Einstein spacetime consists of the nonrotatingspin
binary systems of neutrinos. There are the 4 different binary systems. They are
the carriers of the photons and gluons. There is one type of the two photons, i.e. the left and
righthanded, and 8 types of gluons. Due to the fourneutrino symmetry, the next greater
object than the 8 different gluons should contain 8 · 8 = 64 gluons. This means that the
heterotic E8×E8 theory follows from the fundamental bosonic string theory and the Type I
115
superstring theory. In the Everlasting Theory nomenclature, the objects containing the 64
gluons are the chains. They can be the open or closed loops or quadrupoles.
Heterotic SO(32) theory: There are the 4 different carriers of the photons and gluons. This
means that due to the fourneutrino symmetry, the next greater object than the 4 different
carriers should contain 4 · 4 = 16 binary systems. But there are the virtual particleantiparticle
pairs so we must multiply this number by 2. Then we obtain the 32 binary systems. We can
see that the heterotic SO(32) theory follows also from the fundamental bosonic string theory
and the Type I superstring theory. In the Everlasting Theory nomenclature, the objects
containing the 32 gluons are the binary systems of supergroups. They can be the particleantiparticle
pairs.
In the heterotic theories, there are the binary systems of neutrinos in which the neutrinos
have the same or opposite internal helicities (see Table 8). This follows from the fact that the
two neutrinos have to differ by the sign of the weak charges.
Gravity: In the gravitational fields, there are the nonrotatingspin bidipoles of the
neutrinos. Their spin is 2 and they are the carriers of the gravitational energy/mass. There is
some analogy between the four different neutrinos, which lead to the bidipoles, and the four
different binary systems of neutrinos in the heterotic theories. This means that the gravity
should look similarly as the heterotic theories in the very lowenergy limit.
Sduality: The Everlasting Theory shows that the Type I superstring theory describes the
weak and strong interactions whereas the heterotic SO(32) theory the strong interactions via
the gluons. This means that there are in existence similar string theories that vary due to the
values of the coupling constants.
There are the fermion tori/’loops’ and the boson loops which arise inside the fermion tori.
The circular axes of the fermions overlap with the bosonic loops but there is the separation of
the bosons/loops from fermions/tori. This causes that we do not need the higher dimensions to
describe the internal structure from which the fermionboson symmetry follows.
116
Perihelion precession of Mercury and Venus
The perihelion precession of planets we can calculate applying the Newtonian mechanics
and then we can add the correction following the General Relativity. But we obtain very bad
result for Venus (about 1075’’, i.e. 1075 seconds of arc, in comparison to the observational
fact in approximation 204’’). The Everlasting Theory shows that the perihelion procession of
Mercury and Venus as well is associated with the very deep past of evolution of the region
where the solar system is located. Under the Schwarzschild surface of the neutron black holes
and their associations (see Paragraph “Cosmology of the Solar System and Massive Spiral
Galaxies” in Chapter “New Cosmology”) there arose the entangled radiation fields composed
of the entangled carriers of photons, emitted in the nuclear fusions, so of the electronpositron
pairs also. It was after the Protoworldneutrino transition but before the inflows of the dark
energy into the cosmic loop i.e. the early Universe. The region under the Schwarzschild
surface refers to the d=0 and d=1 states only i.e. refers to the orbit of Mercury and Venus
only. Assume that some radiation mass of Mercury is distributed in a ring that width is the
distance between the perihelion and aphelion. Such radiation ring behaves like mass in centre
of the sun. This means that gravitational interaction of the abstract radiation mass of Mercury
in the centre of the sun with the real radiation ring causes that there appears the spin speed of
the radiation ring and this spin speed is the speed of the perihelion as well. On base of these
explanations we obtain
v 2 perihelion,Mercury = GMradiation,Mercury/RMercury. (247)
Due to the interactions of the entangled primordial radiation field with the radiation ring of
Mercury, there is the resonance for the angular velocities of these two fields. Venus partially
behaves as a singlearm lever. Due to the singlearm lever, for Venus we obtain
v 2 perihelion,Venus = v 2 perihelion,Mercury(MMercuryRVenus/(MVenusRMercury)) = av 2 perihelion,Mercury, (248)
where MMercury = 3.3022·10 23 kg, RMercury = 5.7909100·10 10 m, MVenus = 4.8685·10 24 kg, RVenus
= 1.08208930·10 11 m whereas a = 0.1267432. The square of speed of the perihelion of Venus
is directly proportional to the mean radius of orbit (the arm lever) and is inversely
proportional to mass of Venus (greater inertia then smaller the speed of perihelion). We can
see that there is satisfied following formula
vperihelion,Venus = sqrt(a)vperihelion,Mercury = 0.35601vperihelion,Mercury. (249)
Calculate the radiation mass of Mercury. Due to the gluonphoton ‘transition’ (strongelectromagnetic
transition) there leaks the internal structure of nucleon. By an analogy to
formula (79), there should appear following factor g = 2αsαem. The radiation mass of electron
is x = melectron – mbare(electron) whereas the radiation mass of proton is equal to the distance of
masses between the neutron and proton i.e. y = mneutron – mproton. The protonneutron
transitions are due to the large loops so the αs = 1 (see formula (77).
Mradiation,Mercury = gxMMercury/y = zMMercury = 2.2545·10 18 kg, (250)
where z = 6.8272·10 6 .
Now we can calculate the vperihelion,Mercury = 5.0973·10 2 m/s. Calculate the perihelion
precession of Mercury per century T(100 years) = 3.155693·10 9 s:
φMercury/T[ o /T] = 360 o vperihelion,MercuryT/(2πRMercury) = 0.159153 o = 573.0’’. (251a)
For Venus is
φVenus/T[ o /T] = sqrt(a)φMercury/T[ o /T] = 204.0’’. (251b)
For the observational result for Mercury we obtain for Venus (204.39 ± 0.23)’’.
117
Foundations of Quantum Physics
Due to the fasterthanlight particles (i.e. the tachyons and binary systems of closed strings)
the quantum physics is nonlocal i.e. points separated spatially (i.e. which cannot
communicate in defined time, for example, during the time of decay of a particle, due to
exchanges of photons, gluons or subluminal particles) can communicate. The behaviour of the
renewable particles shows that the quantum physics is partially unreal, for example, mass of
electron (not electric charge) or energy of entangled photon can be simultaneously in many
places of space. We can see that existence of the two spacetimes, i.e. the imaginary
Newtonian spacetime and Einstein spacetime, leads to the nonlocality of nature.
The first phase transition of the imaginary Newtonian spacetime leads to the closed strings
(spin is halfintegral) and the binary systems of closed strings (spin is equal to 1). This causes
that nature conserves the spins of particles. The spin equal to 1 of a virtual large loop (mass is
67.5444 MeV) responsible for the strong interactions must be conserved because then they
still have the same spin as the carriers of the elementary gluons and photons i.e. the neutrinoantineutrino
pairs the Einstein spacetime consists of. The Uncertainty Principle ΔEenergyTlifetime
= h defines spin of virtual loop. The loop consists of the binary systems of neutrinos so its
mass cannot change. Its spin velocity is perpendicular to the relativistic velocity i.e. vrel 2 +
vspin 2 = c 2 . The lifetime of the loop is defined as Tlifetime = 2πr/vspin = 2πr/(c(1  vrel 2 /c 2 ) 1/2 ) i.e.
the lifetime increases when relativistic speed increases. From the Uncertainty Principle
follows that then energy of the carriers of the strong interactions decreases. This leads to the
running coupling for strong interactions. We can see that the classical definition of lifetime,
the invariance of spin and the perpendicularity of the spin and relativistic velocities, lead to
the Uncertainty Principle i.e. to the conclusion that indeterminacy in distribution of energy is
inversely proportional to lifetime. The Everlasting Theory shows also that the behaviour of
the quantum/renewable particles (they disappear in one place and appear in another and so on)
causes that there is distribution of energy and mass so to describe such particles we must
apply the wave functions and equations in which the distributions can change over time.
The resultant wave function for many growing spinning loops is the sum of the constituent
wave functions. For a constituent growing spinning loop is
x = vradial t + λφ/2π, (252)
118
where
v 2 radial + v 2 spin = c 2 . (253)
The growing loop accelerates its expansion. We can see that the axis x overlaps with the
loop whereas the axes of time t are radial and begin with the loop.
For vradial t >> λ is vradial = c (since mvspinr = h then for increasing vradial, so also r, the spin
speed decreases) then
x = ct + λφ/2π. (254)
Since k’=p/h, λ=h/p, 2πν=ω and E=hν=hω we obtain
k’x – ωt = φ. (255)
Moving rotatingspin loop (the transverse wave) we can describe using following function
(see Chapter “Fractal Field”):
ψ(x,t) = ae iφ = a(cosφ + isinφ), (256)
where φ = k’x – ωt.
Define following operators E = ih∂/∂t and p = – ih∂/∂x. We can see that
Eψ = ωhψ = ih∂ψ/∂t (257a)
whereas
ppψ = p 2 ψ = – h 2 ∂ 2 ψ/∂x 2 . (257b)
For vrelativistic
119
Foundations of General Theory of Relativity
In an inertial reference system, we can define the distance between two neighbouring points
in spacetime as the square of interval that is a quadratic form of differentials of coordinates
ds 2 = dx i dx i (i = 0 (for time coordinate), 1, 2, 3). In a noninertial reference system (there
appear fields that curve the spacetime) there appear the dx α dx β as well and some coefficients
gαβ (ds 2 = gαβdx α dx β ). In generally, for the 4 dimensions we obtain 16 such coefficients that
we can write as a metric of field(s). The coefficients gαβ and gβα are multiplied by the same
product dx α dx β so gαβ = gβα and we can reduce the number of the coefficients to 10. The gαβ is
a symmetric tensor of rank two. Finally, the metric tensor gαβ is related to the energymomentum
tensor Tαβ of the matter distribution by Einstein’s field equations. Due to the noninertial
reference systems in the General Theory of Relativity (the GR), in this theory the
notion of reference systems has not the same meaning as in the Special Theory of Relativity.
There is conclusion that properties of motion of bodies are different in different reference
systems. This causes that selection of proper reference system is very important in the GR. To
choose proper reference system we must know the internal structure of the two spacetimes
and the bare particles. Wrongly selected reference systems lead to the wrong interpretations
within the GR. In the GR is neglected the fact that the Einsteinspacetime components are the
nonrelativistic particles. For the components in a loop we can write following formula
v 2 relativistic + v 2 spin = c 2
(259)
The inertial mass of the Einstein spacetime components is equal to their gravitational mass.
Sometimes the GR is very simple when reference system is properly chosen. A wrongly
chosen reference system leads, for example, to conclusion that there is an acceleration of
expansion of the Universe.
The Everlasting Theory shows that there are satisfied following conditions which lead to the
GR. When a carrier of photon loop is moving in spherical gravitational field then its
relativistic speed overlaps with a radius of emitter (the distant star) whereas the spin speed is
tangent to an orbit in the gravitational field. When directions of the radial/relativistic velocity
and spin velocity of a loop are perpendicular then formula (259) must be satisfied. There is
different situation when a photon loop overlaps with the equator of the sun (see Figure
“Curving of light in gravitational field”). The spin vector of the photon loop rotates in the
120
plane of the figure so the plane of the figure is the plane of polarization of the photon. When
the photon loop overlaps with the equator of the sun then there should be v’spin = sqrt(GM/R),
where M is the mass of the sun whereas R is the radius of the sun. But it is not true. The radial
speed of the photon loop in relation to the distant star (the emitter) cannot be higher than the c
so there appears the pivoting point for the plane of polarization. This causes that the spin
speed of the components of the photon loop in distance 2R from the pivoting point is two
times higher
vspin = 2sqrt(GM/R). (260)
This spin speed decreases the radial speed of the photon loop in relation to the emitter.
Since the resultant speed must be equal to the c so there appears the radial speed in relation to
the sun. The plane of polarization of the photon must be perpendicular to the resultant speed c
(the electromagnetic waves are the transverse waves) so the radial speed in relation to the sun
leads to the rotatory polarization. Radius of a nucleon black hole is rbh = GM/c 2 whereas spin
speed of an object in distance r is vspin = sqrt(GM/r). For vspin = c the angle between the planes
of polarization must be φ = π/2 that means that the black hole captured the light in distance
two times smaller than the radius of the Schwarzschild surface. This condition leads to
following formula
tg(φ/2) = rbh/r = v 2 spin/c 2 . (261)
When the photon loop overlaps with the equator of the sun we obtain
tg(φ/2) = 4GM/(Rc 2 ) = 4.244·10 6 . (262)
Then
φ = 4.864·10 4 [ o ]. (263)
When we multiply this result by 3600, we obtain the result in the seconds of arc φ = 1.75’’.
This result is consistent with the results obtained within the GR and the observational facts.
Because the Everlasting Theory leads to the result obtained within the GR, we can say that
the Everlasting Theory leads to the GR. The General Theory of Relativity and the Quantum
Physics follow from the behaviour and properties of the loops composed of the entangled
Einsteinspacetime components i.e. the neutrinoantineutrino pairs.
121
Combination of Quantum Physics and General Theory of
Relativity
The Quantum Physics and General Theory of Relativity disappear for mass/energy density
equal to the Planck critical density. The QP and GR are associated with the properties of the
Einstein spacetime. For the Planck critical mass/energy density, the neutrinos decay into the
free binary systems of the closed strings i.e. the Einstein spacetime disappears i.e. E = 0. For a
black hole that has radius equal to the Planck critical length rbh,critical = Rcritical = λcritical/(2π) is
rbh,critical = GMcritical/c 2 = 1.6162·10 35 m whereas ωcritical = Mcriticalc 2 /h, where Mcritical =
sqrt(ch/G) = 2.1765·10 8 kg. This leads to following formula for mass densities higher than
the critical mass/energy density (it is in approximation the density inside a neutrino for the
geometric mean of the mass/energy of a nonrotatingspin neutrino (see Chapter “New Big
Bang Theory”)
1 – 2πrbh,critical/λcritical = 0, (264a)
1 – ωcritical rbh,cricital/c = 0. (264b)
The last formula leads to the definition of the critical mass i.e. Mcritical = sqrt(ch/G).
Now we can generalize the Schrödinger equation adding the gravity
– (h 2 /(2m))∂ 2 ψg(x,t)/∂x 2 + V(x,t)ψg(x,t) = ih∂ψg(x,t)/∂t. (265)
The definitions of the momentum and energy operators are the same i.e. p = – ih∂/∂x and E
= ih∂/∂t.
We can see that following wave function satisfies the generalized Schrödinger equation
ψg(x,t) = ae iφ = a(cosφg + isinφg), (266)
where
φg = (k’ – 1/rbh)x – (ω – c/rbh)t. (267)
The rbh is the hypothetical radius of a black hole that has mass equal to the sum of masses of
all objects in the sphere that radius is equal to the distance between the centre of the
hypothetical black hole and the object for that the formula (265) is written.
Now we can write the generalized formula for energy for vrelativistic
122
General Relativity in Reformulated Quantum Chromodynamics
and New Cosmology
The Friedman isotropic model leads to a singularity due to the initial simplification that
there is the symmetry. In reality, there was the lefthanded rotary vortex in the Einstein
spacetime so we should consider the flat anisotropic model. In the nature the spatial distances
do not disappear for distances approaching zero. This means that there are not in existence
singularities of the oscillatory mode as well. But there is an oscillatory mode in the approach
to singularity.
The strong fields behave similarly as the strong gravitational fields. For both types of fields
is in force the TitiusBode law (r = A + dB) and for both types of fields the ratio A/B has
practically the same value 1.39. This means that there should be some tangent points for the
General Theory of Relativity and the reformulated Quantum Chromodynamics for interiors of
gravitational black holes and cores of baryons i.e. the black holes in respect of the strong
interactions.
I explained before that inside the core of baryons the Einstein spacetime is flat but due to
the properties of the electric/strong charge (the torus), the strong field has internal helicity and
due to the shape (the torus and the loops) the strong field is anisotropic but mass density of
the strong field is 509 times lower than the Einstein spacetime (see formula (11) and Tables
2a and 7). It looks as the flat anisotropic model in the General Relativity. Within the GR, the
flat anisotropic model leads to the form of the metric (Edward Kasner, 1921, [1]) for which
the solutions are the same as in the reformulated QCD presented within the Everlasting
Theory.
From the reformulated QCD follows that the electric/strong charges of the sham quarks and
their masses are directly proportional to the radii of the gluon loops from which the sham
quarks arise. The electric/strong charges of the basic sham quarks associated with the core of
baryons, i.e. the black hole in respect of the strong interactions, are ±1Q/3, ±2Q/3, ±1Q and
for the sham quarkantiquark pairs is 0. We can see that the generalized lower and upper
limits of the intervals obtained within the anisotropic model [1] can define the electric/strong
charges of the basic sham quarks or their pairs produced inside the core of baryons. The
intervals [1] and the reformulated QCD show that there are in existence other charges as well.
We can see that for the core of baryons, for the basic sham quarks or their pairs, the charge Q
is multiplied by following basic numbers 0, ±1/3, ±2/3, ±1, but there can be all numbers from
the interval .
We know that there is the ternary symmetry for the strong and electric interactions of the
torus in the core of baryons (i.e. for the electric/strong charge) and the resultant electric/strong
charge of three charges (a, b, c) in a virtual structure in a proton or antiproton must be equal to
±1 (this follows from the law of conservation of electric charge) i.e.
a + b + c = ±1. (270)
Moreover, due to the flatness and homogeneity of the Einstein spacetime in which the
virtual particles arise, the masses of the charges a, b and c, are directly proportional to the
radii of the gluon loops from which the sham quarks arise. Thus from the formula for spin for
virtual particles (spin = ETlifetime) we obtain that spin of a sham quark is directly proportional
to square of its charge. On the other hand, resultant spin of the virtual ternary structures must
be equal to 1 i.e. must be the same as the Einsteinspacetime components. These remarks lead
to following formula
a 2 + b 2 + c 2 = 1. (271)
The electric/strong charge equal to 1Q1 relates to the loop that radius is 1A1. This
means that due to the shape of the core of baryons and the TitiusBode low for strong
interactions probabilities of creation of following virtual pairs are highest ±1Q/3, ±2Q/3, ±1Q,
123
±1.72Q, ±2.44Q and ±3.88Q. The only three first virtual pairs concern the core of baryons i.e.
the Kasner metric. The formulae (270) and (271) lead to following two basic solutions for
virtual ternary structures in proton (+1Q)
0, 0, +1, (272a)
–1/3, +2/3, +2/3, (272b)
and to following two basic solutions for antiproton (–1Q)
0, 0, –1, (272c)
+1/3, –2/3, –2/3. (272d)
The Kasner metric [1] is the exact solution of the Einstein equations for ‘empty’ spacetime
i.e. in the Everlasting Theory nomenclature such spacetime consists of the nonrotatingspin
neutrinoantineutrino pairs moving with speed equal to the c. Such pairs cannot transfer any
energy to other systems i.e. we can assume that the ground state of the Einstein spacetime is
‘empty’. The exact solution is 0, 0, 1, i.e. in both cores of proton and antiproton arises a
virtual large loop only (mass is ±67.5444 MeV) and simultaneously two virtual loopantiloop
pairs i.e. a quadrupole of loops. Spins of loops in a pair must be antiparallel. For example,
there can arise simultaneously two neutral pions and one large loop L i.e. (π o , π o , L) or (virtual
π o , real π o , L) or (virtual π + π  , real π + π  , L). Such ternary structures are in the mesonic nuclei
(see Chapter “Structure of Particles (continuation)”). We can notice that a virtual/real
charged ternary structure consists of five elements, for example, (±1/3, ±2/3, +1) or (±2/3, ±1,
+1) or (±1, ±1.72, +1). The last structure does not concern the Kasner metric but satisfies the
Kasner solution (272a) and is important in the reformulated QCD that follows from the atomlike
structure of baryons. There are two more solutions applied in the reformulated QCD that
satisfy formula (272a) also i.e. (±1.72, ±2.44, +1) and (±2.44, ±3.88, +1). For very small t the
Kasner metric is an approximate solution. Then, the metric concerns the excited states of the
spacetime.
As some recapitulation we can say that the generalized flat anisotropic model (E. Kasner,
1921) and generalized oscillatory approach to a singularity (BKL model, [2]) lead to the
reformulated QCD presented within the Everlasting Theory i.e. to the electric/strong charges
of the basic and other sham quarks produced by the core of baryons i.e. by the black hole in
respect of the strong interactions. There is a similarity of the internal structure of the
neutrinos, cores of baryons and the protoworlds. This suggests that the BKL model is
applicable to the three types of objects. We can say that the BKL oscillatory model leads to
the phase transitions described within the Everlasting Theory. The protoworlds have not
electric/strong charge whereas their gravitational ‘charge’ (i.e. the mass) is positive. This is
the reason why the Kasner metric does not lead to the formula a + b + c = –1.
The Einstein spacetime and the cores of baryons consist of the neutrinoantineutrino pairs so
we can say that the BKL model is applicable to infinite space. The neutrinos consist of the
binary systems of closed strings and today there is not in existence a spacetime composed of
the binary systems of closed strings. We can see that the spaces composed of the binary
systems of closed strings are the finite spaces inside the neutrinos. This means that the BKL
model we can apply to both finite and infinite spaces. The same conclusion follows from the
BKL model.
The BKL model shows also that some perturbative action leads to oscillatory mode (the
phase transitions) on approaching the singularity but a transition to a new state is more
energetic than the initial perturbation. The same we can say about the protoworldneutrino
transition. A very small perturbation (a small mass added to the stable protoworld) causes the
transition but the involved energy in the transition exceeds very much the range of the very
small perturbation. Moreover, such transition forced the exit of the early Universe from the
blackhole state.
124
If we assume that circumference of the equator of the torus is equal to 1 then circumference
of the circular axis is 2/3, of the internal equator is 1/3 whereas of the point mass is in
approximation zero i.e. we obtain following finite series S1: 0, 1/3, 2/3, 1. If we assume that
circumference of the circular axis is 1 then we obtain following finite series S2: 0, 1/2, 1, 3/2.
When in physics appear the sets containing the elements of the first or second series
multiplied by a factor then there is very high probability that such eigenvalues are associated
with the internal structure of the core of baryons i.e. it is due to the leaking internal structure
of the core i.e. due to the gluons for the strong interactions or due to the photons from the
gluonphoton ‘transitions’ for the electromagnetic interactions. For example, the isospin I is
defined as follows N = 2I + 1, where I = S2. The magnetic energy of electrons in atoms is
directly proportional to the Lande factor g. If we define the g as follows g = 2g’ then the g’
for 2 P1/2 is 1/3, for 2 P3/2 is 2/3 and for 2 S1/2 is 1 i.e. g’ = S1.
The Everlasting Theory has the strong foundations which follow from the General Theory
of Relativity. I proved that the last theory leads to the tachyons and the phase transitions of
the fundamental spacetime. The Everlasting Theory leads also to the invariance of the speed
of light and equivalence of the inertial and gravitational masses i.e. to the postulates in the
GR. Moreover, I proved that my theory leads to the basic equations applied in the Quantum
Physics. The Everlasting Theory is the lacking part of the ultimate theory.
References
[1] Kasner Edward; “Geometrical Theorems on Einstein’s Cosmological Equations.”;
American Journal of Mathematics 43 (4): 217 – 221 (1921)
[2] Khalatnikov I. M. and Lifshitz E. M.; “General Cosmological Solution
of the Gravitational Equations with a Singularity in Time.”;
Physical Review Letters 24 (2): 76 – 79 (1970)
125
Electroweak Interactions, NonAbelian Gauge Theories
and Origin of E = mc 2
The Everlasting Theory leads to the electroweak theory [1] for energies higher than 125
GeV. In the theory of electroweak interaction, the lefthanded component of electron’s wave
function forms a weak isospin doublet with the electron neutrino. There is also the righthanded
singlet associated with the electrontype lepton fields. This leads to following gauge
group SU(2)L×U(1)L×U(1)R. On other hand the Everlasting Theory shows that internal
helicity of electron is lefthanded, of positron is righthanded and of electronantineutrino,
which forms stable structure with electron (see Chapter “Structure of Particles
(continuation)”), is lefthanded. This suggests that the electroweak theory describes the
electron antineutrino interacting with electronpositron pair. The electromagnetic binding
energy of an electronelectronantineutrino pair with the core of baryons is in approximation
m = 3.097 MeV (see the description below formula (35)). The mass m is indirectly associated
with the transition of the core of baryons from the charged state to the neutral state. The
density of the Einstein spacetime is in approximation 40,363 times higher than the weak field
i.e. than the point mass in the centre of the core of baryons (see the description below formula
(75). This means that the mass of the Einstein spacetime that occupies the same region as the
electromagnetic binding energy is MH = 3.097·40,363 = 125 GeV. The last LHC experiments
lead to such mass of the Higgs boson. For a pair, i.e. for the mass 2m, we obtain 2MH = 250
GeV. In the mainstream electroweak theory it relates to the vacuum expectation value of the
Higgs field. The 250 GeV is close to the vacuum expectation value i.e. the electroweak scale
that is the typical energy of processes described by the electroweak theory. From it follows
that the electroweak scale is for a pair of the Higgs bosons.
Within the mainstream electroweak theory the mass of the W and Z boson are calculated for
energy in approximation 90 GeV. For such energy, the fine structure constant applied in the
electroweak theory is close to the value calculated within the Everlasting Theory (see formula
(87): 1/129.7).
Mass of the W boson I calculated in Chapter “Neutrino speed” (80.380 GeV) whereas the
calculated mass of the Z boson is 92.0 GeV (see “Reformulated Quantum Chromodynamics”)
or 90.4 GeV (see formula (120)). Notice that the mean mass of the Z boson is 91.2 GeV.
The new theory of the weak interactions described within the Everlasting Theory shows that
appropriate rotary vortex of energy (the H bosons), which appears due to the entanglement of
the components of the carrier of such energy (such vortex has left or righthanded internal
helicity), decreases local pressure (so increases local mass density) of the Einstein spacetime
in such way that the spacetime components that are inside the region occupied by the carrier
of the electromagnetic binding energy start to interact weakly i.e. they are closer one to
another. This causes that there appears the visible mass for detectors. Due to the weak
interactions, the H boson is the concentration of the local Einstein spacetime. The factor F =
40,363 causes that the energy of the H boson is as follows
MH = Fm, (273)
where m is the electromagnetic binding energy for the H + H o transition.
For the energies lower than the 125 GeV the weak interactions of baryons are associated
with the point mass Y = 424.1245 MeV, not with the Z and W bosons.
The described within the Everlasting Theory mechanism is not the Higgs mechanism. The
energy of the conversion we can refer to as the H boson because it is indirectly associated
with the H + H o transition. The arising mass gap follows from the atomlike structure of
baryons and properties of the spacetimes. Physical conversion of massless energy into mass
via some masslessenergy condensation is impossible. The inertialmasses/volumes/piecesofspace
and their rotational energies are the everlasting attributes of spacetimes.
126
NonAbelian gauge theories
In the Einstein spacetime arise the components of the fractal field. Due to the entanglement,
there appear the fractal, closed loops that spontaneously break global symmetry of the
Einstein spacetime. The mass density of such loop is the same as the mean mass density of the
Einstein spacetime. This means that the massless energy and mass of such loop visible for
detectors are equal to zero. In the strong interactions, a binary system of such loops behaves
as the electronelectron pair in the ground state of an atom so the zerospin loops (for
detectors) behave as fermions. We can see that such loops behave as ghosts so such loops I
will refer to as the ghost loops. There can appear ghost fields composed of loops with
different radii. Consider, for example, the strong field of a proton composed of the gluons.
State of such field with the electric/strong charge we can describe via a wave function ψn(x).
When we add to the gluon field with the charge the ghost field then energy does not change
because the ghost field is the part of the ground state of the Einstein spacetime. We can call
such transformation the first gauge transformation and write it symbolically as follows E E
+ 0, where the E is the energy of the field defined by ψn(x) whereas the zero defines energy
and mass of the ghost field that ‘see’ the detectors. Such gauge transformation means that we
change the phase of the wave function (see Chapter “Foundations of Quantum Physics”). The
derivatives of ψn(x) do not transform as ψn(x). To write a gaugeinvariant Lagrangian we need
derivatives that contain ∂ψn(x) and transform like ψn(x). This forces the introduction of the
second gauge transformation. It looks as follows: vectorfield vectorfield + derivativesofghostfield.
Symbolically it looks as follows: M M + 0, where the zero defines mass of the
ghost field that energy is not equal to zero. This means that the loops are open. For example,
the electromagnetic energy 3.097 MeV can be a catalyst for the H boson creation i.e. the low
massless energy largely breaks local symmetry of the Einstein spacetime. We can use the
vector field to construct a gaugecovariant derivative that transforms like ψn(x). The
derivative of the ghost field is the ghost field carrying energy visible for detectors. Its mass is
equal to zero. The vector field consists of the ghost loops carrying energy and mass. The
ghost field carrying mass consists of the nonzerospin rotary vortices/loops. A ghost loop
carrying energy (it has internal helicity) decreases local pressure in the Einstein spacetime that
forces the inflows of the mass from the surrounding Einstein spacetime. The energy of the
massless loop is E whereas the total energy/mass of the loop carrying energy and mass is as
follows: energy = Mc 2 + E = 2E. This formula leads to the Einstein formula E = mc 2 . We can
see the discrepancy between the mass and total energy of such loop. The massless energy
carries information. The Everlasting Theory shows that for massless energies the coupling
constants are equal to zero. Only carriers carrying mass lead to binding energies. For example,
value of the fine structure constant follows from the mass of the electronpositron pairs
created by electric charges via photons. The Everlasting Theory shows that the mass of the
large loops responsible for the strong interactions inside baryons is 67.5444 MeV and spin
associated with this mass is unitary. The ghost loops or ghost loops carrying such energy, not
mass, arise on the circular axis and they do not violate the laws of conservation of the spin
and charge associated with the torus inside the core of baryons. The ghost loops carrying
energy acquire their mass outside the core. However on the circular axis can appear the binary
systems of the large loops carrying mass that spin is equal to zero i.e. the neutral pions or π – π +
pairs because such structures does not change spin and charge of the core of baryons.
Origin of E = mc 2
Electromagnetic energy, i.e. massless, near electric charges can insignificantly increase
mass density of the local Einstein spacetime (one part in 40,364 parts) in such way that the
spacetime components start to interact weakly. It is the broken symmetry of the local Einstein
spacetime. On surface of the volume with broken symmetry appears the surface tension γ
127
because the Einstein spacetime behaves as a gas whereas the volume with the broken
symmetry as a liquid. Size of the volume, i.e. the diameter of the volume, is 2λ, where λ is the
length of the electromagnetic wave. Due to the surface tension, there appears the positive
internal pressure ρ in the liquid and there is satisfied following formula
γ = 2λp. (274)
The absolute values of the positive internal pressure and the negative pressure created by the
rotary vortex of the electromagnetic energy are the same. The rotary vortex has internal
helicity due to the spinrotation of the carriers of the electromagnetic wave.
Following formula defines the internal pressure
p = ρc 2 /2. (275)
From formula (274) and (275) we obtain
c 2 = 2πγ/(λρ). (276)
On the other hand, for a wave on surface of deep water we obtain [2]
v 2 = 2πγ/(λρ), (277)
where v is the speed of a waterwave. We can see full analogy for the two different
phenomena. This means that formula (276) is correct for electromagnetic waves which
amplitude is very small in comparison to the size of the volume with broken symmetry.
We know that λ = hc/E so from formula (276) we obtain
E = c 2 hcρ/γ = c 2 h/(λc). (278)
This formula shows that the Einstein formula E = mc 2 is correct for following condition
mcλ = h i.e. for loops which spin is unitary.
The masses behave analogically as the mass Y = 424.1245 MeV. This leads to conclusion
that the coupling constants for the gravitational interactions we can calculate similarly as the
coupling constant for the weak interactions of baryons i.e. a mass is the source and carrier of
gravitational interactions αgr = GM 2 /(ch).
The mass visible by detectors we can calculate from following formula
m = 4π(ρ – ρE)λ 3 /3 = 4fπρEλ 3 /3, (279)
where f ≈ 2.478·10 5 .
References
[1] Steven Weinberg, The Quantum Theory of Fields, Volume II Modern Applications;
pp: 305317 (1996)
[2] Walter Weizel, Lehrbuch der Theoretischen Physik; Volume I, 1; SpringerVerlag,
Berlin (1955) or Polish edition, PWN (1958), pp: 348355, formula (27).
128
Recapitulation and Ultimate Equation
There are a few excellent theories wrongly located and/or misinterpreted.
The string/M theory is wrongly located and misinterpreted. There are closed strings,
however, they are inflexible ideal circles and have other properties (the radius is about 10 45
m). There are also large loops (where the radius is about 0.465 fm). Whereas the external
radius of the torus of a neutrino (in estimation we can treat such a torus as a closed
string), i.e. of the weak charge of a neutrino, is equivalent to the string/M theory (the
radius is about 10 35 m). The phase space of neutrino has 26 elements and the neutrino
consists of the inflexible closed strings. The phase space of a closed string has 10 elements. A
neutrino is not a flexible object. The Mtheory becomes the useful theory due to the phase
transitions of the Newtonian spacetime.
Quantum gravity: The neutrinos are the ‘carriers’ of the gravitational constant. There are
only 4 different neutrinos (the electron neutrino and its antineutrino and the muon neutrino
and its antineutrino). The graviton could be the rotational energy (its mass is zero) of particle
composed of the four different neutrinos in such way that the carrier of graviton is the binary
system of binary systems of neutrinos with parallel spins, i.e. spin of carrier of graviton is 2.
We will call such carrier the neutrino bidipole. Due to the internal structure of the neutrino
quadrupole, when it rotates there appear two transverse waves i.e. it behaves as two entangled
photons, not a graviton. Gravitational energy is emitted via the flows in the Einstein
spacetime composed of the nonrotatingspin neutrino bidipoles. Gravitons and gravitational
waves are not in existence.
The neutrinos, binary systems of neutrinos, bidipoles of neutrinos, and so on, produce the
gradients in the Newtonian spacetime that is impressed on the Einstein spacetime too. We can
describe the gravity via such gradients. When time of an interaction is longer than about 10 60
s then the Newtonian spacetime looks for interacting particles composed of the Einstein
spacetime components as a continuum and we can apply the Einstein equations. Such
continuum leads to the symmetries and the laws of conservation too.
Since spin of carriers of gravitons is 2 whereas of the neutrinos 1/2 then the quantum gravity
leads to conclusion that the neutrinos have only two flavours i.e. there are in existence only
four different neutrinos. The tau neutrinos are not in existence.
The Kasner solution (1921) in the General Theory of Relativity is the foundations of the
Quantum Gravity. Electron consists of the Einstein spacetime components and due to the
fundamental/Newtonian spacetime can disappear in one place and appear in another and so
on. Such behaviour leads to wave function. We can see that quantum behaviour follows from
existence of the two parallel spacetimes. Value of the gravitational constant depends on the
internal structure of the neutrinos and inertial mass density of the Newtonian spacetime. This
means that Quantum Gravity is associated with the quantum behaviour of the neutrinos.
Neutrinos consist of the closed strings so neutrinos can be the quantum particles only in
spacetime composed of the closed strings. Such spacetime was in existence only in the era of
inflation. During this era, this spacetime decayed into small regions and the finite regions
were frozen inside the neutrinos. The Quantum Gravity was valid in the era of inflation only.
Today the gravity is classical because due to the lack of spacetime composed of the closed
strings there cannot be created the neutrinoantineutrino pairs from such spacetime
components similarly as the electronpositron pairs from the Einstein spacetime components.
Inflationary theories need reformulation. Due to the flows of finite regions of the
Newtonian spacetime (in a cosmic scale) the concentrations and next inflations of tachyon
fields are possible. Inflations of tachyon fields are possible also due to collapses of
tremendous masses. To destroy gravity is needed inertial mass density higher than in
approximation 10 38 kg/m 3 . To destroy the closed strings the inertial mass density should be
129
higher still. This is impossible in our Universe. Inflation can lead to the Protoworld and to the
cosmic loop i.e. to the early universe.
Supersymmetry is misinterpreted. The Newtonian and Einstein spacetimes are more
symmetrical when particles arise as particleantiparticle pairs (bosons). The electronpositron
pair is the superpartner of the electron, the neutrinoantineutrino pair is the superpartner of the
neutrino and so on. There is also the fermionboson supersymmetry that follows from the
phase transitions of the imaginary Newtonian spacetime. Inside the stable objects (fermions)
appear the loops (bosons). The ratio of the masses of a stable object to the associated loop is
10.77. The postulated exotic particles are not in existence.
Unification of fundamental interactions needs revision. Due to the dynamic viscosity of
the tachyons, there is in existence the fundamental force. Due to the phase transitions of the
Newtonian spacetime, there appear the four known different interactions and the
entanglement. There is needed a coherent description of all interactions dependent on mass.
We must reformulate the description of the weak and strong interactions especially at low
energy. Unification of all interactions via a superforce is impossible. When we destroy
internal structure of baryons then the strong interactions disappear. Then the baryons decay
into the Einstein spacetime components.
Imaginary Newtonian spacetime: Stephen Hawking has written about and analysed
imaginary time. I believe that imaginary time exist together with imaginary space i.e. the
imaginary Newtonian spacetime composed of structureless tachyons that have a positive
inertial mass. Free tachyons are imaginary because they have broken contact with the rest of
nature – they are bare particles without an internal structure. For quantum physics, the
theories of relativity, inflation and longdistance entanglement require tachyons.
Broken symmetries: Origin of the matterantimatter asymmetry is associated with local
asymmetry of the Einstein spacetime. In symmetrical Einstein spacetime, a particle and its
antiparticle have the same lifetime. It is inconsistent with the assumptions applied in the today
mainstream theories.
Higgs mechanism: The mass gaps arise due to the weak interactions of the Einstein
spacetime components. They produce negative pressure inside and near them in the
Newtonian spacetime (it is the modified Higgs field which is the gravitationally massless field
and in approximation scalar field). When the regions with negative pressure partially overlap
there appears the attraction between the Einstein spacetime components what increases local
mass density of this spacetime. This means that there can appear the mass gap(s). The inertial
mass is more fundamental than a pure energy (which mass is equal to zero). The fields having
inertial and/or gravitational mass density not equal to zero (for example, the Newtonian
spacetime and Einstein spacetime) carry the pure energy.
QED: In the Everlasting Theory, the weak mass of bare electron is equal to its
electromagnetic mass. The QED describes the creations and annihilations of the electronpositron
pairs. The electromagnetic mass of a pair is equal to the bare mass of electron. The
renormalization in the QED leads to the radiation mass. It is the product of subtraction of the
real mass of electron (this is the parameter in the QED) and the bare mass of electron (the
same value for both theories). This means that both theories should lead to the same
theoretical results. We can see that within the QED we secretly assume that electromagnetic
mass of electron is two times smaller than the bare mass of electron. This is the ‘hocuspocus’.
We must change the mainstream picture of electron. We must eliminate the hocuspocus.
Then the QED will become the very simple nonperturbative theory of electron
described within the Everlasting Theory. We can formulate a new electroweak theory
equivalent to the QED. This is possible because the Einstein spacetime and electron carry the
electromagnetic and weak interactions. The theoretical results obtained within the QED are
calculated only for a few the first orders of the perturbation theory so the theoretical results
130
obtained within the QED must be worse than the calculated for electron within the Everlasting
Theory.
Electroweak theory is correct for following interval of energies (125 GeV, 18 TeV). Due
to the hierarchymass error, this theory is incorrect for energies lower than in approximation
125 GeV.
Neutrino speed: Generally, the speed of neutrinos is equal to the speed of light but in
specific processes there can appear the superluminal neutrinos as, for example, the neutrinos
emitted in the supernova SN 1987A explosion. I showed that the neutrino speeds higher than
the c are associated with the nonperturbative stadium inside baryons. This is obvious that the
coupling constants for the weak interactions of the muons, pions and W bosons differ. This
means that on the neutrinos in the weak decays inside the strong fields act different forces.
This theory shows that neutrino mass cannot change. Then, from the Newtonian mechanics
follows that they should move with different speeds. These speeds should depend on the
lifetimes of the particles interacting weakly with the interior of the nonperturbative structure
of the baryons.
YangMills theory in the nonperturbative regime: YangMills theory is a gauge theory
with a nonAbelian symmetry group (given by a Lagrangian) based on the SU(N) group and
QCD is a SU(3) YangMills theory. YangMills theory in the nonperturbative regime, i.e. for
big value of the running coupling for the strong interactions or at energy scales relevant for
describing atomic nuclei, is the unsolved problem. At low energy, confinement has not been
theoretically proven. Since the potential vector can be arbitrarily chosen, we must introduce a
ghostunphysicalcomplexscalar field. In highenergy regime the alpha_strong is small so we
can apply the perturbation theory to prove asymptotic freedom. Most of the difficulties appear
at low energy, especially we cannot prove that QCD confines at low energy and we cannot
describe phenomena which lead to the mass gap(s) (Higgs mechanism). Moreover, in the
infrared limit the beta function is not known.
The Everlasting Theory shows that the unsolved problems at low energy follow from the
fact that the mainstream theories neglect the internal structure of the bare fermions but of the
photons and gluons as well because their carriers, i.e. the binary systems of neutrinos, are the
fermionantifermion pairs. In reality, there is a torus and ball in its centre composed of the
carriers of gluons or photons. It is very difficult to describe mathematically the internal
structure of the bare fermions in such way to add it to Lagrangian. The perturbative theories
as the QED and QCD assume that there is the point bare particle that emits and absorbs
respectively the photons and gluons. The photons create the electronpositron pairs whereas
the gluons the quarkantiquark pairs. Then they annihilate. There appear the diagrams. Both
theories say nothing about the internal structure of the Einstein spacetime that is the scene for
these two theories. There is also unsolved problem how point particles can emit and absorb
anything. This suggests that in reality the point particles are not the point particles. The
Feynman QED has no problem to predict experimental data whereas the QCD does not lead to
the exact mass of the up and down quarks so to the properties of particles composed of these
quarks also. This must follow from the fact that we neglect the internal structure of the
Einstein spacetime and the bare particles. The QED has no problems because all photons in
the Einstein spacetime behave the same. This is because the Einstein spacetime has not
internal helicity. The internal helicity of the strong field follows from the internal structure of
the bare baryons i.e. the core of baryons. When we neglect this structure, there appear the
problems in the QCD.
The QED and QCD are the perturbative theories whereas the Everlasting Theory is the nonperturbative
theory. Why the ultimate theory must contain the nonperturbative and
perturbative theories? The ground state of the Einstein spacetime consists of the nonrotatingspin
neutrinoantineutrino pairs. The total internal helicity of this state is zero and it consists
131
of particles which spin is unitary. In such spacetime, cannot appear loops having internal
helicity i.e. carrying mass. In reality, a unitaryspin loop (the loop state) is the binary system
of two entangled halfintegralspin loops (total spin is 2·1/2 = 1) with opposite internal
helicity i.e. the resultant internal helicity is zero. Then in such spacetime do not appear
turbulences. Such loop can easily transform into a fermionantifermion pair (the fermion
state). Perturbation theories concern the loop states whereas the nonperturbative theories the
fermion states. In nonperturbative theory such as the Everlasting Theory, we cannot neglect
the internal structure of the bare fermions (there is torus and ball in its centre and virtual
pair(s) of fermions outside bare fermion). In the QED the both states, i.e. the loop state and
fermion state, are separated in respect of time whereas in the QCD are not. Moreover, the
QED and Everlasting Theory are energetically equivalent so within these theories we should
obtain the same theoretical results. In baryons, the both states are valid all the time but the
nonperturbative fermion state dominates at low energy whereas the loop state dominates at
high energy. But it is easier to describe the liquidlike plasma within the fermion state. Since
there are the creations from loops and annihilations to loops of the fermionantifermion pairs
so both states (loop and fermion) are energetically equivalent but the barefermion state is
mathematically much simpler.
At the beginning, there was assumed that for the strong interactions are responsible the
loops. We can assume that the pairs of particles (i.e. the electronpositron pairs and the quarkantiquark
pairs) arise respectively as the photon or gluon loops with spin equal to 1, which
transform into the torusantitorus state. The spin polarization of the tori components leads to
the circular and point/ball mass. After the period of spinning, due to the emissions of the
surplus neutrinoantineutrino pairs, the masses of the pairs vanish. We can see that the
perturbative theories concern the phenomena associated with the processes of emission of the
surplus neutrinoantineutrino pairs the Einstein spacetime consists of. Due to the surplus
energy there appear processes described by the 1loop, 2loop, 3loop, and so on, diagrams.
The increasing number of loops in the succeeding diagrams follows from the fact that the
succeeding states must differ. We can see that we neglect the loop/torus state. The loop/torus
state is the stable state for the period of spinning of electron and is stable all the time in the
cores of baryons. This means that this state we can describe via a nonperturbative theory.
This nonperturbative state is very important in the QCD because the loops produced inside
torus, which are responsible for the strong interactions, have internal helicity similarly as the
gluons exchanged between the sham quarkantiquark pairs produced in the strong field. This
leads to the new phenomena inside baryons. Such phenomena are not important in the QED
because for electrons the perturbative state (i.e. the phenomena after the disappearances of the
masses of the fermionantifermion pairs) begins just after the period of spinning of electron
i.e. after the nonperturbative state. In contrary to the renewable/quantum particles such as
electrons, or quarkantiquark pairs in strong fields, inside the core of baryons there is all the
time the stable torus and ball in its centre. This means that the both states, i.e. the nonperturbative
and perturbative, have been in existence all the time. This is the reason why the
QCD is not such precise as the QED. We can apply the perturbative QCD for very high
energies or for shortdistance interactions. This is because then the strongweak coupling
constant is small (in my theory but also in the QCD). Due to the very stable core inside
baryons composed from the Einstein spacetime components and the disappearance of masses
of the sham quarksantiquarks pairs, the perturbative and nonperturbative states exist
simultaneously all the time. The number of the disappearances of masses per unit of time
increases when energy increases. This means that contrary to the nonperturbative state that is
valid for whole energy spectrum, the perturbative state is obligatory at high energies and there
should appear big problems at low energy.
132
The field associated with the YangMills is massless i.e. consists of the photons and gluons,
i.e. the rotational energies (so massless) of the Einstein spacetime components. Massless
gluons transform into massless photons outside the strong field so gluons are not the longdistance
particles. This is due to the internal helicities/colours of the strong field and the
carriers of gluons and photons i.e. the entangled binary systems of neutrinos. Due to the weak
interactions of the neutrinoantineutrino pairs, there appear the balls composed of such pairs.
The Einstein spacetime components decrease local pressure in the Newtonian spacetime (it is
the modified Higgs field). In very good approximation, the modified Higgs field is the
gravitationally massless scalar field. This field is gravitationally massless so we can call it the
ghost field. There appears attraction between the Einstein spacetime components when the
regions with negative pressure overlap partially. This is the confinement. The local mass
densities inside the balls are higher than the mean mass density of the Einstein spacetime.
There appear the masses composed of the carriers of gluons. We can see that the particles
acquire their mass through symmetry breaking in the fields carrying the massless fields. Due
to the coupling constants for the weak interactions, the masses are equal to the masses of the
W and Z bosons (in this book there are the very simple calculations of these masses) but these
bosons are not responsible for the weak interactions in the lowenergy regime. We can see
that my theory shows that the YangMills theory has the mass gap(s).
There is no proof that QCD confines at low energy. From my description follows that there
is not a confinement at very low energy but my QCD ‘confines’ at low energy due to the
internal helicities/colours of the strong field and the carriers of gluons and photons. Simply,
outside the strong field we can neglect the internal helicities/colours so the gluons behave as
photons. We can say that it is due to the properties of the carriers of gluons and photons i.e.
due to the mass of the Einstein spacetime components. On the other hand, the finite range of
the strong fields follows from the circumference of the large loops that are responsible for the
strong interactions.
At the beginning of inflation, in the ghost field there were produced the closed strings from
the tachyons and next the neutrinos from the binary systems of the inflexible closed strings.
The Quantum Gravity concerns the behaviour of the neutrinos in the very short era of
inflation.
The internal structure of the bare fermions eliminates the singularities and infinities from
theory.
The above description is the prelude to the nonperturbative Mtheory that is the essential
part of the Everlasting Theory. The Everlasting Theory shows that there is the atomlike
structure of baryons and that this theory is not an alternative theory in relation to the Standard
Model. This theory is the fundamental lacking part in the Standard Model and includes
Gravity. The nonperturbative Mtheory concerns the gluon large loops produced inside the
torus in the core of baryons, photon loops, stable states of tori and the balls whereas the
perturbative mainstream theories concern the phenomena caused by energy emitted in the
annihilations of the fermionantifermion pairs. Due to the creations of the loops from this
energy, there appear the nloop diagrams. It is the reason why within the perturbative theories
we cannot decode the internal structure of the bare fermions. We cannot compare the nonperturbative
state with the perturbative state because they are not the descriptions of the same
phenomena. The nonperturbative state is the fundamental complement of the perturbative
state.
For very high energies of collisions, the atomlike structure of baryons is destroyed so there
are the weak signals of existence of such structure only for the medium energies.
The important conclusions: The gravity is associated with the Newtonian spacetime (the
gas composed of tachyons) and with the Einstein spacetime (the gas composed of the nonrotatingspin
binary systems of neutrinos). More precisely, the gravitational constant depends
133
on the internal structure of neutrinos and inertial mass density of the Newtonian spacetime.
Neutrinos consist of the superluminal binary systems of the closed strings. The closed strings
produce the jets in the Newtonian spacetime. The gravitational interactions we can describe as
the gradients in the Newtonian spacetime. The gradients are impressed on the Einstein
spacetime also. The Everlasting Theory shows that there are 8 different rotating binary
systems of neutrinos (the 4 lefthanded and 4 righthanded) and each has mass in
approximation 6.7·10 67 kg. Due to the lack of the spacetime composed of the binary systems
of the closed strings, the neutrinos cannot change their mass. This means that neutrinos, which
appear in different weak decays inside the strong field, should have different speeds. The
binary systems of neutrinos carry the massless photons and gluons – they are the rotational
energies of the Einstein spacetime components. The internal structure of the baryons causes
that the internal structure of the Einstein spacetime components (the 8 different rotating
components) are disclosed. The entangled gluons transform inside the core of baryons into the
loops. When a loop overlaps with the circular axis of baryons (the large loop) then its mass is
67.5444 MeV. Such large loops are responsible for the strong interactions of mesons and the
running coupling for low energy is 1. The binary systems of such loops, i.e. the neutral pions,
are responsible for the strong interactions of nucleons. Such loops are responsible for the
strong interactions of baryons and the running coupling for low energy is 14.4. Acceleration
of a nucleon causes that its mass increases. This follows from the formula for spin (mvspinr =
h/2) for the stable fermions. In the same time the mass of the loops decreases so the running
coupling also. This follows from the formula for spin (ΔE·Tlifetime = h, where the lifetime is
inversely proportional to the spin speed vspin) for the virtual large loops responsible for the
strong interactions. There is asymptote for high energies equal to 0.1139. Range of the gluon
loops is equal to the circumference of loop, i.e. 2.92 fm, and such is origin of the
‘confinement’ of the gluon loops responsible for the strong interactions. What is mechanism
of the disclosure of the properties of the Einstein spacetime inside the baryons? The torus
inside core of baryons has internal helicity so the gluon loops emitted by the core adopt this
helicity. The components of carrier of a not entangled gluon (i.e. the two entangled neutrinos)
also have the internal helicities. The three internal helicities of a not entangled carrier of gluon
lead to the 8 different gluons. We can say that the internal structure of the Einstein spacetime
and the core of baryons are responsible for the transformation of the photons into gluons in
distances smaller than 2.92 fm from centre of nucleons. In centre of the core of baryons arises
sphere inside which the Einstein spacetime thickens. Radius of this sphere is 0.871·10 17 m
whereas mass (the mass gap) is 424.124 MeV. This thickened Einstein spacetime is
responsible for the weak interactions of the baryons. Mass density of the thickened volumes is
only by 1/40,363 higher than the Einstein spacetime. The four interactions associated with the
Einstein spacetime components we can describe by means of the Riemann metric and Einstein
equations applied in the General Theory of Relativity written for phase space containing more
elements to have room for all types of forces. In reality, there are not in existence the higher
dimensions. The numbers 10 and 26 are the numbers of elements of the phase spaces
respectively for the single or binary systems of closed strings and the single or binary systems
of neutrinos. Phase space contains elements describing position, shape and motions of a
particle. The Everlasting Theory and Special Number Theory presented together with the
Everlasting Theory show origin of the magic numbers which appear in the string/M theory i.e.
the 8(10) and 24(26). Due to the ideas presented in the Special Number Theory, these magic
numbers can appear in different mathematical expressions but nature realizes only one. It
looks similar as the theory of great numbers – not all correlations have physical meaning.
Properties of the closed strings lead to the phase transitions so the massenergy part in the
General Relativity is dual. The greater tori consist of smaller tori, and so on. There arise the
neutrinos, cores of baryons and the protoworlds. Outside the core of baryons is obligatory the
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TitiusBode law for the strong interactions. Einstein tried to change the massenergy part in
his equations to describe internal structure of particles but it failed. We can see that we can
generalize the Einstein equations applied in the General Relativity. The enlarged Riemann
metrics includes the gravity and the YangMills fields which leads to the photons, gluons and
the regions with thickened Einstein spacetime (such regions have mass because the Einstein
spacetime has mass density not equal to zero) responsible for the weak interactions of
baryons. The weak interactions between the thickened regions of the Einstein spacetime are
possible when their surfaces are in distance equal to or shorter than 3482.87 times the external
radius of a neutrino. We can see that the weak field practically overlaps with the thickened
regions. This means that the weak interactions are the shortdistance interactions. Exchanged
small loops composed of the binary systems of closed strings are responsible for the
entanglement of particles (for the longdistance entanglement also). Due to the symmetrical
decays of the virtual bosons in the strong field, outside of the core of baryons is obligatory the
TitiusBode law for the strong interactions. Due to the new theory of weak interactions, to
calculate the radiation masses, we can apply two dual methods i.e. the Feynman diagrams or
the nonperturbative theory described within the Everlasting Theory. The last theory is much
simpler and gives better results. Due to the properties of the Einstein’s spacetime is possible
quantization of the YangMills fields. A torus of the electron is the entangled and specifically
polarized zeroenergy photon. The electric chargeanticharge pairs arise from the loops
composed of the Einstein spacetime components and radii of the loops are equal to the radii of
the equators of the tori/electriccharges. The core of protons and torus of positrons have the
same electric charge but there is place for the sham quarkantiquark pairs. This theory leads to
masses of the quarks and shows that the other properties of the quarks are different. The
YangMills theory (which leads to the gluons too) is correct whereas the theory of quarks is
correct only partially. Because the quark theory is partially incorrect, within the QCD we
cannot calculate exact rest masses of the up and down quarks.
The E. Kasner solution for the flat anisotropic model (1921) in the General Theory of
Relativity leads to the numbers characteristic for the bare fermions, especially for the tori. On
the other hand, the internal structure of the bare fermions leads to the known interactions and
the quantum behaviour of the electron. Electron consists of the Einstein spacetime
components and due to the fundamental/Newtonian spacetime can disappear in one place and
appear in another and so on. Such behaviour leads to wave function. We can see that quantum
behaviour follows from existence of the two parallel spacetimes. Value of the gravitational
constant depends on the internal structure of the neutrinos and inertial mass density of the
Newtonian spacetime. This means that Quantum Gravity is associated with the quantum
behaviour of the neutrinos. Neutrinos consist of the binary systems of the closed strings so
neutrinos can be the quantum particles only in spacetime composed of the binary systems of
the closed strings. Such spacetime was in existence only in the era of inflation. During this
era, this spacetime decayed into small regions and today the binary systems of the closed
strings are inside the neutrinos. The Quantum Gravity was valid in the era of inflation only.
Today the gravity is classical because due to the lack of spacetime composed of the closed
strings there cannot be created the neutrinoantineutrino pairs from such spacetime
components similarly as the electronpositron pairs from the Einstein spacetime components.
The Kasner solution and the scales for the charges (weak, electric and strong) in the
generalized Kasner solution and the BKL oscillatory model, lead to the phase transitions of
the fundamental spacetime and to the Protoworldneutrino transition that caused the exit of
the early Universe from the blackhole state. The phase transitions are the foundations of the
modified/useful string/M theory. There is also the ultimate equation that combines the masses
of sources of all types of interactions. The Kasner solution leads to the new cosmology as
well. We can say also that the Kasner solution is the foundations of the Quantum Theory of
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Gravity and Quantum Theory of Fields without singularities and infinities. The Kasner
solution is asymmetric in time because there appear the stable structures. The reduction of the
state vectors is asymmetric in time as well. The Kasner solution shows that the theory of
gravity is the more fundamental theory than the Quantum Theory of Fields. This postulated
Roger Penrose.
The ultimate equation: We can notice that the range of the weak interactions of the
neutrinos Rweak(neutrino) = 3482.87rneutrino divided by the Compton length λ of the bare electron
(see formula (17)) is equal to the Reynolds number NR for maximum dense Newtonian
spacetime (see formula (1)). Such state of spacetime is inside and on surface of the closed
strings from which the neutrinos consist of. Applying the above formula and formulae (1)
(49), especially (6), (13)(16) and (47)(49), we can write the ultimate equation which ties the
properties of the pieces of space i.e. tachyons with the all masses/sources responsible for the
all types of interactions. To simplify the ultimate equation we assume that the ratio of the
mean distance between the neutrinoantineutrino pairs in the point mass to the distance in the
Einstein spacetime is equal to 1. In reality, the ratio is (ρE/(ρE + ρpoint(proton))) 1/3 = 0.9999917,
where ρE is the mass density of the Einstein spacetime. This means that there are the five
significant digits.
The ultimate equation looks as follows
4πmtachyonρ/3η = (2mclosedstring/h) 2 (2mneutrino/ρE) 1/3 (mbare(electron)/2)c(X/H + ) 1/2 . (280)
The 4π/3 on the left side of the ultimate equation shows that the tachyons are the balls. The
mean mass of tachyons is the mean mass of the source of the fundamental interaction that
follows from the direct collisions of tachyons and their dynamic viscosity. The ρ is the mass
density of the pieces of space i.e. the tachyons (it is not the inertial mass density of the
Newtonian spacetime). The η is the dynamic viscosity of the pieces of space i.e. of the
tachyons.
The two masses of the binary systems of closed strings (their total spin is 2·h/2 = h) on the
right side of the ultimate equation are the source of the entanglement. The two masses of
neutrinos, i.e. the neutrinoantineutrino pair, are the source of the gravitational field. The mass
of single neutrino is the smallest gravitational mass. In the equation the smallest gravitational
mass is multiplied by 2 that means the nonrotatingspin neutrinoantineutrino pairs (the 2) are
the components of the ground state of the Einstein spacetime (the ρE in the denominator). The
half of the mass of the bare electron is the mass of the electric charge i.e. the mass of the
source of the electromagnetic interaction. The c is the speed of photons and gluons. The
transitions of the carriers of the photons and gluons, i.e. of the neutrinoantineutrino pairs,
from the electromagnetic field to the strong field force the photongluon transitions. The X
is the mass of the torus inside the core of baryons in which the large loops arise (they are
responsible for the strong interactions). The X is the mass of the strong charge/mass. Outside
the strong field, due to the gluonphoton transitions, it behaves as electric charge of positron.
The H + = X + Y – bindingenergy, where Y is the point mass of the core of baryons. The Y is
the source of the weak interaction in the baryons in the lowenergy regime. It is the relativistic
object so it can produce the W and Z bosons also. The ratio X/H + appeared in the formula (82)
that defines the mass of the source of the strongweak interactions for colliding protons. The
calculations lead to the running coupling for the strongweak interactions. We can see that due
to the phase transitions of the Newtonian spacetime as the first appears the Planck constant,
next gravitational constant associated with the mass of neutrino and next the electric charge
and speed c.
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To give possibility for a quick verification of correctness of the ultimate equation, I write
once more the needed values. I do not write the units. They are in the System International
except the X and H + (in MeV).
mtachyon = 3.752673·10 107
η = 1.87516465·10 138
ρ = 8.32192436·10 85
mclosedstring = 2.3400784·10 87
h = 1.054571548·10 34
mneutrino = 3.3349306·10 67
ρE
= 1.10220055·10 28
c = 2.99792458·10 8
mbare(electron) = 9.09883020·10 31
X = 318.295537
H +
= 727.440123
The left and right side of the ultimate equation is 6.9761·10 159  we know that we can write
the five significant digits only.
How can we verify my theory? My theory identifies where mainstream theories are
inconsistent with experimental data:
1. Neutrinos produced in specific processes can move with speeds higher than photons and
gluons. This follows from the atomlike structure of baryons.
2. There should be an asymptote for the running coupling for strong interactions of the
colliding nucleons – the value of it equals 0.1139. This follows from the packing to
maximum the cores of baryons.
3. There should be the upper limit for energy of relativistic proton about 18 TeV. This follows
from the internal structure of the core of baryons.
4. There should be weak signal of existence type W boson carrying mass about 17 TeV. This
follows from the internal structure of the Einstein spacetime and the core of baryons.
5. There should be in existence stable binary systems of neutrinos (spin=1), i.e. the carriers of
photons and gluons, and the nonrotatingspin binary systems of binary systems of
neutrinos (spin=2) i.e. the carriers of gravitational energy.
6. There should not be in existence gravitons and gravitational waves. This follows from the
properties of the two spacetimes.
7. There are the weak signals of existence of new bosons that disappear for high energies.
This follows from the fact that due to the highenergy collisions the TitiusBode orbits are
destroyed.
Turning points in the formulation of the ultimate theory: At the beginning, I noticed that
the following formula describes how to calculate the mass of a hyperon:
m(MeV)=939+176n+26d, where n=0,1,2,3 and d=0,1,3,7.
For a nucleon it is n=0 and d=0 which gives 939 MeV. For lambda n=1 and d=0 which gives
1115 MeV. For sigma n=1 and d=3 which gives 1193 MeV. For ksi n=2 and d=1 which gives
1317 MeV. For omega n=3 and d=7 which gives 1649 MeV. I later noticed that the distances
of the mass between the resonances and distances of the mass between the resonances and
hyperons is approximately 200 MeV, 300 MeV, 400 MeV, and 700 MeV. This was in 1976.
In 1985, I grasped that in order to obtain positive theoretical results for hadrons, we should
assume that outside the core of a nucleon is in force the TitiusBode law for strong
interactions. On orbits are relativistic pions. The year 1997 was the most productive for me
because I described the phase transitions of the Newtonian spacetime, the fourneutrino
symmetry also leading to the distribution of galaxies that is visible today, and I also described
the fundamental phenomena associated with the cosmology of the Universe. In this eventful
year, I practically formulated new particle physics and new cosmology.
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The final recapitulation
The Everlasting Theory is the lacking part of the ultimate theory and is free from
singularities and infinities. There are the two longdistance interactions. This suggests that
there are two parallel spacetimes. To explain the inflation, longdistance entanglement,
cohesion of wave function and constancy of the speed of light, we need the fundamental
spacetime composed of tachyons. The gas composed of tachyons is the
fundamental/Newtonian spacetime whereas the gas composed of the neutrinoantineutrino
pairs is the Einstein spacetime. There are the two basic phenomena. The saturation of
interactions of the tachyons leads to the phase transitions of the Newtonian spacetime. The
first phase transition leads to the closed strings the neutrinos consist of, the second leads to the
Einstein spacetime, third to the core of baryons whereas the fourth to the cosmic object, the
Protoworld, after the era of inflation (there appears the new cosmology). The second
phenomenon, i.e. the symmetrical decays of the bosons in very high temperatures, leads to the
TitiusBode law for the strong interactions and to the TitiusBode law for the gravitational
black holes. There appears the atomlike structure of baryons. On base of these two
phenomena and the 7 parameters only, I calculated several hundred basic theoretical results
consistent or very close to experimental data. I calculated the basic physical constants as well.
The nature on its lowest levels once again behaves classically. The bare fermions consist of
torus and ball in its centre. The mainstream theories neglect the internal structure of bare
fermions. The core of baryons is the black hole in respect of the strong interactions whereas
the ball in its centre is the black hole in respect of the weak interactions. Their masses are
quantized so they emit the surplus energy. The same concerns the gravitational black holes.
Taking into consideration these facts we can formulate theory simpler than the Newtonian
mechanics.
The quantum behaviour follows from existence of the two parallel spacetimes. The Kasner
solution for the flat anisotropic model (1921) in the General Theory of Relativity leads to the
numbers characteristic for the bare fermions. Quantum Gravity is associated with the quantum
behaviour of the neutrinos. Neutrinos consist of the binary systems of the closed strings so
neutrinos can be the quantum particles only in spacetime composed of the binary systems of
the closed strings. Such spacetime was in existence only in the era of inflation. Today the
gravity is classical. The Kasner solution and the scales for the charges (weak, electric and
strong) in the generalized Kasner solution and the BKL oscillatory model, lead to the phase
transitions of the fundamental spacetime and to the transition of the Protoworld into neutrino
that caused the exit of the early Universe from the blackhole state. The Kasner solution is the
foundations of the Quantum Gravity and the Quantum Theory of Fields.
The phase transitions are the foundations of the modified/useful string/M theory. There is
also the ultimate equation that combines the masses of sources of all types of interactions.
The ultimate theory must contain nonperturbative and perturbative theories. The ground
state of the Einstein spacetime consists of the nonrotatingspin neutrinoantineutrino pairs.
The total helicity of this state is zero and it consists of particles which spin is unitary. In such
spacetime cannot appear loops which have helicity so mass as well. In reality, a unitaryspin
loop (the loop state) is the binary system of two entangled halfintegralspin loops with
opposite helicities i.e. the resultant helicity is zero. In such spacetime do not appear
turbulences. Such loop can easily transform into a fermionantifermion pair (the fermion
state). Perturbation theories concern the loop states whereas the nonperturbative theories the
fermion states so we cannot neglect the structure of bare fermions.
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Definitions
Acceleration of expansion of the Universe: Due to the decays of the superphotons, the
Universe significantly flared up two times i.e. about 13.2 and 5.7 billion years ago. From the
second flare up follows that an acceleration of expansion of the Universe is an illusion. The
applied formula for the redshift calculated on the base of the observed redshift is wrong and
leads to illusion that the expansion of our Universe accelerates.
‘Antigravity’: In thickened regions of the Einstein spacetime on masses act repulsive forces.
Antiparallel jets: Antiparallel jets produce binary loops when loops in a binary system have
different internal helicity and parallel spins which directions overlap. Such situation is, for
example, in the binary systems of the closed strings and the cores of protogalaxies. Due to the
internal helicities, a binary loop sucks up spacetime from plane perpendicular to the spin and
emits it as the jets along the direction of the spin. In the protogalaxies, due to the fluxes in
spacetime, we should observe the capture of matter by the fluxes from the accretion discs.
Background: The volume filled with internally structureless tachyons (Newtonian spacetime
is the background for gravitational interactions), nonrotatingspin binary systems of neutrinos
(excited states of the Einstein spacetime are responsible for the electromagnetic, weak and
interactions), and virtual particleantiparticle pairs (virtual particles do not change the mean
mass density of background).
Baryons: In their centre is the core composed of torus (it is the electric charge) and point
mass. The point mass is responsible for the weak interactions. On circular axis inside the torus
are produced the large loops responsible for the strong interactions. Outside of the core is
obligatory the TitiusBode law for the strong interactions. On the orbits are one or more pions.
Big bang theory: An enormous region of the Newtonian spacetime can thicken and then
expand with superluminal speeds (inflation). Such events happen every time but due to the
superluminal speeds, probability that this will happen near our Universe is practically equal to
zero. During such inflation, arise the closed strings and the binary systems of neutrinos the
Einstein spacetime consists of. The speed of the entangled neutrinoantineutrino pairs (the c)
stops the inflation Next there appear the neutrons. There the Protoworld and the cosmic loop
i.e. the early universe can appear. However, the ‘soft’ big bangs are associated with the
explosions of universes that have strictly determined mass (they are the cosmic loops
composed of the neutron black holes) – such explosions are due to the Protoworldneutrino
transition. During such transition the thickened Einstein spacetime, i.e. the dark energy,
appears. The dark energy is composed of the surplus nonrotatingspin binary systems of
neutrinos. The inflows of the dark energy into the cosmic loop cause its exit from the blackhole
state. We can see that there are the two main stages associated with the new big bang
theory i.e. there are the inflationary stages associated with the Newtonian spacetime and there
are the protoworld stages leading to the ‘soft’ big bangs of the cosmic loops.
Black holes: The Everlasting Theory shows that the cores of protons are the black holes with
respect to the strong interactions (their mass is 727.44 MeV). The thickened regions of the
Einstein spacetime (this consists of the nonrotatingspin binary systems of neutrinos) in the
centers of the cores of baryons are the black holes with respect to the weak interactions (their
mass is 424.12 MeV). The point mass of the muons also are the black holes with respect to
the weak interactions but in contrary to the point mass of baryons there are the two energetic
neutrinos and each has energy about 17.7 MeV. The greatest neutron stars are the
gravitational black holes. Their mass is about 24.8 times greater than the mass of the sun. The
magnetars have mass from 25 to 50 times greater than the mass of the sun. In their centers are
the biggest neutron stars. The greater stars and the bigger black holes consist of the
magnetars. Due to the new theory of the weak interactions, inside our Universe, the cores of
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nucleons cannot collapse. The black holes are everywhere. Their masses are quantized so they
emit the surplus energy.
Broken symmetry: In symmetrical fields can appear pairs composed of rotary vortices. The
components of a pair have different internal helicity. This means that inside each component
is broken symmetry. Inside a rotary vortex can appear electrically charged pairs in such way
that the components of a pair have different masses. This means that symmetry of a field is
broken two times. There can be also in existence regions in the Einstein spacetime containing
different number of different neutrinos – it breaks symmetry also.
Closed strings: On surfaces of regions with tachyons packed to the maximum closed strings
arise (the radius is approximately 0.95·10 45 m, not approximately 10 35 m as in the string/M
theory). The natural speed of a closed string in the Newtonian spacetime is approximately
2.4·10 59 times higher than the speed of light in spacetimes. The spin speed is practically equal
to the mean linear speed of tachyons. Closed string consists of K 2 tachyons (K=0.79·10 10 ).
Due to the mean linear and angular speeds of tachyons in the Newtonian spacetime only the
identical right or lefthanded closed strings appear. The maximum thickness of a closed
string is equal to the diameter of a tachyon. Closed string is stable due to its shape which
creates negative pressure inside it. Spin of closed strings is halfintegral. Each closed string
produce one collimated jet in the Newtonian spacetime. Because resultant internal helicity of
spacetime must be equal to zero, the closed strings arise as the closed stringantistring pairs.
To describe the position, shape and motions of a closed string we need three coordinates, two
radii, one spin speed, one angular speed associated with the internal helicity and time
associated with the linear speed. In order to describe the rotation of a spin vector we
additionally need two angular speeds. This means that we need ten numbers to describe a
closed string. In order to describe a stringantistring pair we need a phase space containing the
ten elements also because the distance between the components in a pair follows from the
thickness of a closed string.
Coherent mathematics: We cannot formulate coherent mathematics on the base of the points
without size because such points (even an infinite number of them) do not lead to axes, areas
or volumes that have sizes that are not equal to zero. Coherent physics cannot also start from
sizeless points. True abstract mathematics also does not lead to the observed nature. The
ultimate theory should begin from some physical objects.
Colours: They are the three internal helicities of the carriers of gluons (gluons are the 3coloured
particles) and one internal helicity of loops and tori in the strong field (they are the
1coloured particles).
Cosmic loop: The loop inside the torus of the Protoworld composed of the neutron black
holes.
Cosmicray particles: The assumption that the ground state of the Einstein spacetime is the
field composed of the nonrotatingspin binary systems of neutrinos leads to new particle
physics and new cosmology. When a particle more massive than the binary system of
neutrinos accelerates then emits more and more energy. For example, the Everlasting Theory
predicts that at energy above approximately 18 TeV per nucleon, nucleon emits the surplus
energy. Then, why can we detect the ultraenergetic cosmic rays? Such cosmic rays are the
very energetic neutrinos and binary systems of neutrinos. The detected several cosmic rays
above the GZK limit arose at the beginning of the ‘soft’ big bang in the protuberances of the
Einstein spacetime and were emitted by the quasars with the redshift higher than zob=1.
Dark energy: Finite fields composed of the surplus weak dipoles.
Dark matter: The photon galaxies (i.e. the entangled photons – the entanglement is due to
the exchanges of the binary systems of the closed strings) coupling the cosmic objects inside a
galaxy cause an illusion that a dark matter exist.
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The dark matter consists also of the ironnickel lumps produced in explosions of the big stars
just after the beginning of the ‘soft’ big bang. Because the dark matter arose just after the
beginning of the ‘soft’ big bang then temperature of the ironnickel lumps is the same as the
CMB radiation. This means that it is very difficult to detect the dark matter. Today, most of
the dark matter is in the halos of galaxies. The ratio (10.77) of the mass of the core of
nucleons (727.44 MeV) to the mass of the large loop (67.5444 MeV) is almost equal to the
ratio (10.65) of abundance of iron (90.64%) to abundance of nickel (8.51%) in the lumps of
the dark matter. Possible it has some deeper meaning. Are the cores and the large loops the
catalysts in production of iron and nickel?
The photon galaxies interact with the dark matter i.e. the ironnickel lumps. This leads to
conclusion that the dark matter should behave a little as a gas and a little as a solid body. Most
often, the planes of the photon galaxies are perpendicular to the magnetic axes of the massive
galaxies so due to the TitiusBode law for the gravitational interactions each massive galaxy
should contain a few parallel thin lenses each composed of the dark matter and the photon
galaxies. They should be parallel to the plane of disc composed of the visible matter.
DNA:
The precursors of the Deoxyribonucleic Acids (the DNAs) arose inside the cosmic loop
composed of the neutron black holes i.e. there dominated the strong interactions. With the
strong/electric charge of the torus inside the core of baryons is associated the ternary
symmetry. With each element of a ternary system a neutrino can interact weakly. The three
neutrinos associated with a torus are entangled. Since in a ternary system the components can
be in different states so there can arise trios composed of the same neutrinos also. The trios
are the codons in the precursors of the DNAs. Due to the superphotons, the baryons were
entangled too. Due to the beta decays, there were produced the helices composed of the
protonelectron pairs and with each protonelectron pair was associated one codon composed
of neutrinos. The 2 different electric charges are the analogs to the deoxyribose and the
phosphoric acid. The 4 different neutrinos are the analogs to the four different bases i.e. A, C,
G and T. In atoms, there are the two spin states of an electron in the ground state (up and
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down). This leads to the two threads in the helices whereas the Pauli Exclusion Principle is
responsible for creation of the helices i.e. each next proton in a helix must have different
direction of spin. The electroweak interactions of the precursors of the DNAs lead to the
molecular DNAs.
We can see that precursors of the DNAs look as superphotonlike structure. This means that
the superphotons could be the catalysts. There were about 10 78 superphotons. To create one
our entire genome is a need about 10 36 superphotons. This means that human life should be
usual.
The 4 bases in DNA, the 8 gluons and the spin of the carriers of gravitational energy (the spin
is 2 = 4·1/2) lead to the two families of neutrinos only. The ‘oscillations’ of the neutrinos (in
reality the ‘oscillations’ are the exchanges; neutrinos are the very stable particles) lead to the
illusion that there are the three families of neutrinos.
Due to the ternary symmetry for the strong/electric charges of nucleons and the pairing of the
atoms in the Earth atmosphere (O2, N2) and the electrons in the ground states of atoms, there
appears the sixfold axis of symmetry (3+3=6) typical for the flakes of snow.
Einstein spacetime: The field composed of nonrotatingspin binary systems of neutrinos.
The binary systems of neutrinos are weak dipoles that are composed of two opposite weak
charges. The properties of a weak charge depend on the structure of the torus of a neutrino. It
appears as a miniature of electric charge of proton.
Electromagnetic interaction: Electric charges polarize the Einstein spacetime. In the
Einstein spacetime arise the virtual electronpositron pairs. Their annihilation creates
divergent beams in the Einstein spacetime. Such phenomena create negative pressure in the
Einstein spacetime. In region between the opposite electric charges, the density of the virtual
electronpositron pairs is higher than in other parts. In regions between the same electric
charges, such density is lower. Electric charges can also interact due to the exchange of the
photons since photons also produce real and virtual electronpositron pairs.
Electron: Electric charge of electron arises following the entanglement and polarisation of
the Einstein spacetime components i.e. the neutrinoantineutrino pairs, therefore, the torus of
an electron forms part of the Einstein spacetime. Axes of these dipoles are perpendicular to
the surface of a torus and all senses of spins of the dipoles point the inside of the torus
(charge) or outside (anticharge). The polarized binary systems of neutrinos cross the circular
axis and centre of a torus so they make halfturns in these places  there two masses appear
i.e. the circular mass and point mass. This is because such turns decrease the pressure in the
Einstein spacetime that causes new binary systems of neutrinos to flow into a bare electron
(absorption). On the circular axis of electron, there is a whole charge and only half mass of
bare electron. After the time of spinning (it is the circumference of the equator of the torus
divided by the c), due to the properties of the Newtonian spacetime, the electric charge
disappears in one place and appears in another and so on. The disappearances cause that the
mass of electron vanishes (emission of the surplus neutrinoantineutrino pairs). We can see
that the distributions of charge and mass are different and for very short time that follows
from the mean speed of the tachyons, the electric charge and mass of electron can be
separated spatially. But it is always true that half of the bare mass of electron is associated
with electric charge. The spin polarization of the components of the electric charge of an
electron is an analog to gradients of temperature in a tropical cyclone – they are the effective
causes of the flows/winds in the spacetime/atmosphere that increase the mass density (so also
mass) of the spacetime/atmosphere inside the cyclone/bareelectron (the outcome).
Elementary charge: The torus of an electron and the torus of proton are composed of the
same number of binary systems of neutrinos, therefore, both tori create the same amount of
polarized lines of electric forces in the Einstein spacetime. This means that the densities of the
created lines are the same also. In the torus of proton the mean distance between the binary
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systems of neutrinos is approximately 554.3 times smaller than that found in the torus of an
electron. Furthermore, virtual electronpositron pairs arise near the bare electron.
Elementary photon: It is rotational energy of a neutrinoantineutrino pair. After the period of
inflation, the carriers of photons, i.e. the neutrinoantineutrino pairs, behave classically
whereas elementary photons, i.e. the massless rotational energies, behave as quantum particles
i.e. a massless rotational energy disappears in one place and appears in another and so on – it
leads to wave function.
Entangled particles: The longdistance entanglement of neutrinos is due to the exchanges of
the superluminal quanta composed of the binary systems of the closed strings emitted by the
neutrinos.
Evaporation of neutron black holes: The neutron black holes arose after the period of the
inflation but before the beginning of the ‘soft’ big bang. The massive galaxies arose due to the
evaporation of the neutron black holes the protogalaxies consisted of. The bigger cosmic
structures composed of the protogalaxies arose before the ‘soft’ big bang also. The
evaporation was due to the inflows of the dark energy. The dark energy arose due to the
collapse of the Protoworld before the ‘soft’ big bang. The dark energy is the thickened
Einstein spacetime composed of the nonrotatingspin binary systems of neutrinos. To detect
such binary systems we should measure the mass with accuracy about 10 67 kg. Today it is
impossible. The dark matter consists of the ironnickel lumps entangled via the binary
systems of the closed strings. The dark matter arose in the era of the evaporation of the
protogalaxies. The dark matter is in the halos of the galaxies and its temperature is the same
as the CMB. Due to the temperature is very difficult to detect it. The small protogalaxies
arose due to the explosions of the big protogalaxies during the era of the evaporation of the
protogalaxies. It was due to the inflows of the dark energy. In surroundings of the evaporating
protogalaxies arose stars so there should be the groups of the first stars. We should not
observe their regular distribution.
Finestructure constant: Its value changed in the protuberances in the Einstein spacetime
appearing at the beginning of the ‘soft’ big bang. The finestructure constant is in proportion
to the mass density of the Einstein spacetime to the power of five third. We observe such
changes for the quasars.
Fourneutrino symmetry: There are four different neutrinos (two neutrinos and two
antineutrinos). Binary system composed of the binary systems of neutrinos, when consists of
four different neutrinos, can have total spin and total internal helicity equal to zero.
Entanglements of such objects lead to cosmic structures but solve also many other problems.
Fractal: An object composed of solitons having different sizes.
Fractal field: A field composed of threads consisting of binary systems of neutrinos in such a
way that the spins are tangent to the thread.
Gluonphoton transitions: The neutrinoantineutrino pairs are the carriers of the elementary
gluons and photons. The pairs have the three internal helicities (the three colours) but their
internal structure is disclosed in the strong field only because this field in contrary to the
electromagnetic field has internal helicity due to the properties of the strong charge/mass.
Gravitational interaction: All particles composed of neutrinos interact gravitationally. The
neutrinos transform the chaotic motions of free tachyons into divergently moving tachyons.
This means that near and near a bare particle pressure in the Newtonian spacetime decreases.
Such is the origin of gravitational attraction. This gradient is impressed on the Einstein
spacetime which means that Einstein gravity appears.
Gravitons: The graviton could be the rotational energy (its mass is zero) of particle
composed of the four different neutrinos in such way that the carrier of graviton is the binary
system of binary systems of neutrinos with parallel spins, i.e. spin of carrier of graviton is 2.
We will call such carrier the neutrino bidipoles. Due to the internal structure of rotating
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neutrino quadrupole, there appear two transverse waves. This means that rotating neutrino bidipole
behaves as two entangled photons, not as graviton. Gravitational energy is emitted via
the flows in the Einstein spacetime composed of the nonrotatingspin neutrino bidipoles.
Gravitons and gravitational waves are not in existence.
Hadronization and deconfinement in the Everlasting Theory: The confinement described
within the Everlasting Theory leads to the gluon balls. Due to the atomlike structure of
baryons, the gluon balls transform into the sham quarkantiquark pairs i.e. into vortexantivortex
pairs. We can see that between the quarks can be exchanged the gluon balls. The
exchanged gluon balls, due to the confinement, produce the spokes i.e. the physical traces in
the Einstein spacetime. Action does not depend on length of a spoke but it is obvious that
must be proportional to area of crosssection of a spoke. The spokes are the regions in the
Einstein spacetime in which the mass density of the Einstein spacetime is a little higher than
the mean. Such regions produce turbulences in the Einstein spacetime. The nature tries to
eliminate the turbulences. How it can do it? Assume that in a room are many chaotically
running cats so there is many collisions so there arise turbulences i.e. regions in which
number densities of cats are different than the mean density so there appear the not planned
by cats trajectories as well. Pressure inside the room depends on number of the cat collisions
per unit of time. What the cats should do to reduce maximally the pressure? They should run
with the same spin speed in a cat vortex. The same does the nature to eliminate the turbulence.
From the spokes arise vortices. To conserve symmetry there arise the vortexantivortex pairs.
But then the physical traces produced in the Einstein spacetime look as tubes. This means that
now action is proportional to perimeter of the tubes. Emphasize that gluon balls produce
confined spokes and action is proportional to area of the crosssections of the spokes whereas
vortexantivortex pairs produce tubes and action is proportional to perimeters of the tubes. On
the other hand, we know that in gauge theory the confining phase (for example, it can be the
hadronic phase) is defined by the action of the Wilson loop. It is the trace/path in spacetime.
In a nonconfining theory, the action is proportional to perimeter of the loop (tubes) whereas
in a confining theory, the action is proportional to area of the loop (spokes).
We can see that the transition of the spokes into the quarkantiquark pairs (the hadronization)
causes that confined quarks due to the spokes become the free quarkantiquark pairs (they are
the mesons or the entangled baryonantibaryon pairs). Due to the atomlike structure of
baryons, the emitted pairs simulate the known hadrons.
We can see that a hadron jet “observed” by detectors consists of the tubeantitube pairs.
Similar confinement can appear in electromagnetic field but because internal helicity of this
field is equal to zero so such confinement is colorless.
The quarkgluon plasma mostly consists of the cores of baryons, precisely of the coreanticore
pairs. The coresanticore pairs are tangent so there is very small volume between the pairs in
which the quarkantiquark pairs and the spokes can be created. We can say that the not
numerous spokes at once transform into the known hadrons. This looks as a deconfinement.
Higgs field, Higgs boson, Higgs mechanism, hierarchy problem, confinement and mass
gap(s) in the Everlasting Theory: In the Everlasting Theory the modified Higgs field is the
fundamental/Newtonian spacetime composed of the tachyons. Due to the tremendous pressure
it behaves as liquid. We need the spacetime composed of tachyons to explain the inflation,
longdistance entanglement, cohesion of wave functions and constancy of the speed of light.
Smoothness/symmetry of the modified Higgs field is broken inside and nearly the Einstein
spacetime components i.e. the binary systems of neutrinos. The inflexible binary systems of
the closed strings the binary systems of neutrinos consist of, transform the chaotic motions of
the tachyons in the modified Higgs field into the divergent jets. It decreases the local pressure
in the modified Higgs field inside and nearly the Einstein spacetime components. When the
regions of the negative pressure overlap at least partially then there appears the confinement
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which breaks smoothness/symmetry of the Einstein spacetime. It is the broken symmetry
between gravitational force and weak force. Confinement increases local gravitational mass
density of the Einstein spacetime so the broken symmetry between gravity and weak force
leads to mass gap. It is the Higgs mechanism which describes as particles acquire their mass.
In the Everlasting Theory the Higgs bosons are in reality the Einstein spacetime components
which today are the classical particles. The Everlasting theory shows that gravity acts due to
the divergent jets produced by the Einstein spacetime components. Because the jets consist of
the tachyons so the gravitational constant depends on the density of the modified Higgs field
whereas the finestructure constant, which characterize the electromagnetic interactions,
depends on density of the Einstein spacetime. The ratio of the density of the Einstein
spacetime to density of the modified Higgs field is tremendous i.e. in approximation 4·10 42 . It
is the reason why the electroweak interactions are much stronger than the gravitational
interactions.
The Planck critical mass (in approximation 2.2·10 8 kg), which is of the same order of
magnitude as the geometric mean of the tremendous energy frozen inside a neutrino (not
mass) and the very small mass of the neutrino (the geometric mean is in approximation 8·10 8
kg), is very great in comparison with the mass of the Higgs bosons in the Everlasting Theory
but in the Standard Model as well. It is the hierarchy problem. We can see that within the
Everlasting Theory it is very easy to show the origin of the hierarchy problem. Just due to the
phase transitions of the modified Higgs field, the energy frozen inside a neutrino is about
0.6·10 119 times higher than the mass of the neutrino. It is the reason why the mass of the Higgs
bosons in the Everlasting Theory is such small in comparison with the Planck critical mass.
This proves that the lowest excitation of a YangMills theory without matter fields has the
finite mass gap associated with the Einstein spacetime (the vacuum state). I proved also that
the described confinement is valid in the presence of additional fermions as, for example, the
two energetic neutrinos in the ball in centre of muon (the ball is responsible for the weak
interactions). Such ball is in existence due to the confinement of the Einstein spacetime
components. Due to the confinement described within the Everlasting Theory there can
appear the sham Higgs bosons which masses are much greater than the Einstein spacetime
components and the detected Higgs boson carrying mass 125 GeV, in reality, is the sham
Higgs boson.
Due to the Newtonian spacetime, i.e. in approximation the scalar field, there can appear the
vortexantivortex pairs which spin is equal to zero, for example, the pions. Due to the Einstein
spacetime, i.e. the vector field, there can appear the vortexantivortex pairs which spin is
unitary, for example, the fermionantifermion pairs in which the components are entangled.
But to eliminate turbulences, the internal helicity of both types of bosons must be equal to
zero.
In the Everlasting Theory, the Newtonian spacetime is some analog to the Higgs field i.e. the
massless scalar field. The Newtonian spacetime consists of the tachyons which have the
inertial mass but have not the gravitational mass i.e. we can say that the Newtonian spacetime
is the gravitationally massless spacetime. Mean spin of the tachyons is in approximation 10 67
times smaller than the reduced Planck constant (i.e. the h divided by 2π). This means that we
can in approximation assume that the Newtonian spacetime is the scalar spacetime. The
Einstein spacetime described within the Everlasting Theory is not invariant in respect of
gauge group. It is because the Einstein spacetime components decrease pressure in the
Newtonian spacetime near the components. The modified Higgs field, i.e. the Newtonian
spacetime, introduced to the YangMills Theory causes that this theory is renormalized. The
mechanism which leads to the mass gaps in the massless gauge fields we can call the
confinement.
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Inside the four from five basic bare fermions, i.e. neutrinos, cores of baryons, bare electrons
and protoworlds, there is tirelike torus and there is ball which represents an axis of a wheel.
Moreover, the exchanged Einstein spacetime components inside the core of baryons and bare
electrons between tirelike torus and ballaxis produce confinements which look as spokes.
The spokes composed of the confined components of the Einstein spacetime appear outside
the bare particles as well.
In the quarkgluon plasma, the cores of baryons are tangent so there cannot appear
confinement between the cores. Just due to the “deconfinement” the plasma behaves as liquidlike
plasma.
When energy of collisions increases then there arise more and more regions with acting the
confinement i.e. the quarks can be screened and the gluons thickened. Interactions via
thickened Einstein spacetime do not depend on distance between interacting particles. It is
because the components of the Einstein spacetime cannot change their mass. There changes
local mass density of the Einstein spacetime, not the mass of its components. Separation of
particles interacting via the thickened Einstein spacetime causes that there arise new particles
from the additional mass “created” due to the confinement.
Due to the phase transitions in the Einstein spacetime or the internal structure of the core of
baryons, the gluons and quarks reorganize themselves. It is the hadronization. The quarks
inside baryons can arise only as the quarkantiquark pairs and spin of the components of a
pair must be antiparallel.
Hypernova: A stabilization of temperature inside a supernova or hypernova is due to
transition of the hot electronpositron pairs into cold charged pionantipion pairs. The mass of
a magnetar is greater than mass of neutron black hole (its mass is approximately 25 times the
mass of the sun) and smaller than 50 times the mass of the sun. When mass of a hypernova is
greater than about 100 masses of the sun then there appears granulation of the hypernova
leading to the rotating neutron tetrablackhole. There the four magnetars laying on the same
plane and rotating around axis perpendicular to this plane appear. The granulation is very
energetic because the neutron black holes have strictly determined mass – the arising four
neutron black holes, due to the gravitational collapse, emit tremendous energy and push the
redundant mass out from the region between the black holes with very big force. Due to the
very high angular momentum of the neutron tetrablackhole, the redundant mass in its centre
moves along the axis of rotation. There arise the jets. The more massive black holes than the
smallest hypernova consist of the magnetars. There strictly determined number of the
magnetars in the black holes appears. The number of the magnetars in a hypernova determines
following formula D=4 d , where d=0,1,2,4,8,16,… they are the numbers appearing in the
TitiusBode law. The next greater hypernova than described above should be 400 times
greater than the mass of the sun.
Inflation: It is the expansion with superluminal speed of a tachyonic concentration. During
the inflation, there appear the binary systems of closed strings and the neutrinoantineutrino
pairs the Einstein spacetime consists of. The entangled neutrinoantineutrino pairs (their speed
is the c) stop the inflation.
Interactions: The fifth force (fundamental) follows from the direct collisions of the tachyons.
The known four interactions are associated with the Einstein spacetime. The binary systems
of the closed strings a neutrino consists of transform the chaotic motions of the tachyons into
the divergently moving tachyons. It produces gravitational gradient in the Newtonian
spacetime but also in the Einstein spacetime. The gravitational constant G is associated with
each neutrino. The exchanged regions of thickened Einstein spacetime are responsible for the
weak interactions. Such exchanges take place when surfaces of the regions are in distance
equal to or smaller than 3482.87 times the radius of the equator of the torus of neutrino. For
the strong interactions are responsible the exchanges of the large loops (mesons) and binary
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systems of the large loops (baryons) produced on the circular axis of the torus of the core of
baryons. The virtual and real photons produce the electronpositron pairs in the Einstein
spacetime. Their annihilations create divergently moving binary system of neutrinos fluxes in
the Einstein spacetime. Such processes are responsible for the electromagnetic interactions.
The unitary spins of the Einstein spacetime components enforce that the carriers of
interactions have unitary spin also. Exchanges of the binary systems of the closed strings lead
to the entangled photons and other entangled particles. This is the sixth force.
K 2 constant: It is number of tachyons a closed string consists of.
Large loop: Arises inside the torus of baryons and consists of weak dipoles.
Limitations for gauge invariance: Gauge invariance of equations applied in the Theory of
Fields is directly associated with the constancy of charges (weak charge, electric, strong and
superstrong). The assumption that the charges are invariant leads to conclusion that following
transformation of vector potential A: A’ = A + grad f (the gradient invariance), where f is an
arbitrary function dependant on coordinates and time, and following transformation of scalar
potential φ: φ’ = φ  c 1 ∂ f / ∂ t, where the sign ““ follows from the definition of the distance
ds in spacetime (the metric): ds 2 = x 2 + y 2 + z 2 – c 2 t 2 , causes that the equations are invariant
under such gauge. What is origin of such gauge invariance? In the Everlasting Theory the
charges are defined by properties of the tori inside the bare fermions. Due to the entanglement
of the components the tori consist of, their interactions are saturated, i.e. they cannot interact
with fields, but they polarize the spacetimes. Moreover, properties of the charges depend on
the properties of the two spacetimes, for example, on their mass densities. This means that the
constancy of charges was not valid in the era of inflation and in the protuberances of the
Einstein spacetime just at the beginning of expansion of the Universe. This expansion took
place after the era of inflation. The observational facts indeed show that the finestructure
constant varied in the era of quasars. The Everlasting Theory shows that when we add to
vector potential associated with a charge a constant vector, for example, spinpolarized
Einstein spacetime and/or to scalar potential an arbitrary constant, for example, the
gravitationally massless Newtonian spacetime (today its mass density is constant) then such
changes cannot change the charges. But the theory shows that the constancy of charges is not
valid when the densities of spacetime(s) changes. For example, there was phase transition of
the cosmic superstrong charge just before the start of expansion of our Universe. This means
that we cannot apply the gauge invariance to such period, the same as to inflation. We can
assume that the Universe is inside a blowhole inside timeless space. Then today the
properties of the spacetimes cannot change. It leads to the constancy of the charges. Due to
the saturation of interactions concerning the charges, today there is some freedom in the
Quantum Theory of Fields to define vector and scalar potentials but such freedom follows
from the fact that we neglect the internal structure of the bare fermions. To eliminate the
freedom, we must add the Everlasting Theory to the today mainstream theories. The nature
chose only not numerous solutions.
Lines of forces: Spins of binary systems of neutrinos (the weak dipoles) overlap with the
electric lines. The magnetic lines are associated with spinning electric loops.
Liquidlike plasma: The Everlasting Theory leads to an atomlike structure of baryons,
therefore, also of the nucleons. The internal structure of neutrinos and new theory of their
interactions show that it is very difficult to destroy the cores of baryons – they are the tori
with mass in their centers and consist of the Einstein spacetime components i.e. of the binary
systems of neutrinos. Inside our Universe, density of energy and mass is too low to compress
the cores of baryons. The liquidlike plasma consists of the cores of baryons packed to the
maximum.
Local time: Inside the gas composed of tachyons, I define local time as being directly in
proportion to the number of all direct collisions of free tachyons in some local volume of the
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Newtonian spacetime. This analogy and definition is also relevant for the Einstein spacetime
that is composed of weak dipoles.
Local unit of length: The local unit of length is the local mean distance between free
tachyons that the Newtonian spacetime consists of. This is also the case for the Einstein
spacetime.
Local unit of time: The local unit of time is the mean time between the direct collisions of
free tachyons that the local volume of the Newtonian spacetime consists of. This is also the
case for the Einstein spacetime.
Magnetar: This is the neutron black hole. Its mass is greater than 25 times the mass of the
sun and is smaller than 50 times the mass of the sun.
Magnetic monopoles and magnetic force: Magnetic monopoles are not in existence. The
entangled weak dipoles, an electron consists of, polarize the Einstein spacetime in such way
that along the polarized lines arise the polarized virtual electronpositron pairs i.e. the virtual
electric dipoles. Electric lines of forces are tangent to spins of the polarized virtual electronpositron
pairs so to the spins of the weak dipoles as well. The whole structure is entangled.
The torus of an electron is the locally polarized Einstein spacetime. It is spinning. It means
that due to the entanglement, the virtual electric dipoles notice that the electric charge of the
electron is spinning. Due to the entanglement, there appears force that tries to spin the
polarized electric lines as well i.e. there appear forces perpendicular to the electric lines of the
electron. We can call the force produced by the spinning electric charge the magnetic force.
Due to the entanglement, the magnetic force is directly proportional to distance of an electric
charge from the spinning electric charge so this force is directly proportional to the local spin
speed of the spinning electric lines. The magnetic force is associated with the spinning electric
charge so the magnetic intensity is the axial vector whereas the electric field intensity is the
polar vector. The magnetic force appears only when electric charge is moving because only
then the spin vector is polarized along the direction of velocity of the electron. It is due to the
law of conservation of spin. When electron is in the rest or is moving very slowly then the
direction of its spin changes randomly so the direction of the magnetic force as well. This
means that the resultant magnetic force is zero. When an electron is moving then its spin is
parallel or antiparallel to the velocity of the electron whereas the velocities of the virtual pairs
associated with the motion of the electron as a whole, are parallel to the velocity of the
electron. When magnetic force is not perpendicular to velocity of electron then the magnetic
force is directly proportional to the vector product of the velocity of electron and magnetic
intensity. The spins of electron and positron in a virtual electronpositron pair are parallel so
the both magnetic forces are parallel. We can see that magnetic force can acts on an electric
charge in massless electromagnetic fields as well. It could be more readable after the change
of the term “magnetic forces” into “spin forces”. The magnetic field intensity is the axial
vector so there cannot be in existence an object producing divergent or convergent lines of
magnetic forces.
The weak charge of neutrinos behaves similar to a magnetic monopole i.e. to a magnetic
charge. The neutrinos arose due to the two succeeding transitions of the modified Higgs scalar
field i.e. the Newtonian/fundamental spacetime. The neutrinos arose in the era of inflation so
in the theory of inflation we should eliminate the magnetic charges and introduce the
neutrinos. The weak charges/neutrinos broke the symmetry between the gravity and weak
interactions.
Mass: The inertial mass is directly proportional to the total volume of the tachyons a body
consists of or to number of the closed strings a body consists of. Inertial mass is the more
fundamental physical quantity than energy i.e. pure energy is not in existence without
spacetime/field having inertial mass density not equal to zero. The gravitational mass is
associated with the neutrinos so with the binary systems of neutrinos the Einstein spacetime
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consists of also. For the Einstein spacetime, the gravitational mass is equal to the inertial
mass.
Mesons: They are multisystems of large loops which are created inside the torus of baryons.
They can also be mesonic nuclei that are composed of the other mesons and the large loops,
or they can be binary systems of mesonic nuclei and/or other binary systems. They can be also
the gluon balls or other loops and their associations
Mind: A thought is composed of closed threads built out of the binary systems of neutrinos.
The axes of these weak dipoles are tangent to the threads. Such closed threads can produce
“lines” composed of polarized virtual electronpositron pairs so minds may interact with a
brain or matter electromagnetically.
Mtheory: The Mtheory contains the fundamental bosonic string theory plus the three
superstring theories for which the fermionboson symmetry is obligatory and plus the two
heterotic theories which follow from the internal structure of the Einstein spacetime and
structure of baryons.
Muon: Due to the entanglement of the binary systems of neutrinos, the torus of muon looks
as shrunk torus of electron. We can say that the torus of muons is a zeroenergy entangled
photon but it has mass because distances between the binary systems of neutrinos are shorter
than in the Einstein spacetime. Such shrinkage is forced by the two additional rotating
neutrinos inside the point mass of electron. These two additional neutrinos cause that the point
mass of muon is the black hole in respect of the weak interactions. Muon decays due to the
weak interactions – there is the emission of the two additional neutrinos.
Neutrino ‘oscillations’: The exchanges of the free neutrinos for the neutrinos in the binary
systems of neutrinos the Einstein spacetime consists of, lead to an illusion that the neutrinos
oscillate. Neutrinos cannot oscillate due to the tremendous binding energy (not mass) – it is
equivalent to approximately 4·10 50 kg.
Neutrinos and lacking dark energy: Neutrinos appear as a miniature of core of a proton.
Neutrinos are composed of closed strings. The external radius of the torus of a neutrino is
approximately 1.1·10 35 m. There are the entangled binary systems of neutrinos (mass of one
binary system is approximately 6.7·10 67 kg) which in the today Universe behave as the
classical particles. There are the photon galaxies and the wave functions describe their
behaviour. The c is the natural speed of the entangled photons and gluons (today they are the
quantum particles) in the gravitational gradients produced in the Newtonian spacetime.
Almost all neutrinos are in the binary systems. The spins of almost all binary systems of
neutrinos do not rotate because bound tachyons tend to behave in a similar way to free
tachyons. The Planck time is typical for lifetime of the local Einstein spacetime in an excited
state i.e. in a state when the spins of the binary systems of neutrinos rotate. It is very difficult
to detect the nonrotatingspin binary systems of neutrinos because they cannot transfer
energy to a detector. Neutrinos are very stable particles – we do not see the biproducts of
neutrinoantineutrino annihilations. My theory leads to the conclusion that the internal energy
of a neutrino is approximately 0.6·10 119 times greater than the energy of a neutrino resulting
from the formula E=mc 2 . This is because neutrinos are built of closed strings at a
superluminal speed (approximately 2.4·10 59
times greater than the speed of light in
spacetime). The tremendous amount of energy frozen inside neutrinos excludes the creations
of neutrinoantineutrino pairs in a manner similar to, for example, electronpositron pairs. The
new neutrinos are biproducts of the decay of the rotatingspin or nonrotatingspin binary
systems of neutrinos. The frozen energy inside neutrinos is lacking dark energy. A field
composed of free binary systems of closed strings does not exist, therefore, the transformation
of their rotational energy into mass is impossible. The exchanges of the binary systems of the
closed strings between the binary systems of neutrinos produce the entangled photons and
other particles. Such phenomena led to the visible distribution of the galaxies. There are only
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four different states of neutrinos  the taon neutrino is not in existence. The divergently
moving tachyons (order) produced by the closed strings a neutrino consists of create a
gradient of pressure in the Newtonian spacetime (chaos) in such way that pressure is lower in
places where mean density of the divergent jets is higher. This means that there is created
‘niche’ in the Newtonian spacetime (i.e. the mean distance between the free tachyons is
greater) so time is going slower. This is the mechanism responsible for how neutrino acquires
its own gravitational field by interacting with the Newtonian spacetime. The attractive
gravitational force and the gravitational potential energy are associated with gradient of
negative pressure in the Newtonian spacetime. To describe neutrino, built up of the closed
strings, we need 26 mathematical and physical quantities.
Neutron black hole: Its mass is about 25 times the mass of the sun.
Newtonian spacetime: Ideal gas composed of tachyons. Only very near the surfaces of the
closed string is the Newtonian spacetime highly deformed. Outside closed strings, because of
the superluminal speed of tachyons i.e. because of the tremendous amount of pressure found
in the Newtonian spacetime, this spacetime behaves like a liquidlike substance. For
interactions lasting longer than about 10 60 s, the Newtonian spacetime appears as a
continuous medium.
Nonperturbative theories: There are in existence the stable tori, stable core of baryons and
stable states associated with the atomlike structure of baryons. Even the unstable particles for
the period of spinning are the stable objects. To describe such objects we can apply the nonperturbative
methods. For electrons, the nonperturbative and perturbative stadiums are
separated whereas for baryons they are in existence simultaneously. The nonperturbative
theories are obligatory for all energies. The stable states we can describe via simple formulae
in which the time does not appear. In the mainstream theories, there is tremendous number of
unsolved basic problems associated with the stable structures. The nonperturbative
Everlasting Theory is the lacking part of the ultimate theory and is the foundations of the
correct mainstream theories.
Perturbative theories: These theories concern the phenomena associated with the
disappearances of the circular and point/ball masses of the electrons and sham quarks. They
lead to the diagrams. The number of the disappearances increases when energy increases. This
means that the perturbative theories should lead to wrong results for low energies.
Phase space: The set of numbers and quantities needed to describe position, shape and
motions (internal motions also) of an object. For example, the phase space of a tachyon has 6
elements, for a closed string is 10 whereas for neutrino 26.
Phase transitions: The theory of liquid leads from tachyons packed to maximum to the
closed strings whereas the saturation of the interactions of tachyons due to the fundamental
force leads from the closed strings to the neutrinos, cores of baryons and protoworlds.
Photon galaxies: They arose due to the succeeding decays of the superphotons that were
produced in the cosmic loop. Each carrier of the photon galaxies is composed of 4 16 entangled
neutrinoantineutrino pairs. The arrangement of the components of a carrier of photon galaxy
changes over time but for defined arrangements, the photon galaxies are the stable objects.
The speed c is the speed of wave functions describing the photon galaxies but also the speed
of a photon galaxy in its defined arrangement. Due to the entanglement, we cannot measure
the speeds and energies of the components of a photon galaxy. Due to the entanglement of the
components of a carrier of photon galaxy, the total energy and the speed c of a photon galaxy
are disclosed in the detectors when at least one component of carrier of photon galaxy
interacts with a detector. Localization of a photon galaxy changes over time i.e. it disappears
in some region of the Einstein spacetime and appears in another one, and so on. Such
quantum behaviour of a photon galaxy describes its wave function. Its looks similarly as for
an electron but in an electron apart from the entanglement there appear the shortdistance
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weak interactions i.e. the regions in the Einstein spacetime which have higher mass densities
than the mean mass density. The weak interactions appear when the additional mass density is
the same or higher than in the point masses of electron and proton i.e. in approximation
2.731·10 23 kg/m 3 i.e. about 40,363 times lower than the mean mass density of the Einstein
spacetime. You can see also Paragraph titled “The weak interactions of baryons lead to the
fundamental force” in Chapter “Interactions”. For such density, the mean distances between
the neutrinoantineutrino pairs are (40,363/(40,363 + 1)) 1/3 = 0.9999917 times lower than the
mean distances in the Einstein spacetime. The weak interactions contrary to the entanglement
cause that there appear the relativistic particles and the mass gap in the YangMills theory.
Photons: Quanta of energy carried by entangled binary systems of neutrinos. Mass of photons
(i.e. of the rotational energy i.e. of the excitations of the Einstein spacetime) is equal to zero.
The Everlasting Theory shows that the Einstein formula E=mc 2 is wrongly interpreted. The
transition from pure energy (the mass is zero) into mass is impossible without the Einstein
spacetime having mass density not equal to zero. Inertial mass is more fundamental physical
constant than energy. To know how particles acquire their relativistic mass we must know
internal structure of Einstein spacetime. The cited Einstein formula is correct due to the laws
of conservation of spin and energy. The wave functions describe behaviour of the entangled
neutrinoantineutrino pairs. The c is the speed of the entangled photons and gluons (today
they are the quantum particles) in the gradients produced in the Newtonian spacetime. We can
see that the invariance of the c leads to the quantum physics. In the today Universe, a single
neutrino is the classical object then its speed can be superluminal as well but most of them are
moving with the speed c because they appear mostly due to the decays of the carriers of the
photons.
Pieces of space: They are the internally structureless tachyons. In different regions of cosmos
(in a cosmic scale) speeds of tachyons (so also sizes) can differ. There can be regions in
which the pieces of space are moving with subluminal speeds or can be in rest.
Pion: It is the binary systems of the large loops produced on the circular axis (it is the electric
charge, i.e. the circle, on that the lines of electric forces converge) inside the torus in core of a
baryon.
Planck critical physical quantities: The critical values are defined for a cube whereas there
is the torus of the neutrinos so the calculated values are not consistent with the Planck critical
values but should be close to them. Moreover, the reduced Planck constant is for binary
system of neutrinos, not for a neutrino. Volume of the Einstein spacetime component, i.e. the
binary system of neutrinos, is V = 2π(π + 1)rneutrino 3 /3 = 12.138·10 105 m 3 . Such volume for a
cube leads to the side equal to 2.298·10 35 m (the Planck length is 1.616·10 35 m). The energy
frozen inside neutrino is equal to mass of protoworld. The geometric mean of this energy and
mass of neutrino is 8.087·10 8 kg. Mass of a binary system is two times greater 16.174·10 8 kg
whereas the Planck mass is 2.177·10 8 kg. But most important is the mass which defines the
lowest temperature in which appears the liquid composed of the Einstein spacetime
components. This mass is some analog to the mass 282.93 MeV for the liquidlike plasma
composed of the cores of baryons. Such mass for the neutrinos is in approximation
282.93/727.44 = 0.38894 times lower than the mass of neutrinos. For such mass, the critical
mass density for binary systems of neutrinos is 5.18·10 96 kg/m 3 whereas the Planck critical
mass density is 5.16·10 96 kg/m 3 .
Proton: The core of proton is composed of binary systems of neutrinos. It has a point and
circular mass. Due to the emission and absorption of virtual particles and their subsequent
decay tunnels appear in the Einstein spacetime i.e. holes arise in a field composed of binary
systems of neutrinos. This leads to the TitiusBode law for strong interactions. Within tunnels
can be relativistic pions that are in the S state. In proton, there is only one relativistic pion and
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it is under the Schwarzschild surface for strong interactions so the proton is a stable particle.
Meanwhile, baryons possess an atomlike structure.
Protoworlds: Protoworlds consist of nucleons and arise after the period of inflation. Their
radius is approximately 2.7·10 24 m. The torus of it consists of deuterium. In centre of the torus
is the mass composed of the neutron black holes. Immediately before the ‘soft’ big bang the
Protoworldneutrino transition was possible only if the objects had a strictly determined
mass (approximately 1.9·10 52 kg). The dark energy is the remnant of such transition and is
composed of the additional nonrotatingspin neutrinoantineutrino pairs i.e. inside our
Universe the density of the field composed of binary systems of neutrinos is higher than it is
outside it. This is the positive pressure reducing the negative pressure in the spacetime created
by the mass of our Universe. The Universe arose in a similar way to large loop composed of
binary systems of neutrinos, inside the torus of the core of baryons. Such large loops are
responsible for strong interactions. When dark energy appeared the very young Universe
(mass of which was approximately 1.8·10 51 kg), which was the cosmic loop composed of
neutron black holes grouped in larger structures, started to expand. This was due to the
repulsive force produced by dark energy and the energy emitted during the production of the
first atomic nuclei. The photon galaxies that couple the cosmic structures, lead to the illusory
part of the dark matter. Dark matter also consists of the remnants of the big stars. They are
composed of ironnickel lumps. Detecting these lumps is extremely difficult because their
temperature is equal to cosmic microwave background radiation. The interior of a sphere
filled with baryonic matter contains approximately 5% visible matter, 21% dark matter and
74% dark energy. Protoworlds developed as protoworldantiprotoworld pairs from positive
fluctuations of the field composed of nonrotatingspin binary systems of neutrinos.
Pulsars: Similarly as for the Sun, the magnetic axis of pulsars associated with the spots
rotates. There are two pulses per period. We obtain the correct results when we assume that
pulsar/star period of rotation of magnetic axis associated with the spots T is directly
proportional to surface of these cosmic objects (surface = 4πr 2 ) and the factor of
proportionality is f = 1.15·10 10 s/m 2 (T = f·4πr 2 ). For the Sun (r = 6.96·10 8 m), we obtain T =
7·10 8 s = 22.2 years. For the surface of the biggest neutron star (r = 3.7·10 4 m), we obtain T =
2 s i.e. mean time distance between pulses should be in approximation 1 s. Over time, due to
the surface processes, the pulsars increase their radii so the period T increases as well. For
smaller pulsars the periods T are shorter.
On surface of each pulsar arises the Fe crust and very thin layer of plasma composed of
protons, ions and electrons. To decrease the pressure on surface of pulsars and stars there
appear the charged vortices composed of protons and ions. Their magnetic axes are
perpendicular to the surfaces of the pulsars and stars in such a way that magnetic polarization
of the opposite vortices is the same. Similarly as in a photon, a resultant magnetic polarization
should be perpendicular to velocity of pulsar in relation to the Einstein spacetime. Due to the
rotation of mass, there arises circular positive current in the plasma overlapping with the
equator of pulsar or star. Due to the vortices on surface, on the circular current acts the
Lorentz force so the axis of the circular current rotates. The half of the period of such rotation
is the mean time distance between the pulses emitted by pulsar. Due to the very thin and wide
circular currents, the Fe crust is polarized along the meridians associated with the axis of
rotation of mass. The electric lines of forces are tangent to the parallels associated with the
rotating electric current. We can see that due to the magnetic polarization of the Fe crust and
rotation of the magnetic axis of the circular current, on the plasma acts the Lorentz force so
there appear the radial oscillations of the protons, ions and electrons. Due to the interactions
of the protons and ions with the crust and neutrons, such oscillations produce the linearly
polarized frequencies. Such is the main pulsar clock and radiation mechanism. An observer
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sees the pulses when the direction of observation lies on the rotating plane on which the
circular current lies.
Now I describe the phenomena which lead to the γray frequencies on base of the integrated
pulse profile of the Crab pulsar. When the oscillating protons collide with the crust of a pulsar
and neutrons then there is produced helium. We can distinguish three stages. At the
beginning, the nucleons are in following mean distance d: d = (4πA/3 + 4πA/(3cosα))/2 =
2.939825 fm, where tgα = 1/(2π). During this stage the emitted energy is proportional to
mass/energy of the large loop 67.5444 MeV. Next, the distance is r = A + 4B = 2.704800 fm.
During this stage the emitted energy is proportional to the mass/energy of the S pion on the d
= 4 TitiusBode orbit for the strong interactions 186.886 MeV. We can see that the change in
distance is x = d – r = 0.2350245 fm. In the third stage there is transition to the alpha particle
and the side of the square is y = 1.912583 fm. During this stage the emitted energy is
proportional to mass/energy of the neutral pion 135 MeV. In the integrated pulse profile of the
Crab pulsar we should see the three peaks and because time distances between the subpulses
in the average pulse shape is directly proportional to the ranges x and y then the ratio of the
time distance between the third and second subpulse to time distance between the second and
first should be y/x = 8.14. The observational data lead to 13.37 ms/1.64 ms = 8.15. We can
see that the theoretical result is consistent with the observational facts. We can see also that
the ratio of the amplitudes of the energy fluxes for the three peaks should be 67.5444 :
186.886 : 135 ≈ 1 : 2.8 : 2 i.e. the amplitude of the first subpulse should be lowest whereas of
the second highest. The obtained results for the amplitudes are consistent with the
observational facts as well. Partially the energy emitted as the äray frequencies interacts with
the oscillating electric charges in the plasma so there appear the radio, optical and Xray
frequencies as well. The exact pulse profile at the äray frequencies we can observe at the
radio frequencies associated with the oscillating free electrons. It is because inertia of the free
electrons is much lower than the ions (ions produce the optical frequencies) and electronpositron
pairs interacting with ions (the Xray frequencies arise due to the annihilations of the
pairs).
Now on base of the Everlasting Theory we can calculate the effective temperature. Due to the
four neutrino symmetry, the pions can be composed of 2·4 16 neutrinos so there arise regions
containing 2·4 16 entangled nucleons. From the Wien law follows that temperature of the large
loop (circumference is 4πA/3) is T ≈ 10 12 K. We can see that temperature of the regions
containing 2·4 16 entangled nucleons can be 2·4 16 T ≈ 10 23 K. The obtained theoretical result is
consistent with the observational data.
Besides the helium production there are the synchronized beta decays and the HeFe
transitions. Such pulses are much more rarely but their energy should be higher than the
average. With time, due to the surface processes (i.e. the HeFe transitions), the period of
rotation of the magnetic axis associated with the spots increases because volume of star
increases.
QCD and Everlasting Theory: There are eight 3coloured gluons and six 1coloured basic
sham quarks. The binary systems of neutrinos are the carriers of the massless gluons and
photons. In the strong fields, due to the internal helicity of the core of baryons, we must take
into account the three internal helicities of the binary systems of the neutrinos  this leads to
the eight gluons. Since outside the strong fields the internal helicity of fields is equal to zero
then the internal structure of the carriers of gluons and photons is not important. The gluons
‘transform’ into photons. The quarks are in existence only in the fields composed of gluons.
Quantum gravity: The neutrinos are the ‘carriers’ of the gravitational constant. There are
only 4 different neutrinos (the electron neutrino and its antineutrino and the muon neutrino
and its antineutrino). The graviton could be the rotational energy (its mass is zero) of particle
composed of the four different neutrinos in such way that the carrier of graviton could be the
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binary system of binary systems of neutrinos with parallel spins, i.e. spin of graviton is 2. The
neutrino bidipoles behave as two entangled photons. This means that gravitons and
gravitational waves are not in existence. Gravitational energy is emitted via the flows in the
Einstein spacetime composed of the nonrotatingspin neutrino bidipoles. The neutrinos,
binary systems of neutrinos, bidipoles of neutrinos, and so on, produce the gradients in the
Newtonian spacetime that is impressed on the Einstein spacetime too. We can describe the
gravity via such gradients. When time of an interaction is longer than about 10 60 s then
particles interacting gravitationally, electromagnetically, weakly and strongly ‘see’ the
Newtonian spacetime as a continuum and we can apply the Einstein equations and Noether
theorem. Such continuum leads to the symmetries and laws of conservation.
Since spin of the neutrino bidipoles is 2 whereas of the neutrinos is 1/2, then the gravity leads
to conclusion that the neutrinos have only two flavours i.e. there are in existence only four
different neutrinos. The tau neutrinos are not in existence.
The Kasner solution for the flat anisotropic model (1921) in the General Theory of Relativity
is the foundations of the Quantum Gravity and Quantum Physics without singularities and
infinities. The Quantum Gravity was valid only in the era of inflations. In this era, the
neutrinoantineutrino pairs behaved similarly as the electronpositron pairs.
Quantum particles: See ‘Renewable particles’.
Quantum Theory of Fields limitations: Perturbative theories can be the complete theories
when each order of perturbation describes different interaction/phenomenon. Each
perturbative theory which in next its order describes the same elementary phenomena but
more complex, we always can replace with a nonperturbative theory. It is because in such
perturbative theories we neglect some interactions/phenomena which follow from the internal
structure of the bare particles, for example, of bare electron or the core of baryons described
within the Everlasting Theory. The applied functionals cannot fully describe the all possible
interactions of the bare particles with spacetime and fields. This causes that there appear the
free parameters, minimal subtraction, sliding scale, renormalization, limitations and so on.
The internal structure of the bare particles cannot be described within the methods applied in
the mainstream Quantum Theory of Fields. The Everlasting Theory shows that in the QED we
neglect the weak interactions of the bare electron and its internal structure – there is the
torus/electriccharge and the ball in its centre responsible for the weak interactions. To detect
the torus of bare electron we must apply new methods because the torus is only the polarized
Einstein spacetime. Describing the asymptotic freedom within perturbative theory we neglect
the coupling of the core of baryons with the Einstein spacetime.
It is very difficult to describe mathematically the distribution of matter inside the bare
fermions applying the mathematical methods typical for the nonAbelian gauge theories. Just
we cannot add structure of the bare fermions to Lagrangian. The core of baryons is the stable
structure so it is very simple to describe its structure within classical nonperturbative theory.
On the lowest levels of the nature the physics behaves once again classically. The applied
methods are even simpler than in the Newtonian mechanics. It means that the methods applied
in the mainstream quantum theory of fields are useless to eliminate the parameters applied in
such theory. There are the two or three parameters which do not appear in the Everlasting
Theory. In the perturbative QED and QCD there are two assumptions which cause that we can
fit theoretical results to experimental:
1. We plan how a function should look, respectively the field normalization Z in the QED and
the beta function in the QCD.
2. We introduce some absolute parameters, respectively the mass and charge of electron and
the absolute value for the alpha_strong = 0.1182 ± 0.0027 for the mass of the Z boson (2004).
But we cannot say that the mainstream perturbative theories are useless. From them we can
decipher many properties of the introduced fields, describe some symmetries and so on.
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Real photons: In contrary to the virtual photons they have mass equal to zero. They are the
excitations (rotational energies) of the Einstein spacetime. For massless particles, the coupling
constants are equal to zero because such particles cannot create gradients in the spacetimes
and other fields (they ‘slide’ along a field). Real photons can carry the electromagnetic
interactions only when scattered on electric charges produce the virtual and/or real electronpositron
pairs. In annihilations of such pairs, arise virtual and/or real photons.
Renewable particles: The quantum particles disappearing in one place of Einstein spacetime
or strong fields and appearing in another and so on. They are the real and virtual electrons and
photons in the Einstein spacetime, the real or virtual bosons in the strong field inside the
baryons, and so on. Their states describe the wave functions.
Running coupling of strong interactions: When we accelerate a baryon then to conserve its
spin, mass of the large loops responsible for the strong interactions must decrease so value of
the strong coupling constant decreases also. There appears an asymptote for value in
approximation 0.1139.
Small loops: They are the small loops composed of the binary systems of the closed strings
and produced on surface of the torus of neutrinos. Their circumferences are 2πr and 2πr/3,
where r denotes the radius of the equator of the torus of neutrinos.
‘Soft’ big bang suited to life (the ‘soft’ big bang): The big bang of the cosmic loop suited to
life that arose inside the Protoworld. In such cosmic loop were produced the precursors of the
DNAs.
Soliton: Is the tangle of closed threads composed of weak dipoles and produced by a tangle of
circular electric currents.
Speeds: Due to the properties of the closed strings and the tremendous speed of tachyons, the
gradients/gravitationalfields produced by the divergently moving tachyons are ‘attached’ to
masses. The speed of light c is the natural speed of the carriers of the photon galaxies and
gluon galaxies, i.e. of the entangled neutrinoantineutrino pairs, in the locally dominating
gravitational field. This is because the entangled photons and gluons are the quantum particles
i.e. their states define the wave functions. The redshift can be due to the changing potential of
gravitation or due to the transitions of photons from one dominating gravitational field to
another when distance between centers of the gravitational fields is changing. For example,
such divergent fields appeared in the Einstein spacetime (the protuberances) at the beginning
of the ‘soft’ big bang. The second phenomenon is beyond the mainstream Theory of
Relativity and is responsible, for example, for the redshift higher than 1 for the distant cosmic
objects. There are also motions of static gravitational gradients in static Newtonian spacetime
and almost static Einstein spacetime (the dark energy causes that the second spacetime is nonstatic).
Due to the properties of the gas composed of tachyons, the protuberances in the
Einstein spacetime with speeds higher than the c in relation to the centre of the ‘soft’ big
bang, were quickly damped. This new interpretation eliminates the wrong conclusion that the
Universe without any reason accelerates its expansion and leads to conclusion that our
Universe is older. When velocity of a cosmic object is the same as the local dark energy then
mass of the cosmic object is equal to its rest mass.
Today, in our Universe, the neutrinos are the classical particles so similarly as the tachyons
they can be the superluminal particles too.
Objects greater than a neutrino consist of the binary systems of neutrinos. This means that to
travel with superluminal speeds we must create protuberances in the Einstein spacetime. To
do this we need tremendous energies.
Spin: Halfintegral spin is more fundamental physical quantity than even gravitational
constant associated with internal structure of neutrinos. This is true because neutrinos consist
of the closed strings that have the halfintegral spin.
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Spinor: Spinor is the generalization of vector and tensor. Most important is spinor space
associated with the Lorentz transformation because it describes the fermions that have halfintegral
spin, for example, neutrinos and electrons. Since the Einstein spacetime consists of
the binary systems of neutrinos, there must be the 720 degree turns of neutrinos to obtain spin
of the Einstein field components (i.e. the 1). From this follows that spinor changes sign due to
the 360 degree turns.
Strong charge: This is the torus inside the core of baryons. Its mass is X = 318.3 MeV.
Inside the strong field it behaves as the strong charge/mass carrying the same electric charge
as positron whereas outside the strong field, due to the gluonphoton transitions, it behaves as
electric charge of positron.
Strong interaction: This interaction takes place because of the gradient created in the
Einstein spacetime by divergently moving large loops or groups of large loops arising inside
the torus of the core of a baryon. Whereas the tunnels in the Einstein spacetime, responsible
for the strong interactions also, arise as result of the symmetrical decays of the groups
composed of the four virtual remainders.
Supernovae producing neutron stars: In the central part of the core of sufficiently big star
is liquidlike plasma producing the quanta that have energy equal to approximately 283 MeV.
This energy corresponds to the lower limit of temperature of the liquidlike plasma i.e.
approximately 4·10 12 K. A stabilization of temperature inside core of such star is due to the
transitions of the thermal energy into cold charged pionantipion pairs (their mass/energy is
approximately 280 MeV). Since mass of neutron (939.6 MeV) leads to mass of neutron black
hole equal to approximately 25 times the mass of the sun then the 283 MeV leads to the lower
limit of mass for neutron star approximately 25·283/939.6=7.5 times the mass of the sun.
Mass of neutron stars is greater than 7.5 times the mass of the sun and smaller than 25 times
the mass of the sun. Due to weak interactions, carriers of photons (i.e. the entangled binary
systems of neutrinos the Einstein spacetime consists of) appearing in decay of pions in liquidlike
plasma decay to neutrinos. Since emitted energy is directly in proportion to coupling
constants then for one part of energy carried by photons (coupling constant is approximately
1/137) are 137 parts of energy carried by neutrinos (coupling constant for strong interactions
of pions is 1). This leads to conclusion that 100%·137(1+137)=99.3% of energy released in
explosion of supernovae carry neutrinos whereas 0.7% carry the photons.
Supernova Ia: A stabilization of temperature in core of such star is due to the transition of
the thermal energy into the point mass of muons (point mass is approximately 105.67/2=52.83
MeV). Since mass of neutron (939.6 MeV) leads to mass of neutron black hole equal to
approximately 25 times the mass of the sun then mass 52.83 MeV leads to mass of Ia type
supernova approximately 25·52.83/939.6=1.4 times the mass of the sun.
Superphoton: Superphoton is lefthanded double helix loop that is composed of 2·4 32
entangled photons (there are 2·4 16 photon galaxies i.e. about 4 billion photongalaxy pairs).
Each helix loop is composed of 256 megachains. Antisuperphoton is righthanded double
helix loop. Carrier of photon, i.e. the binary system of neutrinos, has spin equal to 1 and is
perpendicular to the axis of a superphoton. There are produced spin waves in the carriers of
the superphotons. In fact, superphotons arise as entangled gluons that become the photons
outside the strong field.
Supertachyon and cosmic bulb: Supertachyon is a hypothetical tachyonic condensate which
mass is in approximation equal to the sum of masses of the Protoworld (i.e. after the period of
inflation) and the cosmic loop i.e. about 2.2·10 52 kg. During a collapse of a region of the
Newtonian spacetime pressure increases so also speed of tachyons. This means that mean
radius of tachyons decreases. When such supertachyon expands, in the surrounding
Newtonian spacetime composed of slower tachyons, there arises shock wave that can create a
cosmic bulb composed of pieces of space packed to maximum. In different cosmic bulbs, the
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initial four between the six parameters can have different values. Sizes of cosmic bulbs can be
tremendous in comparison to the today radius of our Universe.
Tachyons: All particles are composed of structureless tachyons that have a positive inertial
mass. In our region of the Newtonian spacetime they are moving approximately 8·10 88 times
faster than photons in spacetime. The unchanging mean speed of free and bound tachyons
defines the mean radius of tachyons and leads to the relativity and to the law of conservation
of energy. The high mean linear speed and viscosity leads to the granulation of the eternal and
internally continuous substance. This is because for smaller radii of the tachyons, the
interaction time of them, in direct collisions, is shorter and the area of contact is smaller. This
means that, for strictly determined radii, the grinding of tachyons stops. The tachyons only
interact because of direct collisions – such interactions are associated with the dynamic
viscosity of tachyons resulting from the smoothness of their surfaces. In such a spacetime
there are only possible the four succeeding phase transitions that lead to stable objects. As
tachyons only interact because of direct collisions (they are bare particles), the gaslike
Newtonian spacetime composed of structureless tachyons fills whole volume of our cosmic
bulb. The trajectories of tachyons take all possible directions (chaos). With our region of the
Newtonian spacetime, only one set of physical laws is associated. The inertial mass of a
tachyon is directly proportional to the volume of it. The spin of a tachyon is approximately the
amount 10 to the power of 66 smaller than the Planck constant so they are practically zerospin
bosons.
The direct and indirect evidences that there are in existence the superluminal particles are as
follows. There are the superluminal neutrinos. Entangled photons show that they can
communicate with speeds higher than the c. The wave functions fill the whole our Universe.
The wave function describing our Universe can be the coherent mathematical object if the
very distant points of the wave function can communicate with speeds much higher than the c.
We can say that coherent quantum physics needs the tachyons. Also the MichelsonMorley
experiment leads to conclusion that masses emit the tachyons.
The total energy T we can define as the sum of the energy E which appears in the General
Relativity (the GR) and the imaginary energy N associated with the Newtonian spacetime:
T = E + iN, where i = sqrt(–1).
The word ‘imaginary’ means that the free tachyons have broken contact with the wave
function describing the state of our Universe.
In the GR we apply the formula for energy in which the mass M is for inertial mass equal to
gravitational mass.
The tachyons cannot emit some objects so they have the inertial mass m only. Substitute ic
instead c, iv instead v and im instead M. Then
N = – imc 2 /sqrt(1 – v 2 /c 2 ) i.e. N = mc 2 /sqrt(v 2 /c 2 – 1) .
The m is in proportion to volume of tachyon i.e. m = aV so N = aVc 2 /sqrt(v 2 /c 2 – 1). We can
see that when the speed v of a tachyon increases then its energy decreases. It is possible only
due to the higher grinding of tachyons when they move with higher speed. We can see that the
GR leads to the Newtonian spacetime i.e. to the fundamental imaginary spacetime. We can
see also that the GR is the more fundamental theory than the Quantum Physics. The Quantum
Physics appears on higher level of nature and is associated with the excited states of the
Einstein spacetime. From the formula T = E + iN follows that there are in existence two
spacetimes i.e. the Einstein spacetime and the imaginary Newtonian spacetime. The phase
transitions of the imaginary Newtonian spacetime lead to the Einstein spacetime also.
Tau lepton: It consists of an electron and massive particle, created inside a baryon, which
interact with the point mass of an electron.
Tensor field: Tensor is the generalization of scalar and vector. There are the two spacetimes.
The Newtonian spacetime consists in approximation of scalars i.e. of the spinning tachyons
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which spin is about 10 66 times smaller than the Planck constant. The Einstein spacetime
consists of the neutrinoantineutrino pairs i.e. the weak dipoles. The gravitational gradients
produced in the Newtonian spacetime by the binary systems of neutrinos are impressed on the
Einstein spacetime too. In the today Universe, the gravitational energy is lost due to emissions
of the nonrotatingspin neutrino bidipoles.
TitiusBode law: It is obligatory for the strong interactions inside baryons and for the
gravitational interactions near neutron black holes and their associations. The ratio A/B in the
formula R=A+dB (for strong interactions d=0,1,2,4, whereas for gravitational
d=0,1,2,4,8,16,32,64,128) for both interactions is in approximation 1.39.
Tunnels in the Einstein spacetime: When virtual particles decays into two parts moving in
opposite directions, a hole in a field composed of binary systems of neutrinos is created in
place of decay. Such a set of holes creates a tunnel.
Ultimate Theory: There must be in existence theory which leads to the initial conditions in
the General Theory of Relativity (the GR) and the Quantum Theory of Fields (the QTFs).
Such theory must explain origin of the basic physical constants as well. We can call such
theory the lacking part of the ultimate theory. We cannot formulate such theory on base of the
methods applied in the QTFs. It is because the GR and QTFs neglect internal structure of the
bare fermions. In reality, there is torus and ball in centre of it. We cannot describe
mathematically such structure applying the mathematical methods typical for the QTFs to add
this structure to Lagrangian. Just we must apply new methods. The bare baryons, i.e. the cores
of baryons, are the stable structures, whereas the bare electron is stable for period of spinning.
Moreover, the nature on its lowest levels, once again behaves classically. These facts cause
that the lacking part of the ultimate theory is the very simple nonperturbative classical theory.
The Everlasting Theory is the lacking part of the ultimate theory and this theory shows how
the new methods should look.
It is very easy to distinguish the more fundamental theories from the incomplete. A more
fundamental theory should lead to the initial conditions applied in the incomplete theories,
should contain less the parameters and solve more fundamental problems.
The two longdistance interactions, i.e. gravity and electromagnetism, lead to two spacetimes.
To explain the inflation, existence of wave function and constancy of the speed of light we
need fundamental spacetime composed of tachyons. I call such spacetime the Newtonian
spacetime or the modified Higgs field. The modified Higgs field, i.e. the tachyon gas, behaves
as liquid due to the tremendous pressure in this spacetime. The Reynolds number for such
spacetime leads to the closedstrings/vortices composed of the tachyons. Their spin is halfintegral.
The inflexible binary systems of the closed strings arise due to the first phase
transition of the modified Higgs field. We can say that the reduced Planck constant (i.e. the h
divided by 2π) is the most fundamental physical constant. The second phase transition leads
to the Einstein spacetime, third to the core of baryons whereas the fourth to the new
cosmology. Due to very high temperature or strong fields there appear the symmetrical decays
of the mesons. It leads to the TitiusBode law for the strong interactions outside the core of
baryons and for the gravitational interactions outside black holes.
Today, i.e. in present state of the Universe, the quantum theory is characteristic not for the
Einstein spacetime components but for the phenomena which take place in the Einstein
spacetime. The modified Higgs field is classical also. Just today the quantum physics is valid
in some interval for sizes. Of course, the GR was the quantum theory but only in the era of
inflation i.e. the states of the Einstein spacetime components in the era of inflation we can
describe via wave functions. This means that within the GR we should find a solution which
at least partially should lead to the internal structure of the bare particles which is neglected
within the Quantum Theory of Fields. And it is the Edward Kasner solution (1921) for the flat
anisotropic model. The mainstream classical GR does not concern the inflation so unification
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of the GR and the quantum FTs is impossible i.e. we never will able to describe these two
theories within one coherent mathematical description. But it is possible to formulate more
fundamental theory which leads to the two sets of initial conditions from which the
mainstream theories start and the Everlasting Theory is such fundamental theory.
Inflation concerns the Newtonian spacetime. The Einstein spacetime components cannot
move with speed higher than the speed of light because the c is the natural speed of the
Einstein spacetime components in the modified Higgs field. Our Universe cannot expand with
speed higher than the speed of light so acceleration of expansion is impossible. Origin of the
observed “acceleration” is different and follows from the fact that the GR is the incomplete
theory. Generally, the GR is the correct theory but the initial conditions are incomplete so
there appear the incorrect conclusions as, for example, existence of the gravitational waves or
time loops. Due to the incompleteness there can appear unknown phenomena which concern,
for example, the evolution of black holes.
The QED and QCD are the perturbative theories whereas the Everlasting Theory is the nonperturbative
theory. Why the ultimate theory must contain the nonperturbative and
perturbative theories? The ground state of the Einstein spacetime consists of the nonrotatingspin
neutrinoantineutrino pairs. The total internal helicity of this state is zero and it consists
of particles which spin is unitary. In such spacetime, cannot appear loops having internal
helicity i.e. carrying mass. In reality, a unitaryspin loop (the loop state) is the binary system
of two entangled halfintegralspin loops (total spin is 2·1/2 = 1) with opposite internal
helicity i.e. the resultant internal helicity is zero. Then in such spacetime do not appear
turbulences. Such loop can easily transform into a fermionantifermion pair (the fermion
state). Perturbation theories concern the loop states whereas the nonperturbative theories the
fermion states. In nonperturbative theory such as the Everlasting Theory, we cannot neglect
the internal structure of the bare fermions (there is torus and ball in its centre and virtual
pair(s) of fermions outside bare fermion). In the QED the both states, i.e. the loop state and
fermion state, are separated in respect of time whereas in the QCD are not. Moreover, the
QED and Everlasting Theory are energetically equivalent so within these theories we should
obtain the same theoretical results. In baryons, the both states are valid all the time but the
nonperturbative fermion state dominates at low energy whereas the loop state dominates at
high energy. But it is easier to describe the liquidlike plasma within the fermion state. Since
there are the creations from loops and annihilations to loops of the fermionantifermion pairs
so both states (loop and fermion) are energetically equivalent but the barefermion state is
mathematically much simpler.
Why there are valid the perturbation expansions? Due to the physical laws, the energy
spectrum is quantized. To fit some energy of interaction to the quantized energy spectrum,
most often there are many carriers of interactions in one event of interaction. At first, the
nature chooses a quantized energy from the spectrum close, but smaller, to the energy of
interaction. It is the oneloop interaction described by the first order in perturbation
expansion. When particles interact then the carriers of an interaction cannot be in the same
state. This means that to fit the energy of interaction to the quantized energyspectrum, there
must appear the higher orders containing 2 entangled loops, 3 entangled loops, 4loops and so
on. But most important in the perturbative theories is the fact that there must appear the
changing sliding scale. Only then the higher and higher orders in a perturbation expansion are
smaller and smaller. The sliding scale does not solve the problems at low energy (the coupling
constants are great) because the Everlasting Theory shows that there is the upper limit for
energy of created gluon balls in baryons. The upper limit follows from the rest mass of the
core of baryons (X + Y = 742.4 MeV). Gluon condensate of such rest mass produces particle
which rest mass is 171.8 GeV. It is the mass of the top quark (see formulae (214)(216)). We
can see that the QCD should give best results for sliding scale above but close to the mass of
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the bottom quark but much lower than the mass of the top quark. And it is the known solution
for the beta function. But to obtain the running coupling we need one additional parameter i.e.
the absolute parameter i.e. the alpha_strong for energy equal to the mass of the Z boson.
There must be the minimal subtraction (or QCD scale) as well to eliminate the big values of
the running coupling.
Universeantiuniverse pairs: Similarly as particles, also universes arise as the universeantiuniverse
pairs. The baryonantibaryon symmetry was broken already before the ‘soft’ big
bang (i.e. after the period of inflation). In Einstein spacetime (its ground state consists of nonrotatingspin
binary systems of neutrinos) arise the left and righthanded vortices as the
vortexantivortex pairs. The Protoworld associated with our Universe was lefthanded. Such
internal helicity have neutrons, therefore, in the lefthanded vortex appeared the protogalaxies
composed of neutron black holes. Evolution of the Protoworld leads to dark energy. Inflows
of dark energy into protogalaxies caused their exits from the blackhole states. There is
gravitational attraction between our Universe and its antiuniverse.
Virtual particles: In contrary to the real photons they have mass not equal to zero. For
massless particles, the coupling constants are equal to zero because such particles cannot
create gradients in the spacetimes and other fields (they ‘slide’ along a field). Virtual photons
are the objects composed of nonrotatingspin binary systems of neutrinos. When mean mass
density of a virtual photon is lower than the mean mass density of the Einstein spacetime then
its mass is negative. When such density is higher then mass is positive. Mass of a ‘hole’ in the
Einstein spacetime (i.e. of a region with lower mass density than the mean density) is negative
and imaginary because the lacking mass has broken contact with real particles. This means
that the negative mass is defined as –im, where i = sqrt(1). This definition leads to the
negative square of mass of the ‘hole’ (im) 2 = m 2 . A vortex of massless energy E has mass m
= E/c 2 i.e. the total energy is 2E. This means that in the field of a particle there can arise
simultaneously the bare virtual particleantiparticle pair(s) that total positive mass is two
times greater than the bare mass of the real particle. For example, in the electromagnetic field
of a resting electron simultaneously can be produced only one virtual bare electronpositron
pair.
Weak dipoles: These are binary systems of neutrinos i.e. the neutrinoantineutrino pairs. The
neutrinos carry the weak charges.
Weak charge: This is the torus of neutrinos. It looks as a miniature of the electric charge of
proton. They consist of the binary systems of the closed strings. On surface of the torus of
neutrinos, arise the small loops. Their radii are 2π or 2π/3 times greater than the radius of the
equator of the torus of neutrinos. The small loops are responsible for the short and longdistance
entanglement of particles. The binary closed strings a neutrino consists of suck up the
tachyons from some volume. This leads to the shortdistance weak interactions.
The mass responsible for the weak interactions of baryons in the lowenergy regime is the
point mass inside the core of baryons – its mass is Y = 424.1 MeV. It is relativistic object so it
can produce the W and Z bosons as well.
Weak interactions: Volumes filled with additional binary systems of neutrinos interact
weakly. Weak interactions are due to the exchanges of such volumes. Surfaces of volumes
interacting weakly should be in distance equal to or smaller than 3482.87 times the external
radius of a neutrino.
YangMills existence: The confinement, massgaps and asymptotic freedom described within
the Everlasting Theory are the foundations of the YangMills acting correctly.
Asymptotic freedom in the Everlasting Theory acts as follows. The components of the pions
(the large loops) arise due to the entanglement and confinement inside the torus of the core of
baryons as a closed loop composed of the Einstein spacetime components. The Einstein
spacetime components are moving with the speed of light c. During acceleration of a baryon,
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due to the constancy of the c, the spin speed of the closed loop decreases i.e. their lifetime,
defined by the spin speed, increases. On the other hand, from the Uncertainty Principle
follows that when lifetime increases then energy of the closed loop decreases i.e. during
acceleration of the baryon, energy of carriers of the strong interactions decreases i.e. value of
the running coupling for the strong interactions decreases as well. We can see that the carriers
of the strong interactions behave out of accord with the Einstein formula for the relativistic
mass. Such behaviour follows from the structure of the core of baryons, the Uncertainty
Principle and the coupling of the core of baryons with the Einstein spacetime. In the highenergy
regime there appears the asymptote for the alpha_strong 0.1139.
Confinement in the Everlasting Theory acts as follows. To explain the confinement we need
two parallel spacetimes. The two longdistance interactions, i.e. gravity and
electromagnetism, lead to the two parallel spacetimes. The Einstein spacetime components
suck in the components of the more fundamental Newtonian spacetime (it is the modified
Higgs field) and due to the internal helicity of the closed strings the components consist of,
they transform the chaotic motions of the tachyons into the jets. It causes that there arises the
negative pressure in the more fundamental spacetime inside and near the Einstein spacetime
components. This means that in the nonperturbative regime, there appears the attraction
between the Einstein spacetime components when they are sufficiently close one to another.
But such states are very unstable. The confinement is possible in each place of the two
parallel spacetimes and concerns the zeroenergy photon and gluonfields as well.
Mass gaps in the Everlasting Theory arise as follows. To describe the mass gaps we need
additional phenomena which stabilize the confinement. For example, we need the phenomena
characteristic for the core of baryons: the Einstein spacetime components trajectories, i.e. the
binary systems of neutrinos cross the centre of the core so in the centre their number density is
higher. There appears the ball composed of the confined carriers of the gluons so we can call
it the gluon ball. We can see that there can be in existence balls composed of zeroenergy
gluons as well. There is not increase in mass of the Einstein spacetime components. There
increases a little the mass density of the local spacetime i.e. the mass gaps are associated with
the density, not with the individual components. We cannot detect the notrotatingspin binary
systems of neutrinos. It is because the Lagrangian of the ground state of the Einstein
spacetime is today always constant. Mass gaps follow from confinement but there are needed
processes which stabilize the confinement.
Outside the strong fields, the gluons behave as photons. It is because the carriers of gluons
and photons, i.e. the Einstein spacetime components, and the strong fields have internal
helicity whereas the electromagnetic field has not.
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