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ISBN 978-83-933105-0-0 - viXra

ISBN 978-83-933105-0-0


Copyright © 2012 by Sylwester Kornowski

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ISBN 978-83-933105-0-0

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 copy-editing.

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 Liquid-like Plasma 54

6 New Cosmology 56

7 Four-shell 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 Kaon-to-Pion Ratio 104

14 The Cross Section for Production of the W Boson 106

15 Neutrino Speed 108

16 M-theory 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, Non-Abelian 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 long-distance 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, long-distance 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 Titius-Bode law for the strong interactions and to the Titius-bode

law for the gravitational interactions acting nearly the black holes. Due to the Titius-Bode law

for the strong interactions, there appears the atom-like 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 neutrino-antineutrino 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 black-hole

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 non-Abelian gauge theories become useless. Due to the phase

transitions and entanglement, the new fields have the torus-like 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 low-energy 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 liquid-like plasma obtained in the high-energy collisions of

nucleons consists of the cores of baryons. Within reformulated Quantum Chromodynamics, I

described the electron-positron and nucleon-nucleon 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 Mandelbrot-like 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 4/3-factor problem for mass-energy relation for classical electron. The origin of DNA

follows from the reformulated QCD.

The ultimate theory must contain non-perturbative and perturbative theories. The ground state

of the Einstein spacetime consists of the non-rotating-spin neutrino-antineutrino 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 unitary-spin

loop (the loop state) is the binary system of two entangled half-integral-spin 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 fermion-antifermion pair (the fermion

state). Perturbation theories concern the loop states whereas the non-perturbative 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 Michelson-Morley

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 Titius-Bode law for the strong interactions

is obligatory. This will lead to an atom-like 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 Titius-Bode law for the

strong interactions that leads to the atom-like structure of baryons.

The ground state of the Einstein spacetime consists of non-rotating-spin binary systems of

neutrinos. To detect the non-rotating-spin binary systems of neutrinos we must measure mass

with accuracy about 10 -67 kg. No one has identified the products of neutrino-antineutrino

annihilations. This suggests that in the today Universe the neutrinos are the non-quantum

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


6

disappear in one place of Einstein’s spacetime and appear in another and so on. The nonrotating-spin

binary systems of binary systems of neutrinos (the neutrino bi-dipoles) with

parallel spins carry the gravitational energy. Due to the internal structure of the rotating

neutrino bi-dipoles, 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 (1-x) 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

(1-y) is composed of a neutral core and a positive pion.

2.

We know that the nucleon-nuclear 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


7

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 liquid-like substance appears [2]. This

also suggests that there is a massive core inside a nucleon.

4.

The triplet n-p scattering length is approximately 5.4 fm. The singlet n-p effective range is

approximately 2.7 fm whereas the triplet n-p effective range is approximately 1.7 fm.

Assume that outside of the core of nucleons the Titius-Bode 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 baryon-antibaryon

annihilations leads to the temperature of the Universe today being a few hundred billion

times higher than the measured. This suggests that baryon-antibaryon symmetry was

broken before the ‘soft’ big bang after the period of inflation.

9.

We are unable to see the bi-products of neutrino-antineutrino 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 electron-positron pair is equal to

the bare mass of electron calculated within this theory. This is the Feynman ‘hocus-pocus’


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 non-perturbative 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 coupling-constant=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 long-distance 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 electron-positron 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 electron-positron 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 atom-like 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 atom-like structure. Since the baryons have sizes much greater than the Planck length, so

they should also take the form of an atom-like structure. My theory is that there is a massive

core and outside there is the Titius-Bode law that is obligatory for strong interactions. On

orbits are pions. In strong fields, pions behave in a similar way to electron-electron 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


9

as fermion-antifermion pairs i.e. bosons. Such pairs behave like bosons. For example,

electrons arise as electron-positron pairs, closed strings arise as closed string-antistring 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 low-energy 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 low-energy regime. The Everlasting Theory shows that it is not true that almost whole

mass of resting nucleons (it is the low-energy 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

low-energy regime.

In the theory of the weak interactions, there is the mass-hierarchy error for the low-energy

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 low-energy regime are incorrect. This causes that

there appears the hocus-pocus 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

Yang-Mills 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 M-theory. The useful

M-theory is the part of the Everlasting Theory. To describe the internal structure of baryons,

we need something beyond the useful M-theory i.e. the Titius-Bode 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 Quark-Gluon 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 gas-like Newtonian

spacetime and the internal structure of main particles.

Assume that the Newtonian spacetime is an ideal gas in the zero-dimensional 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 )

Half-integral 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


12

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

gas-like 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 gas-like spacetime is strictly determined. We see

that phase transitions of the gas-like 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)


13

The spin of each closed string is half-integral

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(d-1) , 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 (d-1) .

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 d-1 . (5)

The rest mass of the tori of the stable objects are

md = m1K 2(d-1) , (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 half-turns 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 neutrino-antineutrino 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 neutrino-antineutrino pairs are the carriers of the elementary gluons and

photons. The rotating-spin 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 atom-like

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 λbare-electron 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 fine-structure 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 fine-structure constant

αem = e 2 c/(10 7 h) = 1/137.036001. (21)

Binding energy of the large loop ΔELL, resulting from creations of the electron-positron

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

electron-positron pairs. Since with the rest mass of electron at the same time is associated one


17

bare electron-positron pair then the nine electron-positron 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 α-order correction for the radiation energy created in the interactions of the virtual or

real electron-positron 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(+-) - mem-pion(+-) - 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 particle-antiparticle 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 Titius-Bode 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 Titius-Bode 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 strong-Weak 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 Titius-Bode 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 positroncore-of 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 Titius-Bode 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

1-y is composed of H o and W(+),d=1. From the Heisenberg uncertainty principle follows that

the probabilities y and 1-y, 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

1-x is composed of H o , resting neutral pion and Z o . The mass of the last particle is

mZ(o)=mW(o),d=1-mpion(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(1-x)] 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=1-mpion(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 strong-weak 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 strong-weak 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(large-loop)=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

formula-definition

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 electron-like particle i.e. the point mass of a

muon is equal to the circular mass of it i.e. about (mmuon,free-mradiation(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 electron-muon

transformation

w(electron-muon) = 9.511082·10 -7 . (56)

We see that

Xw w(proton)/w(electron-muon) = (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 electron-proton interactions we

obtain: ’w(electron-proton)≈Gw(Y-gw)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 Y-gw to the mass

M=35.806163. This similarity leads to conclusion that the electron-muon transformation (due

to the weak interactions) is associated with the electron-matter interactions whereas the

electron-proton weak interactions are associated with the electron-matter-dark-energy 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(electron-proton) = ( + 1)w(electron-muon) = 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

electron-positron 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(electron-proton) = 1.11943581·10 -5 . (64)

As a result, we can introduce the symbol

= em/(’w(electron-proton) + 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(electron-proton)/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(electron-proton)/(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(electron-proton) 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

Titius-Bode 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 E-11 m 3 /(kg s 2 )

Half-integral spin (1.054571548 E-34)/2 Js

Speed of light 2.99792458 E+8 m/s

Electric charge 1.60217642 E-19 C

Mass of electron 0.510998906 MeV

Fine-structure 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 E-45 m

Linear speed of closed string 0.7269253 E+68 m/s

Mass of closed string 2.3400784 E-87 kg

External radius of neutrino 1.1184555 E-35 m

Mass of neutrino 3.3349306 E-67 kg

Mass of Protoworld 1.961 E+52 kg

External radius of Protoworld 287 million light-years

Mass of the Universe 1.821 E+51 kg

Radius of the early Universe loop 191 million light-years

External radius of torus of nucleon 0.697442473 fm

Constant K 0.7896685548 E+10

Binding energy of two large loops 0.12273989 MeV

*E-15=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 E-18 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 Titius-Bode 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 E-18 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 electron-proton weak

interaction

1.11943581 E-5

Coupling constant for the electron-muon weak

0.9511082 E-6

interaction

Coupling constant for strong-weak 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 Abo-Shaeer, A Schirotzek, C H Schunck, and W Ketterle; Vortices

and superfluidity in a strongly interacting Fermi gas; Nature 435, 1047-1051 (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 Fundamental-direct 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

electron-positron 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 three-coloured

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

bi-dipoles)

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 bi-dipoles (two

binary systems of

neutrinos i.e. two weak

dipoles; spin = 2; today

the classical gravity)

+ Entanglons Binary systems of closed

strings i.e. half-jet

dipoles (spin = 1)

Quantum particles

Weak bi-dipoles (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

Electron-positron pairs

+ – – –

Table 4 Phase spaces

Stable object Co-ordinates and quantities needed to

describe position, shape and motions

Tachyon 6 (5 + time)

Closed string

10 (9 + time)

Closed string-antistring pair

Neutrino

Neutrino-antineutrino 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=(d-1)·8+2, where N denotes the numbers of needed

co-ordinates 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 string-antistring 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 neutrino-antineutrino pairs in the

Einstein spacetime. The mean distance between the neutrino-antineutrino 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(spin-speed-of-loop)=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 strong-weak interactions of colliding nucleons

The formula (78) defines coupling constant for two strongly interacting non-relativistic

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 strong-weak 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 (energy-of-component-of-field multiplied by spin-period is h;

the spin-period 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 liquid-like substance composed of the cores of

baryons. There is the destruction of the atom-like structure of baryons. This means that a

colliding nucleon and the new sources behave as one source. Strong-weak 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·\integer-of\{(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 strong-weak interactions of colliding nucleons. When we neglect the \integer-of\

in the formula (82) then from (76), (78) and the formulae (79)-(82), we obtain the following

function for strong-weak running-coupling

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 gas-like plasma whereas the asymptotic

packing leads to liquid-like 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 strong-weak 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 non-relativistic 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 liquid-like substance.

Electromagnetic interactions

Within the liquid-like 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 electron-positron pairs appears. The mass of contracted pair is


33

xm=9.0104369 times greater than the mass of the electron-positron pair (see discussion below

formula (23)). From formula αem=Gemm 2 electron/ch, we obtain that at the high-energy collisions

of nucleons the coupling constant for the electromagnetic interactions of the contracted

electrons is xm 2 =81.18797 times greater than the fine-structure constant. There appears one

more contracted pair per each new core-anticore pair. It leads to conclusion that probability of

the electron-positron 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 liquid-like 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 bi-dipole behaves as two entangled photons, not as graviton.

Gravitational energy is emitted via the flows in the Einstein spacetime composed of the nonrotating-spin

neutrino bi-dipoles.

The neutrinos, binary systems of neutrinos, bi-dipoles 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 bi-dipoles 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.

Fine-structure 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 fine-structure 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 electron-positron


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 electron-positron 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=mneutral-pion/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 fine-structure 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

tstrong-minimal = tem-minimal(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)/tem-minimal(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(electron-muon)) = 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)

Four-neutrino 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 pion-antipion 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 spheroid-like structures. Notice that the above

described rules lead to the four-neutrino 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 chain-like 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 four-neutrino 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 non-rotating-spin 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 half-integral 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 N-N 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 proton-proton 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

drange-strong=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 p-p cross section is

σ15MeV(p-p) = π(drange-strong + 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(p-p) = 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 non-transparent. 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(p-p) = 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:

σhigh-antiparallel(p-p) = π(2A) 2 = 61 mb. (109)

The n-p scattering differs from the p-p 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 n-p scattering we consequently obtain:

σ15MeV(p-n) = π(drange-strong + A + B + 2A/3) 2 = 671 mb. (110)

Furthermore, a highly energetic p-n scattering mass of the negative pion is very small so for

both total cross sections, i.e. for p-p and p-n, they should have the same value.

It is easy to calculate that for very energetic π-p 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 pion-proton 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 N-N scattering

The effective ranges are as follows

rsing(p-n) = r1(n-n) = r(p-p) = A + 4B = 2.7 fm. (111)

For the n-n 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(n-n) = A + B + 2A/3 = 1.7 fm. (112)

For the triplet p-n scattering, the effective range is:

rtrip(p-n) = A + B +2A/3 = 1.7 fm. (113)

Se also the theory of deuteron in Chapter titled “Four-shell 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 p-n and n-n

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(p-n) = 2π(A + 4B) + 2(A + 4B) = 22.4 fm, (114)

a(n-n) = 2π(A + B + 2A/3) + 2(A + 4B) = 15.9 fm. (115)

In the p-n triplet state, the directions of the spins overlap and have the same senses.

atrip(p-n) = 2(A + 4B) = 5.4 fm. (116)

See also the theory of deuteron. The exact result is 5.4343 fm.

In the p-p scattering the length of the closed photons is equal to the range of strong

interactions.

a(p-p) = (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 electron-positron 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 neutrino-antineutrino pair), the electron-positron 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 electron-positron 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 vis-a-vis 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 torus-antitorus pair, for

example, into electron-positron pair. Such torus-antitorus 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 electron-positron 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 state-lifetime 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 state-lifetime is the time distance between

appearance and nearest disappearance. We see that the state-lifetime 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 state-lifetime 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 state-lifetime in one state with a determined value of the ‘i’.

State-lifetime 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 non-entangled 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 four-neutrino 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 state-lifetime, 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 four-neutrino 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 vortex-antivortex pairs. We see that such phenomena

broken symmetry of the Einstein spacetime inside the vortices. In both components of the

vortex-antivortex pair, the creation of electron-positron pairs is possible. When mass density

inside a vortex was sufficiently high, there appeared in the left-handed vortex the positronproton

transitions whereas in the right-handed vortex the electron-antiproton transitions.

When the mass of a vortex is strictly determined then there is the possibility of the vortex-

Protoworld transition. Our rotary vortex was left-handed so there the protons and next

neutrons were created because nucleons are the left-handed 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

electron-antineutrinos for the third time in the history of evolution of a left-handed 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 strong-weak 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 four-neutrino symmetry solves many problems associated with particle physics and

cosmology.

The calculated characteristic values for the pion-N and N-N scattering on the basis of an

atom-like 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 E-6 s

Lifetime of the tau 1.88 E-12 s

Lifetime of the hyperon 1.24 E-10 s

Lifetime of the charm baryon c + (2260) 6.5 E-13 s

Lifetime of the neutral pion 0.79 E-16 s

Lifetime of the charged pion 2.8 E-8 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 fine-structure constant

*2.2 E+133=2.2·10

±6.2 E-5

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

p-p total cross section for kinetic energy about 15 MeV 368 mb

p-p total cross section for kinetic energies approximately a

few hundred MeV

27 mb

p-p total cross section for kinetic energies approximately a

few rest mass of protons

42 mb

p-p total cross section for kinetic energies approximately a

few rest mass of proton for antiparallel beams

61 mb

p-n total cross section for kinetic energy approximately 15

MeV

671 mb

p-n total cross section for kinetic energies approximately a

few rest mass of the proton

42 mb

π-p total cross section for very high energies 27 mb

Significant reduction of the cross sections for negative 423 MeV

pion-proton 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 [astro-ph.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 neutrino-antineutrino 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 state-lifetime.

Slowly moving electrons have state-lifetimes 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 electron-positron 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 half-turns 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 half-turns 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 torus-antitorus 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/electric-charge of electron disappears in some place then the mass of

electron in this place vanishes due to the emissions of the surplus neutrino-antineutrino 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 electron-positron 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 electron-neutrino pair. The charged

pion is the four-particle 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 electron-electron 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 Titius-Bode 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 non-relativistic

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 Lamb-Retherford 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 Helion-4. 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 Lithion-7

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 low-energy 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(electron-muon)

(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 high-energy regime abundance of the baryons with destroyed the Titius-Bode

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 Titius-Bode 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 half-integral 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, 1-x, y, 1-y 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{1-1-1-} + 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 strong-weak 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 electron-type 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

electron-positron 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(electron-proton)/(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 orbit-orbit 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

Lamb-Retherford 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(electron-proton) + 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

Lamb-Retherford 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

Liquid-like plasma

The phase transitions of the Newtonian spacetime and the Titius-Bode law for the strong

interactions lead to an atom-like structure of baryons. Such model leads to the pseudorapidity

density, NSD-fraction in the pp collisions, temperature and density of the liquid-like plasma.

Pseudorapidity density in pp collisions

Electron-positron pairs that decay into photons arise close to tori/electric-charges of

colliding protons that have very low energy. The ratio X1 of the energy of particles that have a

transverse-momentum to the energy of emitters (i.e. of protons having atom-like structure) is

X1 = 2melectron/mproton. (157)

When protons collide which have a higher energy, there appears, along a transverse

direction, core-anticore 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 liquid-like 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,

liquid-like plasma appears (i.e. the segments). The segments fill a prolate cylinder. Inside

such a cylinder are core-anticore pairs whereas the protons that have an atom-like 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 liquid-like 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 liquid-like plasma have transverse-momentum –

they are the non-single-diffractive 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 single-diffractive fraction (the SD fraction). This means that the ratio X2 of

energy of the NSD hadrons that have transverse-momentum to the total energy emitted by the

lateral surface of liquid-like plasma (i.e. by the protons having an atom-like 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 liquid-like 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 liquid-like 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=dNcharged-hadrons/dη; η


55

NSD-fraction = 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 atom-like structure on the lateral surface of liquid-like plasma.

This means that the external layers of liquid-like plasma can separate from it explosively.

The temperature and density of liquid-like 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 liquid-like plasma, is equal to the A=0.697442 fm. It follows from the fact that in

liquid-like plasma the Titius-Bode orbits for strong interactions are destroyed. Using the

theory in Wien’s law we obtain that the lowest temperature of liquid-like 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 liquid-like plasma having the lowest temperature i.e.

the 4.155·10 12 K. Because the temperature is directly relative to the NSD-fraction, we obtain

following formula for temperature T for liquid-like 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 liquid-like plasma equal to approximately 7.6·10 12 K.

At the lowest temperature of liquid-like 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 liquid-like 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 liquid-like 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;

Transverse-momentum and pseudorapidity distribution of charged hadrons in pp

collisions at sqrt(s) = 0.9 and 2.36 TeV;

arXiv: 1002.0621v2 [hep-ex] 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 light-years. 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 four-neutrino 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 light-years.

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 four-neutrino 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 spheroid-like structures, and d=3,6,12 for a chain-like

structures.

The four-neutrino 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/black-body 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 electron-antineutrinos. 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 E-mode 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 electron-positron 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(electron-proton) = 12.197 eV/neutron, (166)

where a=0.001159652, mneutron=939.54·10 6 eV, α ’ weak(electron-proton)=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 electron-proton weak interactions. The circumference of the

large loop changes due to the weak electron-proton 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

electron-proton interactions is 1.11944·10 -5 , therefore, the mean amplitude of temperature

fluctuations for the weak electron-proton 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 particle-antiparticle 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 )·(727.44-318.2955)/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 particle-antiparticle 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 E-mode 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 E-mode 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 E-mode 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 atom-like 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 four-neutrino 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


63

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 light-years (precisely 20.7±0.1). Such a radius, in

approximation, also has a sphere filled with dark energy (approximately 20.9±0.1 billion

light-years).

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

light-years, 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 left-handed double helix loop that was composed of protogalaxies.

Electromagnetic interactions of electrons are responsible for the structure of the DNA.

Moreover, electrons are right-handed 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


65

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 four-neutrino 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 Einstein-de Sitter model the critical density is

E-S = 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 E-S = 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

= /E-S = 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 electron-positron 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 four-neutrino 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 Pu-244 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 non-rotating-spin 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


66

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 nucleon-helium transformation is 7.06 MeV. These are

quanta group because of the four-neutrino 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 four-neutrino 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

neutrons-helium transformations. For example, the transformation of 112 neutrons into 28

nuclei of helium releases energy equal to 791 MeV. Moreover, 56 electron-antineutrinos are

emitted.

Assume that now the GASER is implemented. To release energy of approximately 791

MeV 4 nuclei of iron-56 should arrear as a result of helium-iron transformations (about 388

MeV) and 14 nuclei of helium as a result of neutrons-helium 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 electron-antineutrinos are absorbed (because

of the 8 processes inverse to the beta decay), whereas in the second 28 electron-antineutrinos

are emitted (because of the 28 beta decays). Therefore, during these two transformations 20

electron-antineutrinos 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 iron-56, for the helium-4 it has 7.06 MeV. There should, therefore, be

approximately 100%·(8.79-7.06)/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 Lorens-256) 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 alpha-particles).

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% H-1 71% H; 100%·2.05/7.06=29% He 7.06 MeV

20% He-4 20% Fe-56 2.05 MeV

20% 0-16 20% Fe-56 1.11 MeV

20% 64 X 20% Fe-56 0.00 MeV

20% 256 Y 20% Fe-56 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 proton-neutron symmetrical nickel followed by Fe-56, Si-28, N-14,

Li-7. 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 Ni-64,

S-32, O-16.

Table 13 Stars of second generation with working the GASER

Composition at Nuclear transformations Released binding

the beginning

energy per nucleon

71% H-1 H-1 He-4 7.06 MeV

29% He-4 He-4 Fe

For 1 part of the H-1 He-4 is

7.06/1.73=4.081 parts of the He Fe

Over time, the amount of He decreases

8.79-7.06=1.73 MeV

About 0% Fe-56 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


68

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 Einstein-de 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 four-neutrino symmetry, we can see that a virtual pion can interact at

maximum with 2·4 32 neutrinos (this is because of the long-distance 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 oval-shaped) - such structures


69

have a mass approximately 3.3 million times greater than the sun or had one core (some

globular clusters are spherical-shaped) - 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, X-64 (which first transformed into iron), Y-

256 (which first transformed into plutonium Pu-244 and then into lead). From these gaseous

rings arose. The Titius-Bode 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 Uranus-twin rings. This means that the Saturn-twin

ring was tangent to the Neptune ring as well (precisely the Saturn-twin ring split into two

rings tangential in one place). The Dogon myth identifies that the Sun and the star Po-tolo was

binary system, and notes that human life arose on the planet revolving around Po-tolo. In the

distant past the star Sirius, covered an area near the Po-tolo 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 Po-tolo 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

mphoton-megachain = 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 Pu-244 because these nuclei

have a long half-life 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 )

Aconstituent-beginning + Bconstituent-beginning = r(plutonium) = 1.611·10 7 m. (176)

The next, the protonuclei Y-256 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.

Mconstituent-beginning = 4 4 ·4.935·10 31 kg = 1.263·10 34 kg, (177)

whereas

Mconstituent-now = Msun = 1.99·10 30 kg. (178)

The radii of the rings increased

Mconstituent-beginning/Msun = 6348 times. (179)

At the beginning, the radius of the Earth-ring was equal to

rEarth-ring-beginning = Aconstituent-beginning + 2Bconstituent-beginning, (180)

where Aconstituent-beginning=GMconstituent-beginning/c 2 .


70

From this for G=6.674·10 -11 m 3 kg -1 s -2 we obtain Aconstituent-beginning=0.9382·10 7 m.

This means that for a strong gravitational field is

Aconstituent-beginning/Bconstituent-beginning = 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 Earth-ring was

rEarth-ring-beginning = 2.284·10 7 m.

The present radius of the orbit of the Earth should be

rEarth-ring-now = rEarth-ring-beginningMconstituent-beginning/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

Ni-56 Co-56 Fe-56.

Firstly, nickel-56 appeared because this nucleus is the proton-neutron 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

Fe-56 Si-28 N-14 or C-14 Li-7.

The acting GASER produced nuclei that contained 64 nucleons so their symmetrical decay

lead to the development of the following nuclei

Ni-64 S-32 O-16 Li-8 He-4 D-2 H-1.

Because the half-period for C-14 is approximately six thousand years, today we should

detect many C-12 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 He-4 were (and are) the most abundant of all, the probability

of the production of T-3 and C-12 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

C-12 + C-12 Mg-24.

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 Titius-Bode 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 light-years (3.1 ly).


71

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

light-years (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 light-years (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 light-years (this

is if we assume that today there is a binary system of sun-like stars in the centre).

Summary

Table 14 Structures of the Universe

Structures of the Universe Mass

Largest neutron star/black-hole 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 H-1 and He-4 following the era of big

stars when we do not take into account the heavier

elements

Abundance of H-1 and He-4 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 E-mode 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 Abo-Shaeer, A Schirotzek, C H Schunck, and W Ketterle; Vortices

and superfluidity in a strongly interacting Fermi gas; Nature 435, 1047-1051 (2005).


73

Four-shell Model of an Atomic Nucleus

On the basis of the four phase transition of the Newtonian spacetime and the Titius-Bode

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

nucleon-pion 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 well-known 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 1-y=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 1-y have

almost the same values.

b) A neutron exists in two states with the probabilities:

x=62554 and 1-x=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 (1-x+1-y)/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 p-n 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 neutron-proton bound state is

w=y+z whereas of the H o W + state is 1-w. This leads to following the deuteron-nuclear

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)(1-z) + 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 1-w.

The H + protonW - interact from L for a period equal to x-(1-y), 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-(1-y).

The H + neutronW + proton interact from L for a period equal to (1-w).

This leads to the proton-neutron 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(He-4) = (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 atomic-number/symbol-of-element/mass-number

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 magic-number nucleus

This principle, in particular, satisfies nuclei which contain 2k(3p+5n) more nucleons than

the Ca-40 10(2p+2n): Fe-56 [(Ca-40)+2(3p+5n)], Ge-72, Sr-88, Ru-104, Sn-120, Ba-136, Sm-

152, Er-168, W-184, Hg-200 [(Ca-40)+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 four-neutrino 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 0.23-0.25 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 Bi-209, 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(O-16) = (7.1 + 3.33/4) = 8.0 MeV, (197)

E(Fe-56) = (26·8.0 + 6(14.95 - 4) + 24·(14.95 - 5.8))/56 = 8.8 MeV. (198)

When we neglect the proton transitions for Pb-208, we obtain

E(Pb-208) = (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 p-n attraction in a deuteron 0.0366111 MeV

Deuteron-nuclear magnetic moment ratio 0.85230

n-p(triplet) scattering length 5.4343 fm

n-p(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 He-4 7.1 MeV

Binding energy per nucleon for O-16 8.0 MeV

Binding energy per nucleon for Fe-56 8.8 MeV

Binding energy per nucleon for Pb-208 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 physico-mathematical 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 e-1=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 co-ordinates 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 numbers-factorials 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 co-ordinates (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/ideal-gas. This is the 0D volume filled with the free 3D

tachyons.

2.

The number 24 describes the phase space of a non-rotating-spin neutrino. The 24=4!=4D

shows that the spacetime composed of free non-rotating-spin neutrinos which is the 4D

spacetime.

The ground state of the Einstein spacetime consists of the non-rotating-spin 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 co-ordinates and quantities.

For rotating-spin 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 co-ordinates 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 Titius-Bode 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 non-rotating-spin neutrino-antineutrino 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

physico-mathematical 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

neutrino-antineutrino 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


82

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 Titius-Bode 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 Titius-Bode 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 physico-mathematical 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 non-existent 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 gas-like

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/cut-out

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 nonrotating-spin

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 Titius-Bode 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 Titius-Bode law

Rd = A + dB, (200)

where A/B=1.39. This means that the Titius-Bode law is somehow associated with fractal

geometry i.e. travelling half-distances, distribution of sources of interactions, and the creation

of consecutively smaller self-similar physical objects due to symmetrical decay (bifurcation).

How would the fractal field associated with the Titius-Bode law appear?

Assume that the origin of the orbits defined by the Titius-Bode 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

self-similar 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 Titius-Bode 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 self-similar ‘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 non-rotating-spin 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 gas-like

Newtonian spacetime and the Titius-Bode 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 gaslike-Newtonian-spacetimeclosed-strings

transitions. The radius starting from number 1,

containing squares of prime numbers, represents the closed-stringstori transitions.

The Everlasting Theory identifies that there is far more physico-mathematical 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 half-integral 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 Titius-Bode law. We

obtain the Titius-Bode 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 twenty-four succeeding natural numbers) are characteristic

for the Ramanujan modular equations. The Titius-Bode 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


86

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 Titius-Bode law and the Titius-Bode law is

associated with fractal geometry i.e. with travelling half-distances, with the distribution of the

sources of interactions and with the creation of smaller and smaller self-similar 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 twenty-four 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 non-rotating-spin 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 Abo-Shaeer, A Schirotzek, C H Schunck and W Ketterle; Vortices

and superfluidity in a strongly interacting Fermi gas; Nature 435, 1047-1051 (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 faster-than-light 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 cross-section 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 Schwarzschild-surface 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 faster-thanlight

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.


89

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.


90

Reformulated Quantum Chromodynamics

The QCD is the theory of interactions then in this theory appear the distances of mass

characteristic for the atom-like 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 atom-like 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 atom-like structure of the baryons. Within the

reformulated QCD, we can derive the masses characteristic for the QCD from the atom-like

structure of baryons.

Experimental data lead to the atom-like structure of baryons. The phase transitions of the

Newtonian spacetime and symmetrical decays of virtual bosons also lead to the atom-like

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 torielectric-charges).

Then, assume that the sham quark-antiquark 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 Titius-Bode 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 quark-antiquark 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 non-rotating-spin 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 3-coloured 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 Titius-Bode 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 electron-positron 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

baryonic-core-like sham quark-antiquark pairs. This means that mass and electric charge of a

sham quark is in proportion to radius of gluon loop (msham-quark ~ Qsham-quark ~ Rgluon-loop). For

R=A we have Qsham-quark = ±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 quark-antiquark 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 core-anticore 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 Titius-Bode 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 quark-antiquark 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 atom-like

structure of baryons and the sham quark-antiquark pairs production. How to define the

essential part for the sham quark-antiquark 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 fermion-boson

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 quark-antiquark pairs

created in electron-positron 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 electron-positron collisions, the

gluon loops arise as the binary systems of the binary systems of the gluon loops i.e. as the

quadrupoles. Lightest binary-system meson, which consists of four gluon loops, is the kaon

K. The electron-positron-pairfour-gluon-loops(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 neutral-kaonpositive-kaon 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 baryon-antibaryon pairs.

This means that to create two the lightest sham quark-antiquark 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.


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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/gluon-condensate 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 atom-like 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 atom-like structure of baryons. Just for higher and higher energies,

more and more baryons have destroyed the Titius-Bode orbits for the strong interactions. To

‘see’ the atom-like 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 atom-like 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 strong-weak 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 atom-like 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 high-energy regime, the

Titius-Bode 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 127-128 GeV are most important

in the latest LHC-experiment 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 electron-positron 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(electron-muon) = 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 electron-positron 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 atom-like 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 bi-dipoles 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 particle-antiparticle pair)

whereas the R = 2·106 MeV leads to the binary symmetry for the strong interactions (i.e. to

particle-antiparticle 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 electron-positron 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 quark-antiquark 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 strong-weak 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 quark-antiquark mass defines the energy E1

for the transition from the strong to the strong-weak 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 atom-like structure of baryons. Particles can

arise also due to the decays of the gluon condensates.

Origin of limitations in non-reformulated 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

atom-like 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 non-perturbative 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 non-perturbative 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 hep-ex/0407021,

(2004)):

Alpha_strong(mass of Z boson) = 0.1182 ± 0.0027.

The non-reformulated 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 non-reformulated 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 gluon-balls, which

are responsible for the strong-weak 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 gluon-ball(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 gluon-balls 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 high-energy 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, atom-like 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


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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 atom-like 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 non-perturbative 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 atom-like 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

atom-like 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 atom-like structure of baryons, we should reformulate the QCD. There appear the

6 basic sham quarks and 8 gluons. The gluon-loopsbasic-sham-quarks transitions lead to

the essential part of the curve R(s) = f(sqrt(s)). The particlesgluon-condensatesnewparticles

transitions cause the particles transform into new particles. The new particles are the

additional part of the curve R(s) = f(sqrt(s)). The atom-like 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 high-energy 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; Transverse-momentum and pseudorapidity distribution of

charged hadrons in pp collisions at sqrt(s) = 0.9 and 2.36 TeV;

arXiv: 1002.0621v2 [hep-ex] 8 Feb 2010

[3] http://vixra.files.wordpress.com/2011/08/gfitvars.jpg

[4] http://www.atlas.ch/news/2011/figure-combo2.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 non-abelian gauge theories".

Physical Review Letters 30 (26): 1343–1346. Bibcode 1973PhRvL..30.1343G.

doi: 10.1103/PhysRevLett.30.1343


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Proton and Loops as Foundations of Theory of Chaos

This theory leads to the atom-like structure of proton. There is the core and outside it is in

force the Titius-Bode 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 atom-like 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 Mandelbrot-like 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 atom-like 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 Titius-Bode 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

gluon-loopthird-basic-sham-quark 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 Titius-Bode 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 period-doubling 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 period-doubling cascade. The four-neutrino

symmetry leads also to n = 3, 6, 12 period-doubling 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

gluon-photon 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(electron-muon) = 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 electron-positron 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 3-space-dimensional 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


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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 atom-like 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 non-rotating-spin binary

systems of neutrinos with spins tangent to the loops. Entanglement of groups of such sets

composed of the particular loops leads to the Mandelbrot-like set.

Chaos is due to the lack of the initial synchronization with the internal structure of protons

and the four-neutrino 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 electron-positron 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, period-doubling 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 Heinz-Otto,

Richter Peter H., The Beauty of Fractals, p. 151-160, (Berlin: Springer-Verlag, 1986)


104

Theoretical Curve for the Kaon-to-Pion Ratio

Some experimental data leads to the atom-like 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 kaon-to-pion ratio mostly depends on internal helicity of the

electric charge inside pions. Experimental data that concern the kaon-to-pion ratio are

collected on following website [1].

Characteristic values for the kaon-to-pion 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 non-relativistic nucleons αs NN = 14.4. For a very short period of the K and π

production in the nucleon-nucleon collisions, the produced nucleon-antinucleon 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 four-neutrino 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 atom-like 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 atom-like 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 quark-antiquark 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 proton-proton collisions appears the factor g3(±) =

g1(+) + g2(-) = 2 whereas for the proton-antiproton 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 = rpoint-mass/(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 atom-like 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 gluon-ball 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 quark-antiquark pairs and next the muon-antimuon pairs arise in the centre of

the core of baryons as the gluon-ball quadrupoles i.e. as the quadrupoles of pure energy. This

means that such objects are also the non-relativistic 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 neutrino-antineutrino pairs i.e. the weak dipoles carrying spin equal

to 1 so they are the non-relativistic 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 gluon-ball 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(Tlifetime-of -particle/Tlifetime-of-neutron) = (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 gluon-ball pairs carrying energy equal to the mass of the

muon-antimuon 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 gluon-ball 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 time-distance

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 gluon-ball pairs carrying energy equal to the

mass of the W boson-antiboson 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 Tlifetime-W-boson = 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

time-distance 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 time-distance between the fronts of the

neutrino and photon beams. The observed on the Earth the 3-hours 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 low-energy 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 non-relativistic 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 atom-like structure of baryons, there is

the natural broadening in the spectrum of the superluminal speeds of neutrinos. In the

neutrino-speed 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.


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Summary

The calculated neutrino speed for the MINOS experiment is 1.000050(21)c. The maximum

neutrino speed is 1.000071c. The calculated time-distance 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 time-distance

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 atom-like structure of baryons. In MINOS dominated neutrinos from decays

caused by gluon-ball pairs which energy is two times greater than the mass of muon. In

OPERA dominated neutrinos from decays caused by gluon-ball pairs which energy is two

times smaller than the mass of the core of baryons whereas in the supernova SN 1987A


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explosion by gluon-ball 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(beta-decay)/αw(decay-of-muon) = 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 electron-positron 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 [hep-ex].

[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

M-theory

We cannot formulate an useful M-theory 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.

M-theory: My Everlasting Theory is some extension of the useful M-theory. Within the

non-perturbative 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 M-theory i.e. the Titius-Bode 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 bi-dipole 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 half-integral 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 M-theory). 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 fermion-boson 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.

T-duality: 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 nonrotating-spin

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

right-handed, and 8 types of gluons. Due to the four-neutrino 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 four-neutrino symmetry, the next greater object than the 4 different

carriers should contain 4 · 4 = 16 binary systems. But there are the virtual particle-antiparticle

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 non-rotating-spin bi-dipoles 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 bi-dipoles, 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 low-energy limit.

S-duality: 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 fermion-boson 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 electron-positron

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 single-arm lever. Due to the single-arm 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 gluon-photon ‘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 proton-neutron

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 faster-than-light particles (i.e. the tachyons and binary systems of closed strings)

the quantum physics is non-local 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 non-locality of nature.

The first phase transition of the imaginary Newtonian spacetime leads to the closed strings

(spin is half-integral) 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 rotating-spin 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 co-ordinates

ds 2 = dx i dx i (i = 0 (for time co-ordinate), 1, 2, 3). In a non-inertial 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 Einstein-spacetime components are the

non-relativistic 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

Einstein-spacetime components i.e. the neutrino-antineutrino 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 non-rotating-spin 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 left-handed 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 Titius-Bode 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 quark-antiquark 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 Einstein-spacetime 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 Titius-Bode 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 non-rotating-spin

neutrino-antineutrino 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 loop-antiloop

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 neutrino-antineutrino 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

black-hole state.


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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, Non-Abelian 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 left-handed component of electron’s wave

function forms a weak isospin doublet with the electron neutrino. There is also the righthanded

singlet associated with the electron-type 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 left-handed, of positron is right-handed and of electron-antineutrino,

which forms stable structure with electron (see Chapter “Structure of Particles

(continuation)”), is left-handed. This suggests that the electroweak theory describes the

electron antineutrino interacting with electron-positron pair. The electromagnetic binding

energy of an electron-electron-antineutrino 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 right-handed 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 atom-like structure of

baryons and properties of the spacetimes. Physical conversion of massless energy into mass

via some massless-energy condensation is impossible. The inertial-masses/volumes/pieces-ofspace

and their rotational energies are the everlasting attributes of spacetimes.


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Non-Abelian 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 electron-electron pair in the ground state of an atom so the zero-spin 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 gauge-invariant 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: vector-field vector-field + derivatives-ofghost-field.

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 gauge-covariant 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 non-zero-spin 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 electron-positron 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 spin-rotation 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 water-wave. 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: 305-317 (1996)

[2] Walter Weizel, Lehrbuch der Theoretischen Physik; Volume I, 1; Springer-Verlag,

Berlin (1955) or Polish edition, PWN (1958), pp: 348-355, formula (27).


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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 M-theory 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 bi-dipole. 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 non-rotating-spin neutrino bi-dipoles. Gravitons and gravitational

waves are not in existence.

The neutrinos, binary systems of neutrinos, bi-dipoles 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 neutrino-antineutrino pairs from such spacetime

components similarly as the electron-positron 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 particle-antiparticle pairs (bosons). The electron-positron

pair is the superpartner of the electron, the neutrino-antineutrino pair is the superpartner of the

neutrino and so on. There is also the fermion-boson 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 long-distance entanglement require tachyons.

Broken symmetries: Origin of the matter-antimatter 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 non-perturbative 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 hierarchy-mass 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 non-perturbative 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 non-perturbative structure

of the baryons.

Yang-Mills theory in the non-perturbative regime: Yang-Mills theory is a gauge theory

with a non-Abelian symmetry group (given by a Lagrangian) based on the SU(N) group and

QCD is a SU(3) Yang-Mills theory. Yang-Mills theory in the non-perturbative 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

ghost-unphysical-complex-scalar field. In high-energy 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

fermion-antifermion 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 electron-positron pairs whereas

the gluons the quark-antiquark 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 non-perturbative and

perturbative theories? The ground state of the Einstein spacetime consists of the non-rotatingspin

neutrino-antineutrino 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 unitary-spin loop (the loop state) is the binary system

of two entangled half-integral-spin 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 fermion-antifermion pair (the fermion

state). Perturbation theories concern the loop states whereas the non-perturbative theories the

fermion states. In non-perturbative 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

non-perturbative fermion state dominates at low energy whereas the loop state dominates at

high energy. But it is easier to describe the liquid-like plasma within the fermion state. Since

there are the creations from loops and annihilations to loops of the fermion-antifermion pairs

so both states (loop and fermion) are energetically equivalent but the bare-fermion 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 electron-positron pairs and the quarkantiquark

pairs) arise respectively as the photon or gluon loops with spin equal to 1, which

transform into the torus-antitorus 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 neutrino-antineutrino 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 neutrino-antineutrino pairs the Einstein spacetime consists of. Due to the surplus

energy there appear processes described by the 1-loop, 2-loop, 3-loop, 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 non-perturbative theory.

This non-perturbative 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 quark-antiquark 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 fermion-antifermion pairs) begins just after the period of spinning of electron

i.e. after the non-perturbative state. In contrary to the renewable/quantum particles such as

electrons, or quark-antiquark 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 short-distance interactions. This is because then the strong-weak 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 quarks-antiquarks pairs, the perturbative and non-perturbative 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 non-perturbative 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.


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The field associated with the Yang-Mills 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 neutrino-antineutrino 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 low-energy regime. We can see

that my theory shows that the Yang-Mills 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 non-perturbative M-theory that is the essential

part of the Everlasting Theory. The Everlasting Theory shows that there is the atom-like

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 non-perturbative M-theory 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 fermion-antifermion pairs. Due to the creations of the loops from this

energy, there appear the n-loop 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 non-perturbative state is the fundamental complement of the perturbative

state.

For very high energies of collisions, the atom-like 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 nonrotating-spin

binary systems of neutrinos). More precisely, the gravitational constant depends


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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 left-handed and 4 right-handed) 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 mass-energy 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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Titius-Bode law for the strong interactions. Einstein tried to change the mass-energy 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 Yang-Mills 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 short-distance interactions. Exchanged

small loops composed of the binary systems of closed strings are responsible for the

entanglement of particles (for the long-distance entanglement also). Due to the symmetrical

decays of the virtual bosons in the strong field, outside of the core of baryons is obligatory the

Titius-Bode 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 non-perturbative 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 Yang-Mills fields. A torus of the electron is the entangled and specifically

polarized zero-energy photon. The electric charge-anticharge 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/electric-charges. The core of protons and torus of positrons have the

same electric charge but there is place for the sham quark-antiquark pairs. This theory leads to

masses of the quarks and shows that the other properties of the quarks are different. The

Yang-Mills 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 neutrino-antineutrino pairs from such spacetime

components similarly as the electron-positron 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 black-hole 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 neutrino-antineutrino 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 = (2mclosed-string/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 neutrino-antineutrino 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 non-rotating-spin neutrino-antineutrino 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 neutrino-antineutrino 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 – binding-energy, 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 low-energy 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 strong-weak interactions for colliding protons. The

calculations lead to the running coupling for the strong-weak 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

mclosed-string = 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 atom-like 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 non-rotating-spin 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 high-energy collisions the Titius-Bode 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 Titius-Bode 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 four-neutrino

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 long-distance interactions. This suggests that

there are two parallel spacetimes. To explain the inflation, long-distance 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 neutrino-antineutrino

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

Titius-Bode law for the strong interactions and to the Titius-Bode law for the gravitational

black holes. There appears the atom-like 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 black-hole 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 non-perturbative and perturbative theories. The ground

state of the Einstein spacetime consists of the non-rotating-spin neutrino-antineutrino 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 unitary-spin

loop (the loop state) is the binary system of two entangled half-integral-spin 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 fermion-antifermion pair (the fermion

state). Perturbation theories concern the loop states whereas the non-perturbative theories the

fermion states so we cannot neglect the structure of bare fermions.


138

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), non-rotating-spin binary systems of neutrinos

(excited states of the Einstein spacetime are responsible for the electromagnetic, weak and

interactions), and virtual particle-antiparticle 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 Titius-Bode 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 neutrino-antineutrino 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 non-rotating-spin 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 non-rotating-spin 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


139

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 left-handed 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 half-integral. 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 string-antistring 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 string-antistring 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

1-coloured particles).

Cosmic loop: The loop inside the torus of the Protoworld composed of the neutron black

holes.

Cosmic-ray particles: The assumption that the ground state of the Einstein spacetime is the

field composed of the non-rotating-spin 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 ultra-energetic 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 iron-nickel 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 iron-nickel 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 iron-nickel 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 Titius-Bode 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

proton-electron pairs and with each proton-electron 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 superphoton-like 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 six-fold axis of symmetry (3+3=6) typical for the flakes of snow.

Einstein spacetime: The field composed of non-rotating-spin 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 electron-positron 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

electron-positron 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 electron-positron pairs.

Electron: Electric charge of electron arises following the entanglement and polarisation of

the Einstein spacetime components i.e. the neutrino-antineutrino 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 half-turns 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 neutrino-antineutrino 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/bare-electron (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 electron-positron pairs arise near the bare electron.

Elementary photon: It is rotational energy of a neutrino-antineutrino pair. After the period of

inflation, the carriers of photons, i.e. the neutrino-antineutrino 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 long-distance 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 non-rotating-spin 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 iron-nickel 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.

Fine-structure constant: Its value changed in the protuberances in the Einstein spacetime

appearing at the beginning of the ‘soft’ big bang. The fine-structure 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.

Four-neutrino 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.

Gluon-photon transitions: The neutrino-antineutrino 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 bi-dipoles. 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 non-rotating-spin neutrino bi-dipoles.

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 atom-like structure of

baryons, the gluon balls transform into the sham quark-antiquark 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 cross-section 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 vortex-antivortex 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 cross-sections of the spokes whereas

vortex-antivortex 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 non-confining 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 quark-antiquark pairs (the hadronization)

causes that confined quarks due to the spokes become the free quark-antiquark pairs (they are

the mesons or the entangled baryon-antibaryon pairs). Due to the atom-like structure of

baryons, the emitted pairs simulate the known hadrons.

We can see that a hadron jet “observed” by detectors consists of the tube-antitube 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 quark-gluon plasma mostly consists of the cores of baryons, precisely of the core-anticore

pairs. The cores-anticore pairs are tangent so there is very small volume between the pairs in

which the quark-antiquark 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,

long-distance 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 fine-structure 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 Yang-Mills 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

vortex-antivortex 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 vortex-antivortex pairs which spin is

unitary, for example, the fermion-antifermion 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 Yang-Mills 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 tire-like 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 tire-like torus and ball-axis 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 quark-gluon 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 re-organize themselves. It is the hadronization. The quarks

inside baryons can arise only as the quark-antiquark 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 electron-positron pairs into cold charged pion-antipion 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 tetra-black-hole. 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 tetra-black-hole, 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

Titius-Bode 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 neutrino-antineutrino

pairs the Einstein spacetime consists of. The entangled neutrino-antineutrino 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 electron-positron 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 co-ordinates 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 fine-structure

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, spin-polarized

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 blow-hole 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.

Liquid-like plasma: The Everlasting Theory leads to an atom-like 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 liquid-like 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 electron-positron 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 electron-positron 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 multi-systems 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 electron-positron pairs so minds may interact with a

brain or matter electromagnetically.

M-theory: The M-theory contains the fundamental bosonic string theory plus the three

superstring theories for which the fermion-boson 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 zero-energy 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 non-rotating-spin binary systems of neutrinos because they cannot transfer

energy to a detector. Neutrinos are very stable particles – we do not see the bi-products of

neutrino-antineutrino 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 neutrino-antineutrino pairs in a manner similar to, for example, electron-positron pairs. The

new neutrinos are bi-products of the decay of the rotating-spin or non-rotating-spin 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 liquid-like substance. For

interactions lasting longer than about 10 -60 s, the Newtonian spacetime appears as a

continuous medium.

Non-perturbative theories: There are in existence the stable tori, stable core of baryons and

stable states associated with the atom-like 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 non-perturbative and perturbative stadiums are

separated whereas for baryons they are in existence simultaneously. The non-perturbative

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 non-perturbative

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

neutrino-antineutrino 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 short-distance


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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 neutrino-antineutrino 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 Yang-Mills 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

neutrino-antineutrino 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 liquid-like 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 Titius-Bode 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 atom-like 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 non-rotating-spin neutrino-antineutrino 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 iron-nickel 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 protoworld-antiprotoworld pairs from positive

fluctuations of the field composed of non-rotating-spin 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 γ-ray 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 Titius-Bode 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 ä-ray frequencies interacts with

the oscillating electric charges in the plasma so there appear the radio, optical and X-ray

frequencies as well. The exact pulse profile at the ä-ray 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 X-ray 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 3-coloured gluons and six 1-coloured 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 bi-dipoles 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 non-rotating-spin neutrino bi-dipoles. The neutrinos,

binary systems of neutrinos, bi-dipoles 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 bi-dipoles 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

neutrino-antineutrino pairs behaved similarly as the electron-positron 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 non-perturbative 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/electric-charge 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 non-Abelian 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 non-perturbative 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/gravitational-fields 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 neutrino-antineutrino 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: Half-integral 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 half-integral 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 gluon-photon 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 liquid-like plasma producing the quanta that have energy equal to approximately 283 MeV.

This energy corresponds to the lower limit of temperature of the liquid-like 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 pion-antipion 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 left-handed double helix loop that is composed of 2·4 32

entangled photons (there are 2·4 16 photon galaxies i.e. about 4 billion photon-galaxy pairs).

Each helix loop is composed of 256 megachains. Antisuperphoton is right-handed 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 gas-like

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 Michelson-Morley

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 neutrino-antineutrino 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 non-rotating-spin neutrino bi-dipoles.

Titius-Bode 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 non-perturbative 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 long-distance 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 closed-strings/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 Titius-Bode 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 non-perturbative and

perturbative theories? The ground state of the Einstein spacetime consists of the non-rotatingspin

neutrino-antineutrino 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 unitary-spin loop (the loop state) is the binary system

of two entangled half-integral-spin 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 fermion-antifermion pair (the fermion

state). Perturbation theories concern the loop states whereas the non-perturbative theories the

fermion states. In non-perturbative 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

non-perturbative fermion state dominates at low energy whereas the loop state dominates at

high energy. But it is easier to describe the liquid-like plasma within the fermion state. Since

there are the creations from loops and annihilations to loops of the fermion-antifermion pairs

so both states (loop and fermion) are energetically equivalent but the bare-fermion 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 one-loop 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 energy-spectrum, there

must appear the higher orders containing 2 entangled loops, 3 entangled loops, 4-loops 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.

Universe-antiuniverse pairs: Similarly as particles, also universes arise as the universeantiuniverse

pairs. The baryon-antibaryon symmetry was broken already before the ‘soft’ big

bang (i.e. after the period of inflation). In Einstein spacetime (its ground state consists of nonrotating-spin

binary systems of neutrinos) arise the left- and right-handed vortices as the

vortex-antivortex pairs. The Protoworld associated with our Universe was left-handed. Such

internal helicity have neutrons, therefore, in the left-handed 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 black-hole 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 non-rotating-spin 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 particle-antiparticle 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 electron-positron

pair.

Weak dipoles: These are binary systems of neutrinos i.e. the neutrino-antineutrino 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 short-distance weak interactions.

The mass responsible for the weak interactions of baryons in the low-energy 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.

Yang-Mills existence: The confinement, mass-gaps and asymptotic freedom described within

the Everlasting Theory are the foundations of the Yang-Mills 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,


160

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 long-distance 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 non-perturbative 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 zero-energy photon- and gluon-fields 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 zero-energy

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 not-rotating-spin 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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