The Everlasting Theory and Special Number Theory

ISBN 978-83-933105-0-0

1 Copyright © 2011 by Sylwester Kornowski All rights reserved ISBN 978-83-933105-0-0

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 1 Experimental Data and Program of Ultimate Theory 2 Phase Transitions of Newtonian Spacetime, Neutrinos, Nucleons, Electrons, Pions and Muons 3 Interactions 4 Structure of Particles (continuation) 5 Liquid-like Plasma 6 New Cosmology 7 Four-shell Model of Atomic Nucleus 8 Mathematical Constants 9 Fractal Field 10 New Big Bang Theory 11 New Quantum Chromodynamics 12 Proton and Loops as Foundations of Theory of Chaos Recapitulation Definitions

2 3 10 26 43 53 55 72 78 82 86 89 94 99 101

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Abstract The non-perturbative Everlasting Theory shows that the Yang-Mills theory has a mass gap and describes its origin. It leads to the strong coupling for lower energies too and there is the proof that QCD ‘confines’ at low energy. My theory shows that the physical properties of the Newtonian spacetime lead to the initial conditions applied in the Einstein theories of relativity and quantum physics. My theory begins from gas composed of structureless tachyons having a positive mass – known as the Newtonian spacetime. The simple selection rule leads to four phase transitions of this spacetime. As a result of these phase transitions, there subsequently appear four stable objects: closed strings, neutrinos, cores of baryons and objects before the big bangs suited to life. On the surface of it, the last three objects appear similar to the Ketterle surface for strongly interacting gas. On a higher level of nature a field composed of non-rotating binary systems of neutrinos appears. This field is known as the Einstein spacetime. In Einstein’s spacetime quantum effects and fractal objects appear. The mass density of this field leads to the mass of electrons. Outside of the core of a baryon is the obligatory Titius-Bode law for strong interactions. This model leads to the atom-like structure of baryons and to a liquid-like substance when nucleons which have a high energy collide. Within new Quantum Chromodynamics (there appear the eight gluons and six basic sham quarks) 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 set. In applying only seven parameters, I have obtained several hundred theoretical results which are consistent with experimental data. The Newtonian spacetime theory leads to all the physical and mathematical constants applied to in physics.

How can we verify my theory? My theory identifies where mainstream theories are inconsistent with experimental data: 1. There is an asymptote for the running coupling for strong interactions of the colliding nucleons – the value of it equals 0.1139. This is inconsistent with the asymptotic freedom for energies which are higher than a few hundred GeV and the curve for energy ends at approximately 18 TeV – this is due to the internal structure of the cores of baryons. 2. Due to internal helicity, the closed strings the neutrinos consist of produce the gravitational fields because they transform the chaotic motions of the tachyons into divergently moving tachyons. Due to direct collisions of tachyons, the gradient in the Newtonian spacetime (i.e. on the scalar field) appears. This gradient is impressed on the Einstein spacetime (i.e. on the vector field). These two spacetimes (i.e. the scalar and vector fields) lead to the tensor field appearing in the Einstein equations. Higgs bosons do not exist. Photons and gluons are the excitations of the Einstein spacetime. 3. The Yang-Mills theory is correct whereas the quark theory is correct only partially. This causes that we cannot calculate the exact masses of the up and down quarks. 4. My theory of the Universe concludes that the protogalaxies were in existence already before the big bang suited to life (see Chapter titled ‘New Big Bang Theory’). The baryon-antibaryon symmetry was broken before the big bang suited to life.

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Experimental Data and Program of Ultimate Theory

The diagram entitled ‘Main ideas’, shows the main structure of the everlasting/ultimate 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 negative result of the Michelson-Morley experiment suggests that there is in existence the Newtonian spacetime composed of tachyons moving with speeds much higher than the speed of light c in the Einstein spacetime (my theory shows that tachyons are moving with speeds about 8·1088 times higher than the c). Even for a mass moving with speed almost equal to the c the lines of gravitational forces are straight in our Universe and have the same angular speed as the mass. The wave function describing a quantum particle is a coherent mathematical object only if distant points of it can quickly communicate. This means that coherent quantum physics needs particles moving with superluminal speeds i.e. tachyons. Entangled particles separated spatially also need superluminal particles. The symmetry of the energy equation applied in the Special Theory of Relativity leads to tachyons with real masses. The Everlasting Theory starts with three assumptions: 1. That there exists the Newtonian spacetime which 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 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.

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The ground state of the Einstein spacetime consists of non-rotating binary systems of neutrinos. To detect the non-rotating 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 mass density of Newtonian and Einstein spacetimes. In the Einstein’s spacetime, the virtual particleantiparticle pairs can arise. Photons are the rotational energies of the Einstein spacetime components. The c=299,792,458 m/s is the natural speed of the binary systems of neutrinos in the Newtonian spacetime ‘attached’ to a mass. Due to the Newtonian spacetime, the photons can also behave as quantum particles i.e. their energy can disappear in one place of Einstein’s spacetime and appear in another and so on. The binary systems of binary systems of neutrinos (quadruples) with parallel spins carry the gravitons. It can transform into two loops and then into binary system of electron-positron pairs. Annihilations of the electron-positron quadruples create fluxes in the Einstein spacetime. We can see that the gravitational energy is emitted via the electromagnetic phenomena. We can say that quantum electromagnetism destroys the quantum gravity. Similar phenomena concern the quadruples composed of the closed strings and neutrinos and were possible at the beginning of inflation. 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. Gradient produced in Newtonian spacetime by neutrinos produces a gradient which also exists in the Einstein spacetime. The gravitational constant depends on the internal structure of neutrinos and inertial mass density of the Newtonian spacetime. Nature begins from classical objects whereas the quantum physics approach on the higher levels of nature. The phase transitions of the Newtonian spacetime show that cosmology should begin from different initial conditions than the Cosmological Standard Model.

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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 [2] 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 [3] and -1.91 for a neutron [4]. 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 charged pion is W(charged)~216 MeV. Such values of the probabilities and masses leads to the experimental data for magnetic moments. 3. During the extreme energetic collisions of ions a liquid-like substance appears [5]. 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. 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. 6. Observed entangled particles separated spatially need superluminal particles. 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 big bang suited to life. 9. We are unable to see the bi-products of a neutrino-antineutrino annihilation. This suggests that neutrinos are very stable particles and also suggests that the oscillation of neutrinos is impossible. 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.

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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 depends on their internal structures. Various theories suggest that these internal structures are neglected or are difficult understand. As a result, there appear strange properties of the fields and postulated particles to obtain theoretical results consistent with experimental data. We can 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. The new electroweak theory is non-perturbative. The higher dimensions and flexible strings are consequently not necessary because we can replace them for enlarged 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. The non-perturbative everlasting/ultimate 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 mass of the source(s) of interactions being in touch plus the mass of the component of the field whereas the m is the mass of the carrier of the interaction. The constants of interactions G(i) are directly proportionate 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 4.2·1042. 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 photons without mass and gluons violate the hierarchy of interactions, however, photons are responsible for electromagnetic interactions because they produce real and virtual electronpositron pairs having mass. I believe that loops having a mass are responsible for strong interactions whereas virtual electron-positron pairs, also having mass, are responsible for electromagnetic interactions. Scientists and theorists do not fully understand Einstein’s formula E=mc2 and that the origin of energy and mass is significantly different. This formula follows from the law of conservation of spin and constancy of the natural speed of the binary systems of neutrinos in the Newtonian spacetime ‘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 produce the electron-positron pairs i.e. they cannot carry the electromagnetic interactions. 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 Einstein’s spacetime there appears a loop or a particle accelerates, there appears a phenomena (i.e. there decreases local pressure in this spacetime) which increases the mass density of the Einstein spacetime inside a particle. 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. The Higgs bosons do not exist.

7 Can the baryons have an atom-like structure? The definition of the Planck length l=(Gh/(2πc3))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 as fermion-antifermion pairs. 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. We see that supersymmetry is not associated with new particles i.e. with s-particles and the –inos which do not exist. Supersymmetry is associated with the production of fermions via fermionantifermion pairs i.e. via bosons. This is the reason why fields carrying forces are composed of bosons.

Yang-Mills theory in the non-perturbative regime and the ultimate equation How should look the fundamental equations leading to the ultimate theory? The gravity is associated with the Newtonian spacetime (the gas composed of tachyons) and with the Einstein spacetime (the gas composed of the non-rotating binary systems of neutrinos). More precisely, the gravitational constant depends 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 imprint 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 speed. 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. When we accelerate a nucleon then the mass of the loops decreases so the running coupling also. There is asymptote for high energies equal to 0.1139. Range of the gluonic loops is equal to the circumference of loop, i.e. 2.915 fm, and such is origin of the ‘confinement’ of the gluonic 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 gluonic 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 2.915 fm from centre

8 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 is 424.124 MeV. This thickened Einstein spacetime is responsible for the weak interactions of the baryons. We see that the four interactions 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 closed strings and the 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 objects before the soft big bangs suited to life. Outside the core of baryons is obligatory the TitiusBode 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. So once more: The ultimate equation describing nature is the generalized Einstein equation applied in the General Relativity. The enlarged Riemann metrics includes the gravity and the Yang-Mills field which leads to the photons, gluons and the regions with thickened Einstein spacetime (such object has mass because the Einstein spacetime has mass density not equal to zero) responsible for the weak interactions of baryons. On surface of the torus of neutrinos arise the small loops composed of binary systems of closed strings. The weak interactions between the thickened regions of the Einstein spacetime are possible when their surfaces are in distance equal to the circumference of the small loops. We can see that the weak field practically overlaps with the thickened regions. This means that the weak interactions, due to the range of the small loops, are the short-distance interactions. Exchanged opened small loops are responsible for the entanglement of particles (for the long-distance entanglement also). The mass-energy part in the Einstein equations is dual for the bare mass of neutrinos, cores of baryons and the object before the soft big bang suited to life. 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 YangMills field. 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. Is there place for the quarks? See the chapter titled New Quantum Chromodynamics. This theory leads to masses of the four heaviest quarks only and shows that the other properties 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, we cannot calculate exact rest masses of the up and down quarks. I will not write the ultimate equation since the duality of the bare masses of different particles, the Titius-Bode law for the strong interactions and the different methods of calculation of the radiation masses cause that the mass-energy part in the Einstein equation looks not the same for different objects. The Everlasting Theory shows how we can write it.

9 Whereas the Riemann metric for the Yang-Mills field and gravity we can find in many books and papers. The non-perturbative Everlasting Theory shows that the Yang-Mills theory has a mass gap and describes its origin. It leads to the strong coupling for lower energies too and there is the proof that QCD ‘confines’ at low energy.

Summary 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 of 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 new QCD and theory of chaos. References [1] W.-M. Yao et al.; Particle Data Groups: 2006 Review of Particle Physics - Lambda; J. Phys. G 33, 1 (2006). [2] W.-M. Yao et al.; Particle Data Groups: 2006 Review of Particle Physics – Sigma+; J. Phys. G 33, 1 (2006). [3] H. S. Boyne, and P. A. Franken; Magnetic Moment of the Proton in Units of the Nuclear Magneton; Phys. Rev. 123(1), 242-254 (1961). [4] G. L. Greene, N. F. Ramsey, W. Mampe, J. M. Pendlebury, K. Smith, W. D. Dress, P. D. Miller, and P. Perrin; A New Measurement of the Magnetic Moment of the Neutron; Phys. Lett. B 71(2), 297-300 (1977). [5] J Stachel; Has the Quark-Gluon Plasma been seen?; http://arxiv.org/abs/nuclex/0510077 (2005).

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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 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 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 CODATA. The calculated values of the new parameters are as follows: Gravitational constant: G = 6.6740007·10-11 m3/(kg s2) Half-integral spin: h/2= 1.054571548·10-34/2 Js Speed of light in spacetimes: c = 2.99792458·108 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 Mass of charged pion: mpion(+-) = 139.57041 MeV.

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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=8.32192436·1085 kg/m3. 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 is not always possible. The closed strings are inflexible. We can now calculate the number of tachyons K2 a closed string consists of as follows: K2 = 2πr1/(2rt) = (0.7896685548·1010)2. (3) The spin of each closed string is half-integral spin = K2mtvtr1 = h/2 = (1.054571548·10-34/2) Js. (4)

12 We see that a closed string is composed of K2 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 K2, K4, K8, K16 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: K0, K2, K6, and K14 and means that the mass of the stable objects are directly proportional to K2(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 big bangs suited to life. 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 = r1Kd-1. (5) The rest mass of the tori of the stable objects are md = m1 K2(d-1), (6) where m1 is for the closed string.

We know that the surface of a torus can be calculated using the following equation: (x2 + y2 + z2 - a2 - b2)2 = 4b2(a2 - z2). (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 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

13 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 objects before the big bangs suited to life 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 [1]. The tori consists 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 objects before the big bang suited to life 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 (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 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

14 law of conservation of energy, the half-turns 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 the objects before the big bangs suited to life. 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 objects before the big bangs suited to life 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 binary systems of neutrinos in the gas-like Newtonian and Einstein spacetimes c = 3h/(4m4r4) = 3h/(4mtr1K11) = 299792458 m/s, (10) where mass of torus in core of baryons is m4=318.295537 MeV whereas radius of equator of torus in core of baryons is A=3r4/2=0.69744247 fm. 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 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 m3/(kg s2), (11) where the g has the same value for all interactions and is equal to g = vst4/η2 = 25,224.563 m6/(kg2 s2). (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

15 discussion below formula (51)). This leads to conclusion that the masses of neutrinos, cores of baryons and objects before the big bangs suited to life 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) = 8.50712236·1038. (13) Mean distance L1 of binary systems of neutrinos on surface of torus in core of a baryon is L1 = (8π2A2/(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 ke2/(hc) = Gemmelectron2/(hc), (19) 2 7 where k=c /10 whereas Gem=GρE/ρN=2.78025274·1032 m3/(kg s2). From formula (19), we can calculate the electric charge e of electron e = melectron(GρE107/ρN)1/2/c = 1.60217642·10-19 C, (20) and next the fine-structure constant αem = e2c/(107h) = 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 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 below 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.

16 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 memc2 = ke2/C, (24) where k=c2/107, the C is the Compton wavelength of particle. The Compton wavelength of electrically charged particle is C = 2h/(cm). (25) Then from (24) and (25) we obtain mem = Cm, (26) 2  where C=e 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. Mean mass of a field composed of virtual particles cannot be greater than sum of emitted binding energy and mass of bare real particle producing the virtual particles.

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) looks similar for the strong field as the

17 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. 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 - vd2/c2 )1/2. (30) We know that the square of the speed is inversely proportional to the radius Rd (for d=1 is v2d=1=c2 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 range 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) 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)

18 Since there is the positroncore-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 protonneutron 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 3ke2/(2Ac2)=3.097 MeV. If we subtract the mass of electron we obtain Eb1=2.586 MeV. The weak binding energy of the E b1 interacting with the core of baryon is E b2=3GwEb1·mH(+)/(2Ac2)=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 1 2 4

727.440123 423.043 298.243 187.573

724.776800 421.494 297.151 186.886

215.760 181.704 162.013

208.643 175.709 156.668

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 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 Ho 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)

19 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 Ho, resting neutral pion and Zo. 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 Zo (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 = e2[y2 + (1 - y)2]/2 = 0.25e2 (quark model gives 0.33e2) (44) The mean square charge for the neutron is = e2[x2 + (-x)2]/(2x + 3(1 - x)) = 0.33e2 (quark model gives 0.22e2), (45) where [2x+3(1-x)] defines the mean number of particles in the neutron. The mean square charge for the nucleon is = [ + ]/2 = 0.29e2 (quark model gives 0.28e2). (46) 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)e2). We see that it is true.

Is there place for the quarks? See the chapter titled New 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

20 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) = mvd2rd/(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 2 times bigger than the external radius of its torus so this radius is much smaller than the radius of the point mass of a proton. Because v2=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 = c2rp/Y = 1.0354864·1027 m3s-2kg-1. (50) The coupling constant for weak interactions of protons w(proton) can be calculated using the formula-definition w(proton) = GwY2/(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 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 arises the virtual H+,- particles and the particles having masses equal to the distance of masses between charged and neutral pions. They arise as 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 is equal to the sum of the mass of these three virtual particles multiplied by the mass of the point mass and the Gw and divided by 2A/3 this leads to 14.980 MeV and to the mass of the charged core of baryons which 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)).

21 From (50) for a point mass Mp we have GwMp = rpc2, (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 c2=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 object before the big bang suited to life. 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 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

22 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 = mic2. (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 of the electromagnetic mass in the bare mass of the electron, whereas 1- denotes the mass fraction of the weak mass in the bare mass of the electron. 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) 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)

23

Summary 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. 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 theory based on the four phase transitions of the gas-like Newtonian spacetime, described by the new dimensionless constant K, and the Titius-Bode law for the strong interactions provides very good results. S-particles, other –inos, Higgs bosons, and tau neutrinos are not in existence. The ultimate theory contains only seven parameters. Two of them, 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 object before the big bang suited to life must have strictly determined the mass of the object-before-big-bang-suited-to-lifeneutrino transition was possible. Because universes arise as the universe-antiuniverse pairs then the distance between the constituents of a pair must be sufficiently distant.

24

Table 2 Theoretical results Physical quantity Gravitational constant Half-integral spin Speed of light Electric charge Mass of electron Fine-structure constant for low energies Mass of bound neutral pion Mass of free neutral pion Mass of charged pion Radius of closed string Linear speed of closed string Mass of closed string External radius of neutrino Mass of neutrino Mass of object before the big bang suited to life External radius of object before the big bang suited to life Mass of the Universe Radius of the early Universe loop External radius of torus of nucleon Constant K Binding energy of two large loops *E-15=10-15

Theoretical value* 6.6740007 E-11 m3/(kg s2) (1.054571548 E-34)/2 Js 2.99792458 E+8 m/s 1.60217642 E-19 C 0.510998906 MeV 1/137.036001 134.96608 MeV 134.97674 MeV 139.57041 MeV 0.94424045 E-45 m 0.7269253 E+68 m/s 2.3400784 E-87 kg 1.1184555 E-35 m 3.3349306 E-67 kg 1.961 E+52 kg 287 million light-years 1.821 E+51 kg 191 million light-years 0.697442473 fm 0.7896685548 E+10 0.12273989 MeV

25

Table 2a Theoretical results Physical quantity Mass of large loop Mass of torus of core of baryons Point mass of the nucleon Range of weak interactions of the proton Weak binding energy of core of baryons Mass of charged core of baryons Ratio of mass of core of baryons to mass of large loop Mass of electron to mass of bare electron Mass of bound muon Mass of free muon The A/B in the Titius-Bode law for strong interactions Mass of proton Mass of neutron Proton magnetic moment in nuclear magneton Neutron magnetic moment in nuclear magneton Radius of last tunnel for strong interactions Mean square charge for nucleon Mean square charge for proton Mean square charge for neutron External radius of torus of electron Range of weak interactions of electron Weak constant Electromagnetic constant for electrons Coupling constant for weak interactions of the proton Coupling constant for the electron-proton weak interaction Coupling constant for the electron-muon weak interaction Coupling constant for strong-weak interactions inside the baryons

Theoretical value 67.5444107 MeV 318.295537 MeV 424.124493 MeV 8.710945 E-18 m 14.980 MeV 727.440123 MeV 10.769805 1.0011596521735 105.666974 MeV 105.656314 MeV 1.38977193 938.2725 MeV 939.5378 MeV +2.79360 -1.91343 2.7048 fm 0.29 0.25 0.33 386.607 fm 0.7354103 E-18 m 1.0354864E+27 m3/(kg s2) 2.7802527E+32 m3/(kg s2) 0.0187228615 1.11943581 E-5 0.9511082 E-6 d=0: 0.993813 d=1: 0.762594 d=2: 0.640304

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).

26

Interactions Here I show mathematical and physical relations between different interactions.

Types of interactions and phase spaces Table 3 Interactions Name of source Tachyons Closed string Neutrino

Core of baryon

Stable object before the big bang suited to life

St at es 1

What produces gradients in fields?

Fundamental (eternal direct collisions) Tachyon jet

2 4

2

2

Name of interaction

Divergently moving tachyon jets; they produce the gradients in the Newtonian spacetime

Gravitational (due to the Newtonian spacetime, it is the long-distance interaction)

Exchanged regions filled with additional binary systems of neutrinos; for example, when distance of a neutrino from surface of the point mass of an electron is smaller than circumference of the equator of the neutrino then the neutrino can transform into the point mass of the electron; the not entangled rotating binary systems of closed strings and binary systems of neutrinos move in such way that resistances to motions during a period of rotation do not change and are lowest – this leads to the transverse waves only 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); the exchanged opened neutrino loops cause that photons and electrons behave as the quantum particles

Weak (due to the circumferences of the loops composed of the binary systems of closed strings produced by neutrinos (the small loops), it is the shortdistance interaction); the short-distance exchanges of the loops lead to the longdistance entanglement Electromagnetic (due to the Einstein spacetime, it is the long-distance interaction)

Exchanged volumes filled with additional binary systems of neutrinos

Weak

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 and photons are the Feynman partons; the three internal helicities of a carrier of gluons cause that the gluons are the threecoloured particles; due to the internal helicities of the core of baryons and the particles produced inside it, we cannot neglect the internal structure of the carriers of gluons and photons in the strong fields Divergently moving tachyon jets

Strong (due to the circumference of the large loop, it is the short-distance interaction) Range=2.92·10-15 m

Gravitational

27

Table 4 Phase spaces Stable object Tachyon Closed string Closed string-antistring pair Neutrino Neutrino-antineutrino pair

Co-ordinates and quantities needed to describe position, shape and motions 6 (5 + time) 10 (9 + time) 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 Object before the big bang suited to life 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 i.e. it is the ideal gas), 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 vector 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.

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 is composed 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 πrt2. (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 = πrt2 ρtsvt2/2. (74) Next, compare the obtained centripetal force with the centrifugal force Fcft acting on the tachyons that a closed string is composed of Fcft = mtvt2/r1. (75) For both forces we obtain about 2.2·10133 N. It means that closed strings are stable particles.

28

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. Then for the two strongly interacting neutral pions is S = GS(2mpion(0))(mpion(0)/2)/(ch) = v/c = 1, (77) where v denotes the spin speed of the large loop. Then the constant of the strong interactions is GS=5.46147·1029 m3s-2kg-1. Coupling constant for two strongly interacting protons, for low energies, is Spp = 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 TitiusBode 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 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 strong-weak interactions for colliding nucleons. This means that the running constant of the strong-weak 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

29 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 – v2/c2)1/2, (81) where v denotes the relativistic speed of the nucleon. 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 the colliding nucleons 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 protons is Msw = 2mproton + mpion(o)β/2 + X·\integer-of\{(1/β - 1)mproton/mH(+)}. (82) 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 = auβ2 + buβ + cu, (83) au = 0.0187229 = αw(proton), bu = 0.4067, cu = 0.1139.

30 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 of proton 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. 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 = alβ2 + blβ + cl, (86) al = 0.01872, bl = 0.3184, cl = cu = 0.1139. We can see that there is an asymptote for αsw=0.1139. This means that there is asymptotic compression 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 compression leads to liquid-like plasma and is consistent with experimental data. It proves that baryons do not consist of point quarks. This asymptotic compression 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 energy of proton decay (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=1.9·104 times i.e. for energy about 18 TeV. Above this energy, the proton loses the surplus energy.

31 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 xm=9.0104369 times greater than the mass of the electron-positron pair (see discussion below formula (23)). From formula αem=Gemm2 electron/ch, we obtain that at the high-energy collisions of nucleons the coupling constant for the electromagnetic interactions of the contracted electrons is xm2=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(xm2 + 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 1082 times – see (11) and (73)). Since torus of neutrino produces about 6·1019 divergent tachyon jets then for distances greater than about 10-34 m (this distance is about 5 times greater than the size of neutrino), the gravitational constant is constant. Due to the density of the Newtonian spacetime and tremendous pressure (about 10180 Pa), the neutrino stretches the gravitational field to distance 2·1036 m. 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 can 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 graviton is 2. Quantum gravity looks similarly as the electromagnetism. We know that photons (spin is 1) create the loops (spin is 1) in the Einstein spacetime which transform into the electron-positron pairs (spin of electron is 1/2). In the annihilations of the pairs are produced the virtual or real jets in the Einstein spacetime increasing or decreasing its mean mass density. The gravitons (spin is 2) in spacetime composed of gravitons create the loops (spin is 2) which transform into the binary systems of electron-positron pairs (quadruples) (spin of electron is 1/2). We can say that inside the today Universe the quantum electromagnetism destroys the quantum gravity gravitational energy is emitted via the electromagnetic processes. The neutrinos, binary systems of neutrinos, quadruples of neutrinos, and so on, produce the gradients in the Newtonian spacetime which is imprinted 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 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 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.

32 Fine-structure constant for quasars Due to the internal helicity of the object before the big bang suited to life and the cosmic loop (see the 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 having 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 big bang suited to life. 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 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 of 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 big bang suited to life. 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  T4. (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. 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/m4. (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)

33 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 = 2.4·1012, (92) -12 where the lifetime of tau is tw(tau)=1.9·10 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 = 2.4·10-6 s. (93) 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)) = 1.2·10-10 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 = 937 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. Because of the weak mass of the large loop we can calculate using the formula mLL(weak)=mLL·w(proton)=1.26462 MeV 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 is also 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 x2 neutrinos. 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 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 neutral pions. These pions 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 432 other typical black holes because at most such a number of the neutrinos, having weak charges, contain a virtual pion created inside the neutron. In fact, the early Universe contained twice as many such

34 typical black holes because the neutrons have two different states. Therefore, in our early Universe there were around 3.69·1019 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 1.821·1051 kg. Such mass has the baryonic matter (visible and dark) in our Universe. The typical early massive galaxy, which I call the protogalaxy, contained 416 typical black holes. There were 2·416 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 fourneutrino symmetry. This symmetry is obligatory for also following a sequence of numbers: 64 (for example a meson built of four groups, each group built of four pions and each pion built of 4 neutrinos), 642, 644, etc. Such associations are a 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 photons) similarly as our early Universe decayed to the massive galaxies. Each such object decayed to the 2·416 photon galaxies. It leads to 300 million photons in cubic meter in our Universe (see Chapter titled ‘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)/21/2 (see formula (183)). The radius of such a black hole is rbh and the mass mbh which satisfies the following formula: rbh = Gmbh/c2. (99) If N1 denotes the number of neutrons in such black hole then 4rbh3/3 = N1ac3, (100) and mbh = N1 mneutron. (101) Solving the set of formulae (99)-(101) we get N1=2.946·1058, mbh=4.935·1031 kg i.e. about 25 masses of the sun, rbh=3.664·104 m i.e. about 37 km. On the other hand the four-neutrino symmetry follows that the early Universe contained 2·432 gravitational neutron black holes. This means that the baryonic mass of the Universe is 1.821·1051 kg. The baryonic mass in our Universe should be K8 times greater than the rest mass of the large loop (mLL=67.5444 MeV), which means that is satisfied using the following: mLL K8 = 2·432N1mneutron. (102) The question as to why the value of the dark energy mass density calculated within the quantum theory is approximately 10120 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 mneutrinov2 plus the rest energy mneutrinoc2 is equal to the calculated rest mass of the object before the big bang suited to life (which is equal to the msc2 where ms=1.961·1052 kg). This means that there is a possibility of the object-before-big-bang-suited-to-lifeneutrino transition which is the reason why our Universe exited from a black hole state. It also means

35 that the measured energy of a non-rotating neutrino should be K12=0.59·10119 times smaller than the energy (not mass) frozen inside the neutrino. The object-before-big-bang-suited-tolifeneutrino 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 2K9c/3 i.e. 8·1088 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 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=mc2 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 causes 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 half-integral. 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: nv2(spin) + nv2(relativistic) = nc2, (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)

36 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 - v2/c2)1/2. (105) Due to the fact that relativistic mass is directly proportional to the n and 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 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 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. 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) when distance between falling protons and the resting tori is less than the sum of the range of the strong interactions and radius of the large loop 2A/3. 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 - which 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

37 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 appears 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 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)

38

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 the figures titled ‘The uncertainty principle for state lifetime’ and ‘The uncertainty principle for vanishing’) depends on the spins of the objects a field is composed of. For photons, 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. Electrons observed today were created during the era when for the first time the symmetry of field was broken - this is described in more detail below. I only emphasize that there were three different types of broken symmetry in the history of the Universe. In the strong field binary systems of the large loops i.e. the pions can also appear. 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

39 number of the entangled photons a photon consists of. A photon behaves as follows: the ‘i’ entangled 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 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 photons. There are two different times for the renewable/quantum particles. A renewable particle can arise as an energy loop. The lifetime of such a loop is equal to the period of spinning (which I will refer to as the state-lifetime). After the state-lifetime, the loop collapses to the centre of it and the time of such a process is the time of the vanishing of the loop. We see that the statelifetime of a renewable particle is associated with the length of the circumference of the loop whereas the time of vanishing is associated with the radius of the loop. This means that the state-lifetime is 2π times longer than the time of vanishing. The length of a wave is associated with the time of vanishing 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’. There are two different lifetimes for a photon. 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 decays to non-entangled photons composed of entangled photons i.e. the ‘i’ changes value. A photon, after its lifetime, decays to more photons containing less entangled 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 the ‘i’ entangled photons a photon consists of. After the state-lifetime resulting from the sum of the frequencies of the entangled photons, the distribution of the entangled 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=2·432 entangled photons. Such photons, after its lifetime, decay into photons each composed of less number of entangled photons, for example, to the photon galaxies (i=416), 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 2·416 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 which 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 which 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 positron-

40 proton 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object-before-big-bang-suited-to-life 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 four-neutrino symmetry and the entangled neutrinos, the protogalaxies already grouped in larger structures already before the big bang suited to life. Furthermore, because the internal energy of a neutrino is equal to the mass of the object before the big bang suited to life, one day, there was the object-before-big-bang-suited-to-lifeneutrino transition. The released dark energy in such transition caused the expansion of the early Universe (i.e. of the cosmic loop). There appears 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 electron-proton asymmetry and because the Einstein spacetime contains more the electron-antineutrinos than other neutrinos.

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 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 4·1050 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.

41

Table 5 Theoretical results Physical quantity Centripetal force acting on the closed string Lifetime of the proton Lifetime of the neutron Lifetime of the muon Lifetime of the tau Lifetime of the hyperon Lifetime of the charm baryon c+(2260) Lifetime of the neutral pion Lifetime of the charged pion Coupling constant for strong interactions of the non-relativistic protons Coupling constant for strong interactions of the pions Maximum change of the fine-structure constant *2.2 E+133=2.2·10133

Theoretical value 2.2 E+133 N Stable 937 s 2.4 E-6 s 1.9 E-12 s 1.2 E-10 s 6.5 E-13 s 0.79 E-16 s 2.8 E-8 s 14.4038 1 ±6.2 E-5

Table 6 Theoretical results Physical quantity Mass of a typical neutron black hole Radius of a typical neutron black hole Total mass of the dark energy Mass of the baryonic matter Ratio of the hidden dark energy to mass of the neutrino 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) p-p total cross section for kinetic energy about 15 MeV p-p total cross section for kinetic energies approximately a few hundred MeV p-p total cross section for kinetic energies approximately a few rest mass of protons N-N total cross section for kinetic energies approximately a few rest mass of proton for antiparallel beams p-n total cross section for kinetic energy approximately 15 MeV p-n total cross section for kinetic energies approximately a few rest mass of the proton Π-p total cross section for very high energies Significant reduction of the cross sections for negative pion-proton scattering

Theoretical value ~ 25 masses of the sun ~ 37 km 1.961 E+52 kg 1.821 E+51 kg 0.59 E+119 10.769805

368 mb 27 mb 42 mb 61 mb 671 mb 42 mb 27 mb 423 MeV 727 MeV

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Table 7 Values of the G(i) Interaction Strong Weak Electromagnetic interaction of electrons Gravitational

Relative value of the G(i) 1 (for GS=5.46147·1029 m3s-2kg-1) 1.9·10-3 5.1·102 (it is not a mistake) 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

43

Structure of Particles (continuation) Introduction Previeously, 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. The s-particles are the particle-antiparticle pairs. The Higgs bosons are not in existence. Photons are the quanta carried by the field composed of the binary systems of neutrinos. Using the Compton length of an electron, we can calculate the time it takes to vanish whereas the state-lifetime of an electron is 2π times longer. Slowly moving electrons have state-lifetimes about 10-20 s. This means that within one second an electron appears in 1020 places of the Einstein spacetime. This leads to the wave function. Electrons, when going through a set of slits (an electron only appears whereas the wave function is ongoing), appear 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 string, a neutrino, the core of a baryon and an object before the big bang suited to life) from the mvr. The renewable particles 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 both loops in a binary system have the same direction and senses of the spins then rotating spin create only one divergent spin field – it breaks the symmetry of the Einstein spacetime. It enforces an immediate transition (possible because the Newtonian spacetime is composed of tachyons moving at a speed approximately 8·1088 times greater than the light in spacetime) of the two entangled loops into the electronpositron pair. The Compton length of an electron is the radius of the loop. Two tori are associated with the entangled loops (which are the polarized Einstein spacetime). 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. 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 half-turns of the exchanged binary systems of neutrinos increase their energies in such a way that the electron always has a half-integral spin. Only the creation of the torus-antitorus pair does not break the symmetry because the spins of which the binary systems of neutrinos that the tori are composed of are perpendicular to the surfaces of the tori. All spins 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. 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 electron-positron pairs. Certain parts of an entangled photon can be outside the occupied states of an atom. Muons consist of a contracted electron and the two different energetic neutrinos which interact with the point mass of the electron. The point mass of the electron cannot be a stable

44 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 an electron. Mesons, meanwhile, are binary systems of large loops which are created inside the torus of baryons. They can also be mesonic nuclei which 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 which 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, and vice versa. 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 the pion in a strongly interacting field looks analogically as an 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 interactions with the field they do not look the same. The T-B tunnels/orbits inside baryons 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, 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.

45 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 Ko 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 which 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 KoL kaons should live approximately 527 times longer than the KoS. Earlier in this paper I calculated the lifetimes of pions.

46 The mass of W+- and Zo bosons There are in existence the W+- and Zo bosons but they are not responsible for weak interactions. 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)Xw = 90.6 GeV. (120) o It is the mass of the Z bosons. For the two states of the proton is [(mH(o) + mW(+),d=1) - (mH(+) + mW(o),d=1)]Xw = 87.7 GeV. (121) When we add to the distance of mass between the two states of proton the mass of the electron we obtain [(mH(o) + mW(+),d=1) - (mH(+) + mW(o),d=1) + melectron]Xw = 97.7 GeV. (122) Analogous calculations for the neutron lead to the following results [(mH(+) + mW(-),d=1) - (mH(o) + mpion(o) + mZ(o))]Xw = 192.5 GeV, (123) [(mH(+) + mW(-),d=1) - (mH(o) + mpion(o) + mZ(o)) + melectron]Xw = 202.6 GeV. (124) 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) = [(πo(134.966) + π+-(139.570))/2]Fx2 = 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(Ko, 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)/Ny4 = 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

47 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 mass 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.

48 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 (JP=11/2-), m(1520) = 1mS(o),d=1{2-} + m(1115){1/2+} = 1537 MeV (JP=3/2-), m(2100) = 2mS(o),d=1{2+2+} + 1mS(o),d=4{1-} + m(1115){1/2+} = 2145 MeV (JP=7/2-), m(2350) = 2mS(o),d=1{2+2+} + 2mS(o),d=4{1+1-} + m(1115){1/2+} = 2332 MeV (JP=9/2+), m(1765) = 3mS(o),d=4{1-1-1-} + m(1192.5)(mean value){1/2+} = 1753 MeV (JP=5/2-), m(1915) = 4mS(o),d=4{1+1+1+1-} + m(1192.5){1/2+} = 1940 MeV (JP=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=1 mtau,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-,

49 +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.

Table 8 New symbols Particle

Spin Internal Electric Weak New 1) helicity helicity charge charge symbol + L (left) + e(anti) e(anti)L+ R (right) e eRR +  (anti)  (anti)R+ + L L e R e-R e+ + L + e+L + p + L + p+L pR p-R n + L2) + nL 2) n(anti) R n(anti)R 2) R  -R + L2) + + + L R2) + -R + L2) + +  +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 Ko  LL LLA e-R e(anti)L+ + LL LLA e+L eR-, Ko(anti)  LR LRA e-R e(anti)L+ + LR LRA e+L eR-. The mixture of Ko and Ko(anti)  LL LLA LR LRA e-R e(anti)L+ e+L eR-.

50

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 = 2ich/r = h, (145) and therefore  = ic/r, (146) where  denotes the frequency. The coupling constant we can write in following form i = w(proton)Mm/Y2, (147) 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 M is the mass of the needed vortex. The change of the mutual orientation is associated with the two different states of proton. We need a transition between two states of a charged particle in the proton because it changes the weak interactions between the proton and electron in the hydrogen atom. Such transition should create a vortex in the proton. Previously I described following transition: W+d=1  Z+ + πo. Mass of the Z+ in the d=0 state is equal to the mass of the core of baryons i.e. 727.440123 MeV. Now we need the following transition: W+d=1  Zo + π+. The mass of the Zo in the d=0 state (it is the needed vortex of energy) is 685.98457 MeV (see formula (48)). A small part of this energy, ΔE=3.09695296 MeV, forces the transition of the charged core into the neutral core – see the discussion below formula (35). The weak mass of this boson is M = w(proton)[(mW(+),d=1 – mpion(+))·9.0036144 – ΔE] = 12.7856103 MeV. (148)

51 Because the radius of the first Bohr orbit is r1=0.5291772·10-10 m, we obtain  = 1420.434 MHz.

(149)

Lamb-Retherford shift The Lamb shift is associated with the two different states of the proton. We can calculate the Lamb shift using following formula Ei = ich/r = mic2. (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 and the formula (147) we obtain L = ic/(2 · 4r1), (153) where M in (147) denotes the distance of the mass between the relativistic charged W pion in the d=1 state and the charged pion M1 = 215.760 - 139.5704 = 76.1899 MeV. Then L = 1058.05 MHz. (154) 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) -16 From this dr = 2.722496·10 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 Electron magnetic moment in the Bohr magneton (see formula (69)) Muon magnetic moment in the muon magneton 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 Lamb-Retherford Shift

Theoretical value 1.0011596521735 1.001165921508 1420.434 MHz

1057.84 MHz 1058.05 MHz

52

Table 10 Mesons Physical quantity Mass of the K+,- kaon Mass of the Ko kaon Lifetime of KL0/lifetime KS0 Mass of K*(892) Mass of Eta Mass of Eta’ Mass of Ypsilon Mass of Z0 Mass of W+,Mass of D(charm) Mass of D(strange) Mass of B Mass of B(strange) Mass of B(charm) Lifetime of B(charm)

Theoretical value 493.728 MeV 497.760 MeV 527 901 MeV 549.073 MeV 953.971 MeV 9463 MeV 90.6 GeV 79.4 GeV 1867 MeV 1991 MeV 5281 MeV 5354 MeV 6290 MeV 1.9 · 10-13 s

Table 11 Hyperons and resonances Particle Hyperon  Hyperon + Hyperon o Hyperon Hyperon o Hyperon Hyperon  Tau lepton Resonance (1232) Resonance N(2650) Resonance (1520) Resonance (2100) Resonance (2350) Resonance (1765) Resonance (1915) *Assumed positive parity

Theoretical value Mass 1115.3 MeV 1189.6 MeV 1190.9 MeV 1196.9 MeV 1316.2 MeV 1322.2 MeV 1674.4 MeV 1782.5 MeV 1236.8 MeV 2688 MeV 1537 MeV 2145 MeV 2332 MeV 1753 MeV 1940 MeV

Theoretical value J P S 1/2 +1* -1 1/2 +1 -1 1/2 +1 -1 1/2 +1 -1 1/2 +1 -2 1/2 +1 -2 3/2 +1 -3 1/2 3/2 +1 11/2 -1 3/2 -1 7/2 -1 9/2 +1 5/2 -1 5/2 +1

53

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 which 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 which 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 high energies. All particles produced inside the liquid-like plasma have transverse-momentum – they are the non-single-diffractive fraction (the NSD fraction). The protons which have an atom-like structure also produce hadrons which have momentum tangential to the surface of a cylinder – 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 is goes through the surface) X2 = X1πrT2HCMS/(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; η209 7.1 MeV 8.0 MeV 8.8 MeV 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.

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Mathematical Constants In this chapter, I will show that the everlasting/ultimate theory leads to the mathematical constants applied in physics. Today mathematicians and physicists create new formulas and equations everyday. They add to these new equations new parameters and are pleased that they obtain results consistent with experimental data. They do not understand that the gist of the matter (i.e. how to formulate the ultimate theory of physics and mathematics) which is associated with completely different problems. 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 all 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 which lead to stable objects i.e. to the closed strings, neutrinos, cores of baryons and objects before the big bangs suited to life. 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 two 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 objects before the big bangs suited to life. 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

79 appearing in the ground state of nature. I will also show that the numbers-factorials define spatial and time dimensions. 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 neutrino. The 24=4!=4D shows that the spacetime composed of free non-rotating neutrinos which is the 4D spacetime. The ground state of the Einstein spacetime consists of the non-rotating 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 neutrinos with a rotating spin 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 object before the big bang suited to life 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 object before the big bang suited to life produced a 1D loop i.e. the early Universe. The evolution (i.e. cosmology) of the object before the big bang suited to life 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

80 e=2.718…. There are only two spacetimes: the Newtonian spacetime (which leads to Einstein 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 TitiusBode 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 object before the big bang suited to life (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(1) = 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 neutrinos 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 diameter is not equal to π). Because 11=12=13=1 the mass of the closed string should be directly in proportion to its circumference, but also to its area and volume. Mass are directly proportional to number of the closed strings they consist of – these strings are inside the neutrinos 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 which 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.

81 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 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 objects before the big bangs suited to life) 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 everlasting/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 which is composed of internally structureless tachyons which have a positive mass. Such an eternal/everlasting/ultimate 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.

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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 which 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 which 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 which consists of threads that are composed of nonrotating 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

83 high enough to realize the symmetrical decays of the atomic nuclei. When we begin with a nucleus which 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 – this is the mechanism that is associated with travelling half 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 also those inside atoms and brains, 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 [5] 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 self-similar 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 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 11=12=13=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.

84 The transition from a maximum packed gas-like Newtonian spacetime (3D; mass that is directly proportional to the size to the power of three) to closed strings (1D; mass that is directly proportional to the length) suggests a division of the natural numbers into a finite number of sets in such a way that a set containing a prime number also contained a number equal to this prime number to the power of three. Following such division 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 133, 373, 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 gas-like-Newtonian-spacetimeclosed-strings transitions. The radius starting from number 1, containing squares of prime numbers, represents the closedstringstori 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 the 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 which leads to the closed strings always having halfintegral spin and an identical radius. The prime numbers 2 and 3 are also associated with the internal structure of each microquasar and with the tori arising in the phase transitions of the Newtonian spacetime. Each microquasar emits two tones and the ratio of their frequencies is 2:3. This is associated with the ratio of the lengths of the circular axis and the equator in a dense cosmic object – it is 2:3. Also in existence are only one series of prime numbers (prime numbers = 5+d·6, where d=0, 1, 2, 4, 8, 16, 32, 64, and 128) which leads to the 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 [6]. 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

85 arrangements of the spins of the weak dipoles leads 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 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. [5] P G Drazin and R S Johnson; Solitons: an introduction; Cambridge University Press. (1989). [6] B C Berndt; Ramanujan’s Notebooks: Part IV; Springer-Verlag, page 138.

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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 which is characteristic of the energymomentum relation E = p2c2 + m2c4 (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 = mc2/sqrt(1 - v2/c2) (202) is imaginary so the symmetry of this equation forces to multiply the mass in the numerator by the imaginary unit i (where i2 = -1). The solution shows that energy of a tachyon decreases when linear speed increases E = mc2/sqrt(v2/c2 - 1). (203) Because the mean speed of tachyons is 8·1088 times higher than the speed of light in ‘vacuum’ (such value leads to the physical constants) then in approximation the energy of tachyon is in inverse proportion to momentum E(v >> c) = mc3/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/r2, (205) -31 3 where a=0.540031·10 m /s for mean tachyon in the Newtonian spacetime. Mass is directly in proportion to volume of tachyon m = b1·4πr3/3 = br3, (206) where b=3.485879·1086 kg/m3 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 = dr5, (207) where d=1.739225·10143 J/m5. 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 similar to 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 c5/(hG2)=5.1553·1096 kg/m3. This definition is for a cubic meter so we obtain c5/(hG2) = E/(c2L3) = dL5/(c2L3), (208)

87 where L is the side of the cube. The linear speed of such supertachyon is almost equal to zero so the definition M/L3 for the mass density is obligatory. From formula (208) we obtain L = sqrt(c7/(dhG2)) = 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 = 4πc5R3/(3hG2) = 2.2415·1052 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 the object before the big bang suited to life 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 radius of the Schwarzschild surface for such particles RS is two times greater than radius of the circular axis and is RS=3.616·1024 m. Mass of the object is Mo=1.961·1052 kg. Energy frozen inside the binary systems of neutrinos is v2/c2=(2.4248·1059)2 times greater than the M. This leads to the mean energy density inside the sphere which has the radius equal to the Schwarzschild surface radius for the virtual particles produced on the circular axis of the big torus equal to 3Mov2/(4πRS3c2)=5.8·1096 kg/m3. There is a little broadening of the circular axis so also of the Schwarzschild surface so the real value of the energy density is a little smaller. We can say that we obtained the Planck density i.e. the evolution of the object before the big bang suited to life begins 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-than-light closed strings a neutrino consists of mneutrinov2/c2) inside sphere which has radius two times greater than the circular axis of the weak charge of neutrino. The geometric mean mass is mneutrinov/c=8.1·10-8 kg whereas the geometric mean density 5.8·1096 kg/m3. 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 have almost the same value that we applied to calculate the masses of the D and B mesons in approximately Fx=3.7 (it is the ratio of the masses of neutral kaon and bound neutral pion). Physical meaning of this factor is associated with the weak interactions of the point mass and the strong-weak interactions on the equator of the torus inside the core of baryons. 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. A hypothetical cube which have side equal to the diameter of the weak charge and the Planck critical density, has mass about 1.7·10-8 kg – it is close to the Planck mass 2.2·10-8 kg. 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 object before the big bang suited to life and the cosmic loop (i.e. the early universe) is 2.1431·1052 kg plus emitted binding energy (about 2.06 % of this mass). The needed total mass is 2.1835·1052 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

88 expands in the surrounding Newtonian spacetime composed of slower tachyons, there arises shock wave which can create a cosmic bulb composed of pieces of space packed to maximum. Inside such cosmic bulb, the initial parameters cannot change unless the size is sufficiently great new supertachyons can arise. In different cosmic bulbs, the initial four of six parameters can have different values. The maximum mass density of a condensate of tachyons is about 8.3·1085 kg/m3. In the Newtonian spacetime can appear condensates which have different size. To create the object before the big bang suited to life and the cosmic loop, the minimum radius of a condensate of tachyons should be about 4·10-12 m. The eras for such condensate are as follows. 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 1036 kg/m3. This means that volume of the condensate increases about 1050 times so radius about 6·1016 times i.e. to about 200 km (it is in 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. Existence of the neutrinos indirectly proves that the condensates in the Newtonian spacetime can appear. 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 2·1017 kg/m3. This means that volume of the condensate increases about 4·1068 times so radius about 5·1022 times to about 2·1011 m (it is in approximately 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 objects before the big bangs suited to life 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 object-before-the-big-bang-suited-to-lifeneutrino transition, there appears the dark energy and the four inflows of it into the cosmic loop, i.e. into the early universe, what starts the expansion of the early universes. 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’. We can ask following question. Are in existence regions in the Newtonian spacetime composed of tachyons which have different mean size? In such regions, a set of the fundamental physical laws should be the same but values of five 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 7·1017 seconds) and tachyons are moving with mean linear speed 2.4·1097 meters per second. This leads to the lower limit of the size equal to 3·10115 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.

89

New Quantum Chromodynamics 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 new QCD the signs of the charges depend on the spin polarization of the surfaces of the tori-electriccharges). 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 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. 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 quark-antiquark pairs. The colour of sham quarks is associated with their internal helicity. The sham quark-antiquark pairs are colourless. The ground state of the Einstein spacetime consists of the non-rotating 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 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 confinement of gluons and sham quarks for low and high energies.

90 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 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) = ΣQi2, (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 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/3, +1Q and ±1Q, is R(s) = 4.1. 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) = 10. 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 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 and in the Ramanujan modular functions too, 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 assume that total mass of the sham quark pairs created in electron-positron collisions is 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 quadruples. Lightest binary-system meson, which consists of two pions (four gluon loops), is the kaon K. The electron-positron-pairgluon-loop-quadruple transition looks as an analog to the decay of neutral kaon (there are two opposite electric charges) to charged kaon (there is quadruple of gluon loops). Due to the same internal helicity of the electric charge carried by the positive kaon K and charged core of proton, the neutral kaon most often decays in the strong field to the positive kaon K, electron and electron antineutrino. This leads to conclusion that we should not observe the “horn” in the ratio K-/π. The experimental data concerning the K/π ratio are in [2]. In each neutral-kaonpositive-kaon decay, is emitted energy approximately 4 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) = 4.1 we obtain sqrt(s) = 4.6 GeV. For R(s) = 10 we obtain sqrt(s) = 400 GeV. 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

91 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 [3]. Gluon condensates carrying mass following from the atom-like structure of baryons can create new particles. Due to the interactions of the core of baryons with bosons, we observe the mass broadening for the Zo 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 GeV and it is the Zo boson. Due to the interaction of the core with the pion via gluon loops, the mass of the condensate is broadening from 4·187.573 ≈ 750 MeV to m(H+-) + mW(+-),d=1 ≈ 943 MeV. For such condensates R(s) = 4.1 whereas the sqrt(s) respectively are 165 GeV and 67 GeV. 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 quadruple), we obtain R(s) ≈ 3600. The mass of the Zo boson we can calculate also from following formula (mpion(+-)  mpion(o)Xw = 90.6 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 Zo 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 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=1Xw = 140 GeV. (219) Particle carrying such mass I will refer to as Zrel. The obtained theoretical result is consistent with the last data [4]. We can see that the Zrel particle is the type Zo 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) then the transitions are not frequent. Calculate mass of a particle produced by gluon condensate carrying mass equal to the mass of the Φ3(1850) meson (m = 1854 ± 7 MeV [5]). Calculated mass for mass equal to 1847 MeV is 9.45 GeV. This mass is close to the mass of the Y(1S, 9460 [5]). 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 quadruple) is R(s) ≈ 2880. The mass of the π(1800) meson (m = 1816 ± 14 MeV [5]), i.e. the value 1813 MeV, leads to the χb0(1P) meson (m = 9859 MeV [5]).

92 Applying formulae (215) and (216), we can calculate the masses of the three heaviest quarks. 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 quark M = 171.8 GeV. 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 quark M = 4190 MeV. Mass of gluon condensate equal to mass of the Υ(1S, 9460 MeV) leads to the mass of the charm quark M = 1267 MeV. 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. 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-loopsbasic-sham-quarks transitions lead to the essential part of the curve R(s) = f(sqrt(s)). The particlesgluon-condensatesnewparticles 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. New QCD needs six parameters only (the 3 physical constants and 3 masses) or seven only when we start from the properties of the Newtonian and Einstein spacetimes.

93 References [1] http://pdg.lbl.gov/current/xsect; K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) [2] C. Alt et al. (NA49 Collaboration) (2008). “Pion and kaon production in central Pb+Pb collisions at 20 and 30 GeV: Evidence for the onset of deconfinement”. Physical Review C 77: 024903. doi:10.1103/PhysRevC.77.024903 [3] 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 [4] http://blois.in2p3.fr/2011/transparencies/punzi.pdf [5] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010)

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Proton and Loops as Foundations of Theory of Chaos The Everlasting Theory leads to the atom-like structure of baryons, six basic sham quarks and eight gluons. Here I show that the logistic map, Feigenbaum constant and bifurcation applied in the theory of chaos follow from the internal structure of protons and collisions of baryons. Due to the carriers of the gluons and photons, the internal structure of proton ‘leaks’ outside it - there appears the Feigenbaum universality. Entanglement of groups of sets composed of particular concentric loops composed of the Einstein spacetime components leads to the Mandelbrot set. Due to the two spacetimes, we should change interpretation of the quantum mechanics. Nonlinearity follows from the locally changing binding energies. We can eliminate nonlinearity when we take into account internal structure of bare particles and appropriate binding energies. 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 which 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-loopthird-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. 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. To conserve in strong fields the symmetrical fusions/decays, the bosons appear as the groups containing 2d 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

95 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 2n = 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. 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 which 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=1 y + 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 (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

96 structure of proton) causes that different systems behave identically (qualitatively/structurally and quantitatively/metrically) – this leads to the Feigenbaum universality. 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 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 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 = zn2 + 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 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 and arise in other places, 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 linearnonlinear 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

97 gravity. This is due to the internal structure of the virtual bare particles and local binding energies which 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 theories 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 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 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. 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 which 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

98 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)

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Recapitulation: The Mainstream Theories 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. 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 can 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 graviton is 2. Quantum gravity looks similarly as the electromagnetism. We know that photons (spin is 1) create the loops (spin is 1) in the Einstein spacetime which transform into the electron-positron pairs (spin of electron is 1/2). In the annihilations of the pairs are produced the virtual or real jets in the Einstein spacetime increasing or decreasing its mean mass density. The gravitons (spin is 2) in spacetime composed of gravitons create the loops (spin is 2) which transform into the binary systems of electron-positron pairs (quadruples) (spin of electron is 1/2). We can say that inside the today Universe the quantum electromagnetism destroys the quantum gravity gravitational energy is emitted via the electromagnetic processes. The neutrinos, binary systems of neutrinos, quadruples of neutrinos, and so on, produce the gradients in the Newtonian spacetime which is imprinted 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 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 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. Inflationary theories need reformulation. Due to the flows of finite regions of the Newtonian spacetime (in a cosmic scale) the condensations and next inflations of tachyonic fields are possible. Inflation can lead to the object before the big bang suited to life 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. The electron-positron pair is the superpartner of the electron, the neutrino-antineutrino pair is the superpartner of the neutrino… 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. There is needed a coherent description of all interactions dependent on mass. The Einstein gravity and the Yang-Mills theory are correct. We must change description of the weak interactions. 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 which have a positive inertial mass. Free tachyons are imaginary because they have broken contact with the rest of

100 nature – they are bare particles without an internal structure. For quantum physics, the theories of relativity and determinism 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 has the same lifetime. It is inconsistent with the assumptions applied in the today mainstream theories. Higgs mechanism: There is not in existence the Higgs mechanism. The inertial mass is more fundamental than a pure energy (which mass is equal to zero). The fields having mass densities not equal to zero (for example, the Newtonian spacetime and Einstein spacetime) carry the pure energy. QED: We can formulate a new electroweak theory equivalent to the QED. This is possible because the Einstein spacetime carries the electromagnetic and weak interactions. The new electroweak theory is non-perturbative. In such a theory, we have to take into consideration also weak interactions of the electron with the entire matter and dark energy because a state of an electron describes a wave function filling the entire Universe. The new electroweak theory is mathematically very simple. Quark-gluon theory: The Yang-Mills theory describing the gluons is correct. The quark theory is correct only partially. There is an atom-like structure of baryons and there are the large loops (they have mass) responsible for the strong interactions. Electroweak theory is incorrect because the origin of the weak interactions is different. We should return to the Einstein gravity and to the quantum mechanics because these theories are correct. Correct interpretations of these theories leads to the ultimate theory i.e. to the phase transitions of the Newtonian spacetime (1997) and to the atom-like structure of baryons (1985). It is also apparent that all of the symbols applied in physics must have a physical meaning, and also the mathematical constants applied in physics. Most importantly, I discussed and analysed how we can verify my Theory.

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 the outside of the core of a nucleon is obligatory for strong interactions similar to the Titius-Bode law. On orbits are relativistic pions. The year 1997 was the most productive for me because I described the phase transitions of the Newtonian spacetime, the fourneutrino symmetry also leading to the distribution of galaxies which 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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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 basis of the observed redshift is wrong and also leads to illusion that the expansion of our Universe accelerates. ‘Antigravity’: In thickened regions of the Einstein spacetime on masses act repulsive forces. Background: The volume filled with internally structureless tachyons (Newtonian spacetime is the background for gravitational interactions), non-rotating binary systems of neutrinos (Einstein spacetime is the background for electromagnetic and weak interactions), and virtual particle-antiparticle pairs (virtual particles do not change the mean density of background). Binary systems of neutrinos are weak dipoles. 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 happened every time but due to the superluminal speeds probability that this will happed near our Universe is practically equal to zero. During such inflation, arise the closed strings, the binary systems of neutrinos the Einstein spacetime consists of, and next the neutrons. The gravitational fields produced by neutrinos stop inflation. There the object before the big bang suited to life and the cosmic loop i.e. the early universe can appear. However, the big bangs suited to life are associated with the explosions of universes which have strictly determined mass (they are the cosmic loops composed of the neutron black holes) – such explosions are due to the object-before-bigbang-suited-to-lifeneutrino transition. During such transitions the thickened Einstein spacetime, i.e. the dark energy, appears. The dark energy is composed of the surplus nonrotating binary systems of neutrinos. The inflows of the dark energy into the universe suited to life cause the exits of the universes from the black-hole state. We can see that there are the two main stages associated with the big bang theory i.e. there are the inflationary stages associated with the Newtonian spacetime and there are the object-before-big-bang-suited-tolife stages leading to the ‘soft’ big bangs of the universes. 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 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 nucleons cannot collapse. The black holes are everywhere. 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

102 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 2.4·1059 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 K2 tachyons (K=0.79·1010). 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 eleven elements. Coherent mathematics: We cannot formulate coherent mathematics on the basis of points without size because such points (even an infinite number of them) do not lead to the axis, area or volume that have sizes which 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. Cosmic-ray particles: The assumption that the ground state of the Einstein spacetime is the field composed of the non-rotating 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 all 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 big bang suited to life 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. Such illusion we can explain on basis of the new theory of the electroweak interactions and is not associated with a surplus real mass. The dark matter consists also of the iron-nickel lumps produced in explosions of the big stars just after the beginning of the big bang suited to life. Because the dark matter arose just after the beginning of the big bang suited to life 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

103 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. Einstein spacetime: The field composed of free non-rotating binary systems of neutrinos. The binary systems of neutrinos are weak dipoles which are composed of two opposite weak charges. The properties of a weak charge depends 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 creates 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: An electron arises following the polarisation of a field which is composed of binary systems of neutrinos, therefore, the torus of an electron forms part of the Einstein spacetime. Axes of these dipoles are perpendicular to the surface of a torus. 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 which causes new binary systems of neutrinos to flow into a bare electron. On the circular axis of electron, there is a whole charge and only half mass of bare electron. 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 is also the same. In the torus of proton the mean distance between the binary 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. Entangled particles: Entanglement of neutrinos is due to the exchanges of the quanta composed of the binary systems of the closed strings emitted by the neutrinos. The binary systems of the closed strings are not loop-like particles so its range can be tremendous. 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. The evaporation was due to the inflows of the dark energy. The dark energy arose due to the collapse of the object before the soft big bang. The dark energy is the thickened Einstein spacetime composed of the non-rotating 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 big bang suited to life. 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.

104 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, has 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. 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 the near 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: They are the rotational energies (i.e. massless) carried by the binary systems of binary systems (quadruples) of neutrinos with parallel spins. 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=4d, 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. 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 smaller than distance 2π times greater than 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 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. K2 constant: It is number of tachyons a closed string consists of. Large loop: Arises inside the torus of baryons and consists of weak dipoles.

105 Lines of forces: Spins of binary systems of neutrinos (the weak dipoles) overlap with the electric lines and are perpendicular to the magnetic lines. 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 Newtonian spacetime. This analogy and definition is also relevant for the Einstein spacetime which 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. Mass: Mass is directly proportional to number of the closed strings a body consists of. Mass is the more fundamental physical quantity than energy i.e. pure energy is not in existence without spacetime/field having mass density not equal to zero. Mesons: They are binary systems of large loops which are created inside the torus of baryons. They can also be mesonic nuclei which are composed of the other mesons and the large loops, or they can be binary systems of mesonic nuclei and/or other binary systems. 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 are magnetic dipoles so minds may interact with a brain or matter magnetically. 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. 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 binary systems of neutrinos (mass of one is approximately 6.7·10-67 kg) moving with the speed of light in spacetime – this is because the Newtonian spacetime ‘sees’ neutrinos as independently moving particles. 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 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 0.6·10119 times greater than the energy of a neutrino resulting from the formula E=mc2. This is

106 because neutrinos are built of closed strings at a superluminal speed (approximately 2.4·1059 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 or non-rotating 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 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. 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 – it is equivalent to approximately 4·1050 kg. 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 surface 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. Objects before the big bang suited to life: Objects before the big bangs suited to life consist of nucleons (radius of which is approximately 2.7·1024 m). The torus of it consists of deuterium. Immediately before the big bang suited to life the object-before-big-bang-suitedto-lifeneutrino transition was possible only if the objects had a strictly determined mass (approximately 1.9·1052 kg) – then, just before big bang suited to life, is possible the. The Universe arose in a similar way to large loop which is 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 1.8·1051 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. Dark energy is remnant of the object before the big bang suited to life which is composed of nonrotating binary systems of neutrinos 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 photon galaxies which couple the cosmic structures, lead to the illusory part of the dark matter. Dark matter also consists of the remnants of the big stars. They are composed of ironnickel lumps. Detecting these lumps is extremely difficult because their temperature is equal to cosmic microwave background radiation. The interior of a sphere filled with baryonic matter contains approximately 3.8% visible matter, 22.2% dark matter and 74% dark energy.

107 Universes suited to life developed as universe-antiuniverse pairs from positive fluctuations of the field composed of non-rotating binary systems of neutrinos. 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 objects before the big bangs suited to life. Photon galaxy: Is a photon which is composed of 416 entangled photons. Photons: Quanta of energy carried by a field composed of a 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=mc2 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. 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. Pieces of space: They are the internally structureless tachyons. In different regions of cosmos (in 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 which the lines of electric forces converge) inside the torus in core of a baryon. Planck critical physical quantities: The Planck length is equal, approximately, to the diameter of the circular axis of neutrino (diameter of weak charge) 1.5·10-35 m. The critical mass density is associated with the more detailed new Big Bang Theory. 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 are relativistic pions that are in the S state. A relativistic pion is under the Schwarzschild surface for strong interactions so the proton is a stable particle. Meanwhile, baryons possess an atom-like structure. QCD and ET: 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. The Everlasting Theory shows that the masses of the two lightest quarks are much greater. 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 can 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 graviton is 2. Quantum gravity looks similarly as the electromagnetism. We know that photons (spin is 1) create the loops (spin is 1) in the Einstein spacetime which transform into the electron-positron pairs (spin of electron is 1/2). In the annihilations of the pairs are produced the virtual or real jets in

108 the Einstein spacetime increasing or decreasing its mean mass density. The gravitons (spin is 2) in spacetime composed of gravitons create the loops (spin is 2) which transform into the quadruple of neutrinos (spin of neutrino is 1/2). Due to the tremendous energy frozen inside each neutrino (not mass), the loop-quadruple transitions was possible only at the beginning of inflation. Today, inside our Universe, the carriers of gravitons decay to the carriers of photons. We can say that inside the today Universe the quantum electromagnetism destroys the quantum gravity - gravitational energy is emitted via the electromagnetic processes. The neutrinos, binary systems of neutrinos, quadruples of neutrinos, and so on, produce the gradients in the Newtonian spacetime which is imprinted 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 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 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. Quantum particles: See ‘Renewable particles’. Quantum physics: Due to the faster-than-light particles (i.e. the tachyons and binary systems of closed strings) the quantum physics is local i.e. points separated spatially (because of information moving with the speed of light) can communicate. The behaviour of the renewable particles shows that the quantum physics is also real. We can see that existence of the two spacetimes, i.e. the Newtonian spacetime and Einstein spacetime, leads to the classical interpretation of the quantum physics i.e. to the locality and reality of nature. Real photons: In contrary to the virtual photons they have mass equal to zero. They are the excitations (rotational energy) 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 real photons in the Einstein spacetime, the real or virtual bosons in the strong field inside the baryons, and so on. Their state describes the wave equation. 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. Soliton: Is the tangle of closed threads composed of weak dipoles and produced by a tangle of circular electric currents. Speeds: The Einstein Theory of Relativity (the ETR) is correct but incomplete due to the lack of description of internal structure of Einstein spacetime. This internal structure shows that there are possible phenomena beyond the ETR. The ETR leads to conclusion that no mass can move with speed of light in ‘vacuum’ (the c) because then mass is infinite. This is only partially true – neutrinos have mass not equal to zero and move with speed equal to the c. What it means? It suggests that the ground state of the Einstein spacetime is a field composed of non-rotating binary systems of neutrinos. This is vector field and is very difficult to detect such binary systems due to the lack of rotational energy. We can assume that the Einstein spacetime carries the photons – they are the excitations of the Einstein spacetime i.e. they are

109 the rotational energy of binary systems of neutrinos. Therefore, why photons are moving with speed equal to the c? This is because with such speed are moving binary systems of neutrinos the Einstein spacetime consists of. Therefore, why binary systems of neutrinos are moving with speed equal to the c? This is because this speed is the natural speed in the more fundamental spacetime i.e. the Newtonian spacetime. Due to the superluminal speeds of tachyons the Newtonian spacetime consists of, the gravitational fields are ‘attached’ to masses i.e. to binary systems of neutrinos the all masses consist of and are ‘attached’ to binary systems of neutrinos the Einstein spacetime/field consists of. The c is the natural speed of light in relation to gravitational fields ‘attached’ to all masses – this causes that speed of light is always equal to the c (of course, in the ‘vacuum’) in relation to the all masses producing dominating gravitational field. Dark energy is the thickened Einstein spacetime inside our Universe and it arose due to the evolution of the object before big bang suited to life. The distant galaxies are in the rest in relation to the expanding thickened Einstein spacetime – this causes that the distant galaxies moving with very high speeds in relation to Earth, have not the relativistic mass. The Everlasting Theory shows that inflation with speed much higher than the speed of light in ‘vacuum’ (i.e. with speed much higher than the c) is possible. Such superluminal speeds are possible when expands a region with tachyons packed more than in the Newtonian spacetime which has the mean mass density. Due to the tremendous energy involved in such inflation, we never will be able to create jet in the Newtonian spacetime having appropriate size. Small such jets produce the closed strings a neutrino consists of. The theory of entanglement shows that communication (not a traveling) with speed higher than the c will be possible when we will able to build neutrino trap with polarized spins and changing number of neutrinos. The high redshift for some cosmic objects and the varying fine-structure constant for quasars (the Everlasting Theory shows that the fine structure constant is in proportion to the mass density of the Einstein spacetime to the power of five third), show that creation of the jets (also jets in jets) and protuberances in the Einstein spacetime is possible. Due to the smoothness of the Newtonian spacetime (the pressure is about 10180 Pa) the jets and protuberances very quickly disappeared but we observe very high redshift for objects accelerated by them. Redshift higher than 1 is possible only in again and again exploding big cosmic structures (the today interpretation of the high redshift is wrong and leads to illusion that expansion of the Universe accelerates). The Everlasting Theory describes internal structure of the Einstein spacetime so also suggests how to create such jets and protuberances. There are two possibilities to travel with speed equal to the c. We can accelerate some object to speed almost equal to the c but then the relativistic mass would be dangerous for spacemen, or to create jet in the Einstein spacetime and place a spacecraft in it. In the second case, the mass of spacecraft and spacemen is equal to the rest mass similar to the distant galaxies which are in the rest in relation to the expanding thickened Einstein spacetime (the dark energy). 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 which have the half-integral spin. Spinor: Spinor is the generalization of vector and tensor. Most important is spinor space associated with the Lorentz transformation because it describes the fermions which 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 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

110 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 which have energy equal to approximately 283 MeV. This energy corresponds to the lower limit of temperature of the liquid-like plasma i.e. approximately 4·1012 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. binary systems of neutrinos the Einstein spacetime consists of) appearing in decay of pions in liquid-like 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, DNA and RNA: Superphoton is left-handed double helix loop that is composed of 2·432 entangled photons (there are 2·416 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. We can see that the superphoton-matter interactions can lead to the Deoxyribonucleic Acid (the DNA). 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. Replication of the DNA was possible when the superphotons decayed into the photon galaxies i.e. since about 5.7 billion years ago. The RNA is not a precursor of the DNA. The left-handed superphoton consists of the four different left-handed carriers of photons and they are some analogs to the four basis of the DNA i.e. the A, C, G and T. There were about 1078 superphotons. To create one our entire genome is need about 1036 superphotons. This means that human life should be usual. Superphotons are the matrices for the DNAs. Supertachyon and cosmic bulb: It is a condensation of the Newtonian spacetime. Its radius is 1.0125·10-15 m, energy (not mass) is 2.2415·1052 kg whereas energy density is equal to the Planck critical density 5.1553·1096 kg/m3. 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 which can create a cosmic bulb composed of pieces of space packed to maximum. In different cosmic bulbs, the initial four of six parameters can have different values. Percentage of the cosmic bulbs suited to life is very low. Creation of a cosmic bulb is the end of the inflationary period. Due to the superluminal speeds of tachyons, 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 8·1088 times faster than photons in spacetime. The unchanging mean speed of free and bound tachyons

111 defines the mean radius of tachyons and leads to the principle of 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 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 four succeeding phase transitions possible 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. Tachyons lead to coherent quantum mechanics i.e. to coherent wave functions because the superluminal speeds of tachyons means that very distant points of a wave function can quickly communicate. 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. It leads to conclusion that tensor field should consist of mutually interacting scalar field (the Newtonian spacetime) and vector field (the Einstein spacetime). In the today Universe, the gravitational energy is lost due to electromagnetic phenomena. The Kaluza Klein theory also shows that unification of gravity and electromagnetism is via the fifth dimension i.e. via loops i.e. via the tori of the neutrinos. 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. Universe-antiuniverse pairs: Similarly as particles, also universes arise as the universeantiuniverse pairs. The baryon-antibaryon symmetry was broken already before the big bang suited to life. In Einstein spacetime (its ground state consists of non-rotating binary systems of neutrinos) arise the left- and right-handed vortices as the vortex-antivortex pairs. The object before big bang suited to life 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 – neutrons are left-handed particles. Evolution of the object before the big bang suited to life 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 leading to the observed motion of the Universe as a whole. Virtual photons: 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 groups composed of non-rotating 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. Weak dipoles: These are binary systems of neutrinos. The neutrinos carry the weak charges.

112 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. 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 smaller than the circumference of the small loops produced by neutrinos.