The Oscillating Universe Theory ( To the Unified Field Theory )

This paper represents model of oscillating universe theory. We try to realize model of both electromagnetic waves and spectrum of elementary particles from the unified point of view. Consideration of problems of the gravitational optics and dark matter is developing from the solid crystal model for the vacuum. The vacuum is represented as a three-dimensional crystal lattice matter with a very small lattice period, much less than 10 cm. The oscillators are located at the nodes of an infinite lattice. It is shown that an infinite set of equations to describe the coupled oscillations of moving oscillators converges to a system of twelve equations. We have obtained the combined equations for a multicomponent order parameter in the form of the electric and magnetic vacuum polarization, which defines the spectrum and symmetry of normal oscillations in the form of elementary particles. Two order parameters—a polar vector and an axial vector— had to be introduced as electrical and magnetic polarization, correspondingly, in order to describe dynamic properties of vacuum. Vacuum susceptibility has been determined to be equal to the fine structure constant . Unified interaction constant g for all particles equal to the double charge of Dirac monopole has been found (g = e/, where e—electron charge). The fundamental vacuum constants are: g, , parameters of length , e n   and parameters of time , e n   for electron and nucleon oscillations, correspondingly. Energy of elementary particles has been expressed in terms of the fundamental vacuum parameters, light velocity being equal to e e n n c       . The term mass of particle has been shown to have no independent meaning. Particle energy does have physical sense as wave packet energy related to vacuum excitation. Exact equation for particle movement in the gravitational field has been derived, the equation being applied to any relatively compact object: planet, satellite, electron, proton, photon and neutrino. The situation has been examined according to the cosmological principle when galaxies are distributed around an infinite space. In this case the recession of galaxies is impossible, so the red shift of far galaxies’ radiation has to be interpreted as the blue time shift of atomic spectra; it follows that zero-energy, and consequently electron mass are being increased at the time. Since physical vacuum has existed eternally, vacuum parameters can be either constant, or oscillating with time. It is the time oscillation of the parameters that leads to the growth of electron mass within the last 15 billion years and that is displayed in the red shift; the proton mass being decreased that is displayed in planet radiation.

. The term mass of particle has been shown to have no independent meaning.Particle energy does have physical sense as wave packet energy related to vacuum excitation.Exact equation for particle movement in the gravitational field has been derived, the equation being applied to any relatively compact object: planet, satellite, electron, proton, photon and neutrino.The situation has been examined according to the cosmological principle when galaxies are distributed around an infinite space.In this case the recession of galaxies is impossible, so the red shift of far galaxies' radiation has to be interpreted as the blue time shift of atomic spectra; it follows that zero-energy, and consequently electron mass are being increased at the time.Since physical vacuum has existed eternally, vacuum parameters can be either constant, or oscillating with time.It is the time oscillation of the parameters that leads to the growth of electron mass within the last 15 billion years and that is displayed in the red shift; the proton mass being decreased that is displayed in planet radiation.

Introduction
During recent years the science about cosmology has been in rather difficult situation.On one hand, observations of star dynamics in galaxies and of galaxies in clasters show substantial deviation of rotation velocities from Kepler's law; this proves the existence of additional matter (dark matter) which participates in gravitational interaction [1][2][3].On the other hand, more careful examinations of the red shift in the nearer space at the distances of 10 5 -10 7 light years as well as observation of supernova outburst [4,5] show that velocity of the Universe expansion increases with time, and this in turn requires introduction of additional dark energy with anti-gravitational properties.Thus, a contradiction arises.Practically, in one and the same point it is necessary to introduce both dark matter creating additional gravitational field and dark energy having anti-gravitation.Since there is no doubt about the facts above, their interpretation must be revised.
At the present time there are two mutually exclusive points of view.First, despite very distinctive spatial nonhomogeneity of matter, observations show that at the distances of about 10 9 light years (cell of homogeneity) matter is distributed in the space quite homogeneously.Besides, the cosmological principle suggests that these homogeneous cells should cover the entire infinite space.Second, the red shift discovered by Hubble, which he interpreted as Doppler's principle related to the galaxies expansion, made Friedman's model of expanding Universe quite necessary.From Hubble's empirical law that determines dependence of velocity of galaxies on the distance , we can suppose existence of a singularity at a certain time.Since velocity of expansion of the galaxies cannot exceed the light velocity , it follows from the relation 0 , that there is quite a definite size of the Universe growing with time 0 , here 0 is the singularity offset counted from the present moment; Hubble's constant equal to decreases with time; however, observations show, that the value H, on the contrary, increases with time.
If we interpret the existence of a singularity as a Big Bang, we have to bear in mind that the explosion is a phase transition from a metastable state into another more stable state accompanied with release of energy.Before the phase transition, this energy is homogeneously distributed around the space.They sometimes say: explosion power is equivalent to e.g. one kilogram of trotyl; it is obvious that two kilograms of trotyl give off right twice as much energy as one kilogram does.Besides, the phase transition does not begin with the singularity but with the nucleation of a new phase whose size exceeds the critical radius.In this case energy is released in accordance with broadening the new phase at the expense of the phase edge motion.Since the average energy density of the entire matter in vacuum is approximately 0.008 erg/m 3 , this very energy should be released at the phase transition of each cubic meter of vacuum.It is difficult to imagine, however, that electrons and protons could be created out of this homogeneously distributed in space energy, and, besides, in exactly equal quantities.An explosion of a hydrogen bomb in vacuum can serve as a model of a hot Universe.The hydrogen bomb is a local object in a metastable state.There is a mixture of light and heavy nuclei under the temperature of several million degrees at the moment of detonation.According to D'Alambert equation, the electromagnetic pulse and the neutrino pulse will start to disperse with the light velocity.Following electromagnetic pulse relativistic electrons will fly and then light, and heavy nuclei.In a second, the electromagnetic pulse will reach the Moon area and nothing will stay at the point of explosion.Thus, the examined case is also far from the Friedman's model of expanding Universe.
In order to somehow reconcile the model of the infinite matter distribution in space with that of the expanding Universe, Milne offered the following reasoning [6].If we mentally specify a sphere of a definite size in a matter homogeneously distributed around an infinite space, then external layers of the sphere due to their spherical symmetry have no influence on the sphere dynamics.Therefore, we can ignore the external layers and consider the Universe as a sphere of a definite size that precisely coincides with the Friedman's model.However, this statement is a mistake.The thing is that with matter being homogeneously distributed about the entire infinite space, the gravitational potential follows the condition of the translational invariance: . We may consider this constant to be equal to zero, therefore, a gravitational potential only arises at deviation of a matter distribution from an average value.For that reason the equation for the potential can be written as follows: Here 0  is an average density of matter.From Equation (1) we can see that it is not necessary to search for dark energy as the density is both the gravitating and the anti-gravitating matter in the form of and On the other hand, if we mentally specify a sphere of radius R with the density of matter 0  and ignore the external matter, we come to another equation for the potential: This equation has the following solutions: Similar expressions can be used for determining gravitational potentials of planets, stars and galaxies in a form of the sum of the potentials of stars with their specific location.However, for the scales comparable with the size of homogeneity cell and bigger, we come to an obviously non-physical result: the potential in any arbitrary point depends on the radius of a sphere which we mentally specify out of the entire infinite space.Thus, any result depending on the mentally specified radius of the sphere, including the radius of the visible part of the Universe, is physically incorrect.
For instance, we can determine the circular orbital velocity v 1 for the Universe of radius R on the sphere surface from the equality of centripetal and centrifugal forces: If v 1 is equal to the light velocity с, we obtain the following expression for the critical matter density in the Universe: This corresponds to the condition g R r  when g r is a gravitational radius.Therefore, with the definite choice for R we may come to the conclusion that the Universe is a black hole, while, as it follows from the cosmological principle at the scales comparable with the radius of the visible part of the Universe, the gravitational potential has no specific features and its average value is zero.
The same situation takes place when we consider the influence of a pressure on the dynamics of the expanding Universe.For instance, if we take a big vessel with a gas, mentally specify a sphere of radius R in it, and ignore the gas surrounding the sphere, we can state that the gas will broaden and get cool at the expense of the internal pressure.This may remind the model of the expanding Universe.Remember, however, that the specified sphere is surrounded with the same gas at the same pressure; that is why there will be neither broadening nor cooling.Thus, for the infinite Universe both an average gravitational potential and an average pressure are constant; besides, since the expanding dynamics is influenced by the equal to zero gradients of these variables, there cannot be neither expanding nor compression.An infinite system can only stratify according to the energy density and we really observe this stratification on giant scales from the value less than 10 −9 erg/cm 3 for an inter-galaxy space to the value over 10 39 erg/cm 3 for nuclear energy.
Nevertheless, within the frames of the cosmological principle there is a problem, the so called photometric paradox.The thing is that at present time when stars and galaxies radiate light in the entire infinite space, we can introduce an average luminosity L of a unit volume, provided that the densities of a luminous flux intensity at the distance r from a single volume is equal to 2 4π j L r  .The integral over the sphere of radius R gives the total flux intensity equal to J RL  ; it follows that with R approaching infinity the flux intensity must approach infinity as well.Practically, however, we see rather a low sky luminosity.This is the photometric paradox.
In fact, by calculating the intensity, we must take into consideration the retardation effects.The flux that comes to a certain point at a certain time diates at different moments depending on the distance: Expression (3) shows that the flux coming from the deep Universe will be finite if at longer t decreases faster than t Besides, we can divide the entire flux observed at any point of the infinite space into two parts: the flux vis J of a visible part of space 0 R cT  , Т 0 ~ 15 × 10 9 years and the relict flux rel J radiating from the spots with Here summing was carried out over a countable number of galaxies in the visible part of the Universe.Thus, from the expressions given above it follows that the Universe must be non-stationary, not due to an expansion of galaxies', but at the expense of a variation of physical vacuum parameters.Since the relict radiation corresponds to the temperature 3K, the Universe had such a temperature long ago.The one but not the only feature of a non-stationarity is the red shift of atomic spectra that we can interpret as the blue temporal shift of both characteristic Bohr energy and all atomic energy levels correspondingly, at the expense of variation of physical vacuum parameters.Observations show that the characteristic Bohr frequency depends on time and increases with time.By introducing a frequency of an arbitrary atomic level, we obtain the following expression for the Hubble's constant:

 
H t are monotonously increasing functions.The latest observations of the flashes of far supernova [4,5] show temporal growth of H.It is senseless to explain this situation using space-time properties.
Speaking about space-time properties is quite the same as judging about wine quality by the curvature of a bottle surface.Dilettantes are often attracted by the appearance of the vessel, while connoisseurs pay attention to its contents, conservation conditions, and temporal changes.We should regard space like a vessel with the only feature: its volume is infinite [7].Its internal properties are to be discussed.

Hidden Parameters of Vacuum
We should proceed from the experimental fact that the energy and the pulse of any elementary particle are: Here k  -frequency for electron, proton, photon and neutrino, correspondingly, we expressed as follows: By setting up the following solutions: The unified formula for the energy of any elementary particle points to the existence of the universal interaction for fields related to each particle.Besides, the two oscillation branches with the energy gap observed in the excitation spectrum prove an existence of a certain set of discrete oscillators whose interaction causes normal oscillations with frequencies k  .In fact, we can represent vacuum as a crystal object of a cubic or hexagonal symmetry with a very small lattice period, much less than 10 −26 cm.We can estimate the upper limit of a lattice period by the maximum particle energy in cosmic rays equal to 10 21 eV that corresponds to the wave vector of 10 26 cm −1 .The vacuum ground state is the equilibrium position of all oscillators; these are the points of equilibrium forming crystal lattice related to the absolute coordinate system.Under the deviation of an oscillator from the equilibrium position, a dipole moment arises.For the scales exceeding the lattice period we can introduce a macroscopic order parameter as an electric polarization of vacuum:   , , , , exp we obtain the spectrum for normal oscillations: .
Therefore, we can represent physical vacuum as some coherent state with the natural frequency standards in the form of homogeneous polarization oscillations about an absolute coordinate system

P P
Suppose, there are two branches of normal oscillations of field P that we can call electron and nucleon modes.The Hamiltonian for electron and nucleon modes written in the unified form, is: For simplicity, we consider normal oscillations inside the electronic modes.We dimensionlize coordinates and time.We express new variables like this: ; For electronic and nucleonic parts, we introduced the parameters of time e  , n  and length e  , n  that characterize the kinetic and gradient energy of the fields.Besides, we introduced a dimensionless parameter of an elastic coefficient  corresponding to the reciprocal susceptibility common to both modes.These are the latent parameters of vacuum and the available experimental data are sufficient to determine them.
2 , e e   P P By using the minimal action principle for the Lagrange function equal to the difference of the kinetic energythe first member of expression (7), and the potential energy-the second and the third members of (7), we obtain the equation of motion for six independent normal oscillations : , , , , , of the integral-differential equations: Consider the solutions in the form of plane waves: For plane waves, Equation ( 14) reduce to the form By making the determinant of the Equati to zero, we obtain the oscillation spectrum (see Thus, from (18) we obtain the normal spectrum of the oscillations; from Equation ( 16), we obtain the form of the oscillations: Expression (19) allow the definition of the general properties of the normal oscillations for vacuum fields linked by the long-range Coulomb interactio placian operator in Equations ( 14) requires that the polarization components be eigenfunctions of this operator: For lateral (transverse!) oscillations, the depolarizing field equals to zero.As a result, the frequencies for longitudinal and lateral oscillation The problem, however, is th differential equations we may take into consideration both eigenfunctions and eigenvalues, while the amplitude of integrals of ollowing reasons.We know from the th n.The La- The result of the Coulomb interaction is that the oscillations of the polarization are divided into two classes: longitudinal 1 P with at for linear homogeneous the eigenfunctions remains arbitrary.Suppose, an eigenfunction specifies the configuration of the excitation; though the excitation energy and pulse are the motion, and yet they can have arbitrary meanings.Nevertheless, in practice we can see that energy of any excitation has quite a definite meaning both for light quantum and for any elementary particle.Therefore, within the framework of homogeneous equations it is impossible to realize the origin and the physical meaning of the Planck constant.
For linear systems, the amplitude of oscillations turns out to be quite definite under the external force; then we can express the solution by means of the Green function, which meets the homogeneous equation and has quite definite amplitude.Non-homogeneous equations are necessary for the f eory of many-body systems that, if a system consists of discrete particles, the correlation effects substantially decrease the ground state, and local states such as polarons can occur.Therefore, we pass to consideration of the ground state taking into account correlation effects.
From an endless number of particles forming a crystalline vacuum state we examine one particle as a point unit source   e Q   r , which generates longitudinal electric field defined by equations: Thereafter, we can write the interaction energy of the point so vacuum fields as follows: urce with 0 0 .4π Here g is the constant of interaction between the point un l oscillations provide a larizing electric field geneous equation for polarization: Divergence of the left and the right parts of the Equation (22) results in the expression for the induced charge density, related to the electrical polarization for the case when a source is moving with velocity v : It is obvious from (23) that the induced is the Green function for a point source that fulfills the ho tion di es results in the Fourier-harmonics for the induced charge vacuum: charge density mogeneous equation over the entire space except one point; but due to this point, the function acquires quite definite values over the entire space.
At first, we consider a particular solu of Equation (23).Fourier-transformation over coor nat density in Here the corresponding coordinate dependence of the induced charge density for the case, when velocity lies in z-axis, is: Here, it is convenient to proceed to the new integration in addition, to a new coordinate system: 2 ; ; 1 After that, the induced charge density expressed in dimensional units transforms to the equation: .The polarization charge moving relative to the absolute coordinate system, in accordance with the Lorentz transformation, is deformed in such a way that its dimensions decrease along the direction of Total polarization charge as an space is proportional to the co the vacuum susceptibility integral over the entire nstant of interaction g and 1 The total polarization charge does not depend on the particle velocity that we can interpret as the law of conservation of charge.
We can find a scalar potential for the motionless ce from sourthe expression: within an accuracy of a charge sign: kr kr (27) The polarization for the electron is similar to that of the proton   , e n c e n c e n r r r They only differ in the r characteristic wavelength and .The main feature of the solution for the pola is an absence of divergenc that leads to the finite value of the particle energy.
Non-homogeneous Equation (23) defines two parameters: the polarization charge q and the radius of a localization In order ine vacuum parameters, we require that the polarization charge, both for proton and electron, be a source out of a potential energy well, which the source creates for itself: charge ; , c e n r .to determ equal to the electron charge, whereas the particle energy must be equal to the ionization energy of ; .
By adding the definition of the fine structure constant    to the latter equations, we obta the equality It follows that the point source with the interaction polarizes vacuum and induces charges with dimensio , c e for electronic and , c n r nucleonic modes.The electric field energy for both proton and electron is equal to , c e e r and to 2 , c n e r , correspondingly, and it turns out to be 137 times less than the energy related to the electrical polarization.We should notice that the solution for the polarization (28) is formed by three modes of normal vacuum oscillations , , pa In this case, the general solution of Equation ( 22) consists of a rticular solution (28) and two fundamental solutions of the homogeneous wave equation: The characteristic feature of the solution above is that In a general case, the solution for the polariz wave packet moving with velocity should have a soliton form ation for a v : A similar property is natural for the solution of a onedimensional D'Alambert equation that fulfills the condition of deviation from a state of equilibrium for a flexible infinite string     , u x t u x ct   anging the form .A possibility of motion without ch is directly connected lin to a ear excitation spectrum in k-space k ck   .For twoand three-dimensional cases, the solution of the D'Alambert equation substantially differs from the one-dimensional one.An excitation generated in some point starts sp ensional D however, are Nevertheless, a single quantum, w stant star can cover million years without spreading dispersion.After colliding wi on the Earth, the light quantum transfe st ws that it is impo reading (propagating) at velocity c in the form of concentrated circles for two-dimensional case, and in the form of concentrated spheres for the three-dimensional case.The propagation of radio waves strictly follows the three-dim 'Alambert equation, which proceeds from the Maxwell equations.Radio waves, a multiquantum process.
hile having wave properties, yet behaves like a particle.The thing is that a light quantum radiated by an excited atom at a di th a similar atom rs into a similar ate of excitation.Therefore, there must be a solution of a soliton type for a light quantum in the form (34), which gives the origin of ray optics.
Analysis sho ssible to obtain such a spectrum in a three-dimensional isotropic space for one order parameter.Following strictly the terminology, we should consider electromagnetic oscillations as coupled oscillations of a two-component order parameter in the form of an electric and magnetic polarization of vacuum.
Suppose a magnetic polarization with the same Hamiltonian, as that for the electric polarization ( 7) is possible to appear in vacuum: We define a magnetic order parameter, as well as an electric polarization, through the sum of the elementary magnetic moments: Practice shows that electric and magnetic dipole moments create, correspondingly, electric and magnetic fields, similar in configuration: It follows that for a similar distribution of the electric an , d magnetic polarization, electric and magnetic fields will be similar as well.We can reduce expressions (36) to the form: Here 0  is the potential Coulomb function for a unit source 0 1     r r .Under an arbitrary distribution of the electric and magnetic polarization, scalar potentials (37) acquire the form: It follows that the sources of the electric field are the electric charges defined by the relation 4π e div    P , whereas the sources of the magnetic field are the magnetic charges defined by the relation 4π div . As a result, the electric and magnetic fields m tions: Energy of the electric and magnetic fields turns up to be 137 n that of the electric and magnetic polarization, correspondingly.The configurations of the electric and magnetic fie times less tha lds are similar under the similar distribution of the electric and magnetic polarization.For example, if we create a homogeneous electric polarization in a full-sphere, then it causes generation of the depolarizing electric field inside the sphere P 3   E P ; for a sphere is therefore, the depolarization coefficient equal to 1 3 .The situation is the same with a spherical magnet: 3.   H M he long-r Generation of the magnetic field also leads to t ange Coulomb interaction the normal oscillations: We can define the between ., , , , , From there we obtain the combined equations for a plane polarized electromagnetic wave: x y By sett lutions in the form: ing up the so we can obtain the system of equation s: The compatibility condition for the Equations (42) leads to the equation: This gives the spectrum of normal oscillations: After that, the solutions for the electric and magnetic polarization transmitting with the light velocity reduce to the soliton form: ; We proceed from the supposition that the electron radiates a light quantum; then from a wide ra ble solutions we should choose a solution compatible the light quanating along z-axis has a vector k z , we can specify a Fourier-harmonic k z from the scalar tial (27) which defines the field of the el cylindrical coordinate system, the Fourier-harmonic for th nge of possiwith the own field of the electron.Since tum propag wave potenectron.In the e scalar potential becomes: ere H 0 K is the Macdonald function.We express the electric polarization along the x-axis as .
x P x    Thus, for a plane-polarized wave compatible with the field of the electron and fulfilling the system of Equations (40), we obtain the solution for the electric polarization: This solution is a quasi-one-dimensional infinite monochromatic wave propagating at the light velocity along the z-axis and interacting with the similar magnetic polarization y M .In the transversal direction, the monochromatic wave (43) is localized with the dimension equal to the wavelength, since the Macdonald function at big values of argument approximately equals: This precisely corresponds to the experiment, as it is impossible to localize a light ray more than the light wavelength.
Therefore, from the values, which we consider damental , we go over to the set of values, w as fun-, , , , Wave equations can only be applied to the material medium having definite dynamic properties, so the idea of physical vacuum means that the entire infinite space is filled with a definite matter.The particles that we observe-electrons, protons, photons-these are excitations of vacuum in the form of wave packets, which are eige nd oscillation amplitude; specifically for the electric polarization, we define the amplitude by the electric charge.For a multi-component order parameter, the form or symmetry of oscillations is important.In this co t have independent meaning.Researchers introduc d the values of mass and charge, as well as Planck cons nt for particl harge quantization and existence of Planck constant are the consequences of correlation effects related to discreteness of physical vacuum.Now it makes sense to study the concept of mass for a wave packet.
From practice we know that, if we describe the particle oscillation spectrum with the expression: nfunctions of the united system of twelve equations.From the point of view of wave mechanics, we can characterize a wave packet with energy, momentum, angular momentum a nnection, the concept of a particle mass does no e ta es, in different periods of time and so far, they have considered these values as independent ones.As we showed above, c then the particle velocity is equal to the group velocity: If we express the wave vector k from (44) through the group velocity, we obtain the value of frequency in the form: Multiplying terms of (45) by  , we come to the relativistic expression for the particle energy: The expression for the particle mass 2 0 m E c  follows from the latter Equation (46), the concept of mass being not necessary if we specify velocity in terms of light velocity.
The examples given below illustrate how to express some known values in terms of vacuum parameters: De Broglie wavelength: .
Here we have to consider k, the particle wave vector, as a quantum number Compton wave independent of vacuum parameters.length: Classical radius of electron: c e e r c , , We can express Rydberg constant through v cuum parameters: It follows from the above expressions that fine structure constant characterizes not only the fine structure of the hydrogen atomic spectrum but the entire lengths hierarchy of the quantum mechanics as well.It is easy to see that characteristic lengths form a geometrical progression:

B
All the lengths contain neither Planck onstant, nor mass, nor charge of electron.In this connection, it makes se hrödinger equation through the natural parameters of physical vacuum.
The Hamiltonian for the Schrödin hydrogen atom looks like this: In this expression, we take the fundamental constants s of en atom (47, 48), as indepen ent; however, as we demonstrated above, none of these constants ought to f the Hamiltonian of the electron in the nuclear field of a hydrogen atom in a different form: Here, it is convenient to use the dimensionless length .We express the energy in terms of the electron rest energy , c e eg r : The particle velocity is equal to the group velocity of the wave packet

 
exp ikr ; we express the eigenvalue by the equality: 2

k  
Now we find out the Bohr quantization conditions for a hydrogen atom.The circular motion an atomic nucleus is defined by the equality of centrifuga of electron around l and centripetal forces: Bohr assumed a quantization of adiabatic invariants: For the circular motion, the latter relation reduces to the form: ; It follows from ( 54), that we can specify the wave ve   ctor of a scattered light by the relation: Here  is the angle between vectors v and  k ; be- sides, there is a length parameter r that, scientists had only to examine the properties of electron responsible for light radiation and absorption in a quantum way.Albert Einstein, however, considered something different.Since we can observe light quanta, then light is quantized due to existence of quantum of action; "Why?" being quite inappropriate here since physical mechanism for quantization of action just does not exist.We can only say that these are the properties of spacetim ta, a planetary for the radius of photon orbi 1 .After that, the photon energy reduces to the form: . We can obtain such an energy as follows: use the solution for the electron polarization in the form (28), set it up into Hamiltoinfinity to the ra-nian (7) and integrate over space from dius r  .Therefore, th fi n is the same tak that all particles can be considered as excitations o lutions of the unified system of equations for coupl e nature .By radi of atin el g pho ds for photon and ton, an electron electro es off some part of its polarization coat, the intrinsic energy of the electron being reduced.

Gravitational Optics
In the previous part we showed f physical vacuum; they are the so ed oscillations of the multicomponent order parameter   , P M .That is why we can be sure to a certain degree that all particles similarly contribute to the gravitational interaction, particle energy being the interaction parameter.Now we write down the standardized form of the Hamiltonian for a particle in the gravitational field caused by a massive body of mass 1 m   ; .
re He g r is the gravitational radius w vitational potential of a massive body.For an arbitrary potential, the Hamiltonian has the form hich scales gra : In general case, particle en fined by the following expression: In addition, particle velocity equals to From the coordinate system   , , , x y z t uation (58)-t we proceed to o a new mo-a new time t ct  and, in Eq mentum c  p p; then the particle velocity does not depend on the chosen scales of length and time, but be-comes a dimensionless value expressed in terms of light velocity: The second equation that defines the particle motion in the gravitational field looks like this: By taking into account equation ( 6(60), we can rewrite 1) as follows: The second equation in (66) can be after that we obtain the integral of motion corresponding to (66) integrated easily; the momentum conservation law: At the beginning, we consider a circular motion: . Then, the first equation of (66) leads to ; , This exactly coincides with the results of Kepler's problem, the first space velocity on the orbit of radius r being equal to Consequently, the first space velocity attains to the light velocity at .exp .
From the system of equations (70) we obtain the equation that combines 0 r r    and r : and new parameters of the problem: We examine the situation when the radial velocity at ng point is zero.It follows that 0 0 v v   ; after this, Equation (71) acquires the form .
Here, the parameter  rbit.e grav

Mer defines a deviation from the circular motion in an o
We a to the Solar system.Th itational radius of the Sun eq ius of cury orbit is 0.5 × 10 8 km, the ra pply the Equation (73) uals to 1.5 km.The radius of the terrestrial orbit is 1.5 × 10 8 km, the rad dius of the solar sphere is 6. 96 × 10 It enables to obtain the orbit path (74) We can find the complete revolution of th the path from e condition: Consequently, the angle gain over one revolution of the path is The century displace ent of the Mercury perigee means that while the Earth makes 100 revolutions around the Sun, the Mercury makes the number of revolutions equal to m   . From here we obtain The value   is the eccentricity cury elliptic orbit.
From (75) we can obtain the en an elliptic orbit transforms into a parabolic path: 1 2 0.
of the Mer condition wh It follows that the second space velocity is a little less than that of Kepler's problem and is equal to Further, we consider the motion of a photon or a neu-trino in a gravitational field.In this case, for the equ of sume ) ation motion (71), it is necessary to as In order to ca Integral ( 79) is divergent at 1   .It proceeds from the fact that at the gravitational radius a photon has a stationary orbit.For 1 it follows ion of a light beam mov that the deviat ing, for example, along the Sun surface is .The only stationary orbit for a photon is 0.86 g r r  that corresponds to the parameter 1.
  Th ation from unit m n either photon getting off a statio n determine from the integrals of motion (68).Under the given input conditions of the coordinate and ve ocity directed along th from the e slightest devi akes a photo leave for infinity, or fall down to the centre.Figure 1 illustrates a nary orbit.Now we study a radial motion which we ca l e radius, and by using the integrals of motion (68), we obtain the energy of a photon moving away centre: It follows that the photon crosses freely the gravitational radius and at the infinity the photon energy equals to: The radial velocity of the photon remains constant: ; ; 1 .
The velocity of particles with non-zero mass is defined by the equation: From (82) we can define the second space velocity: it follows from (83) that at the initial velocity any particle crosses freely the gravitational radius and leaves for infinity.Note that the first spac equals to e velocity 1 v .

 A circular orbit is steady under dition that
From the equation the con-  66), we can measure time in terms of any periodical process that occurs in the Solar system; for example, in terms of revolution of the the Sun.Further, since we can calculate the periods of re Solar system runs similarly.Moreover, we extend the time over the entire visible part of the Universe; an are quite right when we measure time in billions of years, w ly and straight until no force is applied.Following Galilee, we can say that under the same initial conditions in the gravitational field all particles move along the same paths.For examp same initial conditions an ultra relativistic proton moves in statement that time runs differently in have any physical meaning, since eve ous sec concept that it is the total particle energy which plays the key wn to the centre and as well leaves for infinity along the curve similar to 2, 3 on Figure 1.
Since all bodies in the Solar system obey the same equati Earth around volution for any bodies beforehand, time in the entire d we hereas we measure distance in billions of light years.Therefore, following Newton, we can repeat that a particle moves uniform le, under the the same path as a photon does.However, Einstein's each lift does not ry electron covers the entire infinite space (33) and simultaneously interacts with all particles in the Universe.

Problem of the Dark Matter
In the previ tion we introduced the    p part in the gravitational interaction, but not the rest mass, as it is usually considered.This fact substantially changes the estimations of the matter quantity participating in the gravitational interaction.For example, the protons whose energy achieves 10 21 eV in cosmic rays create a gravitational potential 10 12 times higher than that for protons on the Earth whose energy is 10 9 eV.The situation is similar for neutrino.The mean energy of neutrino emitted by neutron beta decay is about 10 6 eV; whereas zero energy of neutrino, which we usually take into account for gravitational interaction, is estimated by value of 10 eV.Consequently, neutrino contributes into the gravitational interaction 10 5 times more.Photons having zero mass are not considered as carriers of the gravitational interaction at all.Deviation from the straight motion for a photon is caused by the Einstein deflection effect.This point of view contradicts elementary physics.The thing is that, if two bodies exist at positions 1 r and 2 r , and interact according to the law   U  r r , then their momenta 1 p and 2 p follow the equations then, as a consequence of (84 -85), follows the law of total momentum conservation: Thus, the distortion of the trajectory for a photon passing e.g. the Sun shows (demonstrates) the variation of its momentum; it follows from the law of the total ntum of the Sun ake an obvious momentum conservation that the mome changes by the same amount.We can m conclusion: if a photon is attracted to a massive body, then the massive body is attracted to the photon to the same extent.Therefore, photons, like any other particles, participate in the gravitational interaction, interaction intensity being proportional to the proper intrinsic energy of the particle: . The azimuth velocity of stars in galaxies is about 100 -200 km/sec.That is why, the dark matter elements belonging to a certain galaxy at first sight may seem to have the same velocities.Hence, all relativistic particles, such as photons, neutrino, and cosmic rays, are beyond our consideration; as a result, practically none of the observed particles can create an additional gravitational field.In this connection an idea arises that there are heavy cold particles contributing only to the gravitational interaction; they are called dark matter.
However, a possible alternative point of view exists.First, we examine a simple example.A charged ion of a hydrogen atom creates a Coulomb potential where localized states for an electron are formed.Filling up one of the localized states makes the hydrogen atom electrically neutral, as the nuclear ompletely screened by elect .On the other hand, if metal where there is a sea of free field is c an ron we insert a proton into a electrons, the localized state does not occur, but this time the nuclear sc free electrons.The trajectory of each electron is distorted near the nucleus so much, sult, electron density increases exactly to t Any heavy body attracts all free particles space by the gravitational interaction in a Coul as stem inst field is reened by that, as a rehe same extent and it screens the nuclear field completely.A positive charge interacts with all free electrons of metal in a Coulomb way and attracts them.
of a cosmic omb way well.Nevertheless, there is a significant difference between these two processes.Free electrons of metal are attracted to a positive charge, begin repulsive from each other, as a consequence, the electrical field of the positive charge is screened by electrons.The situation is quite opposite with the gravitational interaction.A massive body attracts particles from the surrounding space.Due to this attraction the total gravitational potential increases, thereby increasing the particle attraction even more.A positive feedback or antiscreening arises that can lead to the sy ability.As an illustration, we examine the both situations: screening of an electrical field by free electrons in metal and antiscreening of a gravitational field by free particles (any) in cosmic space.
An external charge with harmonics defined as a sum of external and induced charges: We can express the induced charge through the polarizability of electrons in metal ; TF k is a characteristic wave vector calculated using a Thomas-Fermi approximation [9].As a result, we obtain Here B F k is a Fermi momentum in metal.It follows from (88) that a Coulomb potential of a point charge q , for example, is transformed into a screened potential:   ; e x p .
Now we consider a situation rather close to the gravitational interaction.Suppose, the entire space is filled up with neutral particles that have some homogeneous density 0  and interact according to the law of gravitation.
If any density fluctuation  occurs in the space, then, owing to the gravitational interaction, all other particles begin to adjust to this density; there-after we can re-write the real density in the form: On the analogy of a free electrons susceptibility, we imagine a gravitational susceptibility . Here 0 k depends on the value of 0  and on the distribution function of the particle velocity.Afterwards, the real density acquires the form: Being on Earth, we have no possibility to scan the distribution of a total energy over the entire space.However, judging from the fact that the azimuth velocity of stars moving away from the centre of galaxy remains nearly constant, the total gravitational potential must have the form: Here  is a dimensionless parameter, -a gravitational size of a space belonging to a ce n g .From the expression for the potential and with the aid of the Poisson equation we obtain the space distribution density of matter: . 4π The space integral of density provides a value of mass inside a sphere of radius R : For our Galaxy having the size of about light years and velocity of .
, therefore, mass of a relativistic matter is comparable with that of the cool one . Thus, as a result of the trajectory distortion for relativistic particles, an additional nonhomogeneous distribution of relativistic matter occurs and, consequently, an additional gravitational potential as well.That is why, there is no need to search for a mystical dark matter; relativistic energy is quite sufficient to create an additional gravitational field.Moreover, emission of radiation by stars and galaxies as well as supernova outburst lead to the contional field.Since azimuth and radial motion follows from the general equation of motion, for example in form (63), the radial motion is submitted to the same additional gravitational attraction; for this reason, there is us, if red shift is related to recession of galaxies, then a contradiction arises, because galaxies have to scatter with acce dependence of physical vacuum parameters.Since atomic levels are proportional to Bohr energy, and Bohr energy, in turn, is proportional to the rest energy of electron stant growth of relativistic energy in space.So, observations of the azimuth stellar motion both in galaxies and galaxies in clusters point to the existence of an additional gravita no dark energy to create antigravitation [10,11].Th leration but, judging from the azimuth motion, this is impossible.
It is more natural to consider atomic spectra of far stellar radiation to be time dependent as a consequence of time   moment it equ on the Earth, is still being observed on Jupiter satellites.It is known t Jupiter emits twice as mu the Sun.We can express the Jupiter em the Hubble constant.From the law servatio energy it follows: The red shift indicates that the Hubble constant is a monotonically growing time function and at the present als to 2.5•10 −18 sec −1 .Nowadays the Universe is in a metastable state, energy emission transitions occurring in two opposite directions.On one hand, nucleosynthesis of light nuclei-takes place, which is the source of stellar energy.On the other hand, nuclear disintegration of heavy nuclei (natural radioactivity)-occurs, as well with energy emission.From today's point of view, nuclear fusion looks quite natural as there is a binding energy between nuclei; moreover, the binding energy on one nucleus increases with the growth of atomic number up to iron.Creation of heavier elements turns out to be less gainful; in this connection it is a surprise that heavy elements, up to uranium, exist on Earth.Nuclei of uranium are in metastable state.If we launched a piece of uranium towards the Sun, the uranium nuclei, under neutron bombardment, would decompose into lighter fragments.This means that uranium cannot occur on Sun.Deposits of uranium on Earth, however, prove that the Earth is an earlier formation than the Sun.Chemical composition of the Earth principally differs from that of the Sun.Sun consists of 75% hydrogen, 24% helium and a negligibly small amount of heavier elements, whereas Earth consists of 32% iron, 30% oxygen and a noticeable amount of heavier elements up to uranium.Heavy elements existing on Earth, as well as the red shift, point out to nonstationarity of physical vacuum parameters.Heavy elements could only occur on Earth when they were energetically gainful; variations of physical vacuum parameters led to the transition of heavy nuclei into a metastable state.A further evidence of nonstationarity of physical vacuum parameters is that not only stars, but also planets emit energy; moreover, volcanic activity, similar to that ission via Here Here J l is specific luminosity of the Jupiter which is equal to 3.6 × 10 −26 sec −1 .Taking into consideration the definition of the Hubble constant (90), we can re-write Equation (92) as follows: All values at the right part of (93) are known, therefore, It can be seen from this expression, that the eigen frequencies of electron and proton vary practically with the same rate, with their values approaching each other.Let us present, for the illustration, a table of a specific luminosity of a number of objects (Table 1).
Table 1 shows that the specific luminosity of the Sun is maximum, which is natural due to thermonuclear fusion.The specific luminosity of Jupiter and Saturn are the same, due to their similar composition of light atoms of hydrogen and helium.The specific luminosity of the Earth is much less than that of Jupiter.This can be attributed to the fact that the Earth is composed of heavier elements, and its nuclear energy is determined not only by the energy of the protons, but the binding energy between protons and neutrons.
So, the red shift shows that the rest energy of the electron is growing with time, whereas emission of radiation by planets indicates that the rest energy of the proton is decreasing.The total change of the energy for the elecand proton is so great, that it lead emission of radiation.ce phy eternally, th an only be of tw .At the present mo electron and nuclear freque re moving towards other.Finally, we pay attention to one more mechanism of a gravitational i be eas, the electri ment each nstability.Not coincidentally, there has en some cause for concern so far, that microscopic black holes are possible to occur under the experimental research with Large Hadron Collider in CERN.The thing is that the gravitational attraction between particles grows with increasing particle energy, wher cal repulsion remains constant due to the law of conservation of charge.In this connection we examine two protons which are speeded up to the certain energy in an accelerator.We write down the Hamiltonian for two protons, taking into account an electrical and gravitational interaction: Since masses of the particles are proportional to their energy why the mi oscopic black les are im to appear in the accelerator.From the expre for the critical energy, w define the specific wa vector and the correspon g de Broglie wave length: aximum particle energy in cosmic rays reaches 10 Thus, the considerations above allow attaching a physical sense to the Planck length, which defines the most probable value for the lattice constant of physical vacuum; here c k specifies the edge of the Brillouin zone ink space, and c  -the width of the allowed energy region.

Conclusion
ptics and dark ma or the vacuum.The vacuum is represented as a three-dimensional crystal lattice matter with a very small lattice period, much less than 10 −26 cm.The oscillarges to a system of twelve equations.We have obtained the combined equations for a multicomponent order parameter in the form of the electric and magnetic vacuum polarizatio acuu waves and the spectrum of elementary particles as well.Namely we come to a unified field theory.We have obtained the combined equations for a multicomponent order parameter in the form of the electric and m um polarization, which defines the spectrum and symmetry of normal oscillations in the form of elementary particles.We have restored the fundamental parameters of physical vacuum, such as: susceptibility fo f fine structure), parameters of length and time for the electron and nuclear branches of the oscillations, correspondingly.We have shown he charge quantization is directly connected to discreteness of vacuum co co opole.Elementary particles are excitations of vacuum in a form of wave packets of a soliton type.We e obtained an exact equation of motion for a particle in a gravitational field.En he e infinite space according to the cosmological principle.In this case recession of galaxies is impossible; therefore, itted by far galaxies must be In presented paper we try to consider problems of the gravitational o tter developing from the crystal model f tors are located at the nodes of an infinite lattice.It is shown that an infinite set of equations to describe the coupled oscillations of moving oscillators conve n, which defines the spectrum and symmetry of normal oscillations in the form of elementary particles.Thus, our model for v m is represented as a material medium in which dynamical properties of the crystal specify the spectrum of elementary particles.As we can see from the consideration presented above, the new theory allows describing with a single point of view both the electromagnetic agnetic vacu r the electric and magnetic polarization (equal to the constant o that t nsisting of particles with the interaction nstant equal to the double charge of a Dirac mon hav ergy defines both gravitational interaction and particle inertia, inertia being of an anisotropic value; that is why the statement, that the inertial and gravitational masses are equivalent, is not correct.We have examined the situation w n galaxies are distributed over the entir the red shift of radiation em interpreted as the blue time shift of atomic spectra.As a consequence, it follows that both rest energy and mass of electron are increasing now.Since physical vacuum exists eternally, vacuum parameters can be either constant or oscillating with time.These are time oscillations of    

A1. Determination of the Order Parameters and its Conjugate Forces
In the study presented in the paper above and in attempt is made to create a non-loc ], an scribe elementary particles, which should be taken as the elementary excitations of a particular environment, which is the physical vacuum.Since the discovery of the sibility pos of creation of particles and anti-particles in the vacuum, it became apparent that the vacuum is not empty space, but the environment with specific dynamic properties.It follows from this that there must be an absolute coordinate system tied to the medium (which is the model of vacuum as the three-dimensional rigid crystal lattice structure) in which the photons as excitations of the medium, propagate with the speed of Einstein's postulate that there is no absolute coordinate system is flawed.Therefore, the second postulate of Einstein's that the "speed of light is independent of the source," is wrong.This situation occurs precisely when the l is the excitation of the medium, the dynamic pro-zation: Here,   ,t P r the electric polarization of the vacuum, and the quantity   ,t  r determines the density of the electric charge and is a quite standard definition.Expression (1) is not an equation, but the condition for the onset of the charge density.In the expression (1) a vector   ,t P r is an order parameter, which consists of three arbitrary functions: e parameter r The density of the electric charge,   ,t  r in turn, generates a force, conjugate to th order   ,t P r , which is called the electric field E .It is possible to recover the electric field distribution for an arbitrary distribution of the electric charge density.From the Coulomb interaction between point charges: we get: signa perties of wh speed of sound radiated by the flying aircraft, is not dependent on the aircraft speed v .Notice that the relative em d ; , from which follows the interaction energy: c v  , and for the wave radiated back, the relative velocity is c v  .Mathematical equations have the property that if two physical processes are subject to the same equation, the solutions of this equation after renormalizetion of parameters apply to both the first and to the second physical processes.The main feature of any oscillatory process is the existence of equilibrium points, deviation from which induces an oscillatory process.Actually, these points of balance represent the absolute coordinate system in which the excitations, such as photons, travel at the speed of light.Therefore, the following postulate of Einstein "the speed of light in any inertial frame is the same", contradicts the previous postulate.It should be noted that the Lorentz transformations have appeared before the theory of relativity, and they have brought out to explain the negative result of the Michelson experiments for the coordinate system associated with the Earth, which moves relative to the absolute coordinate system tied to the physical vacuum.In the present work it is shown that the electron cloud of the charge moving relative to the absolute coordi ate system is indeed deformed in strict accordance with the Lorentz transforma-The ssity to introduce the well-defined order parameters for the vacuum environment follows from the terminology that we use.For example, in an electrically insulating medium, which is the physical vacuum, the electric charge can only be the result of vacuum polari- In addition, from the relationships (4) we have an equality: which is included in the Maxwell equations.However, this is nothing more than a definition for the average density of a set of point charges.From (6) it does not follow neither the character of the Coulomb interaction, nor the interaction energy.Actually we use expressions (3 . For example, in the theory of elasticity the strain tensor is the order param returning the system to the equilib-) -( 5), from which, after summing over all the charges we obtain both the electric field configuration and the interaction energy.
In the study of any dynamical system, is necessary first of all to determine the order parameter and its conjugate force eter and its conjugate force is called the stress tensor.In equilibrium, the strain tensor is related to the stress tensor, as a result of the total energy can be expressed either through the strain tensor, or through the stress tensor with help of the coefficient of elasticity.In dynamic processes, the equation of motion can be written only for the strain tensor (the order parameter), and the stress tensor is decomposed into its own force, rium, and the external force, being determin exter for t ls reaction.Therefore, it is first necessary t rameters associated with these here.If the electric field is generated by the harge, then the electric charge in an electrically neutral environment can only be generated by the electric ed by the nal conditions.The equation of motion he stress tensor cannot be written.
In electrodynamics, the electric and magnetic fields determine the force field, so this field Maxwell called the stress tensor.By introducing the force field, the force itself cannot exist on its own, because the force has to be applied to something, as the action equa o determine the order paforces.There is not arbitrariness electric c polarization.In ("The Classical Theory of Fields" by L. D. Landau and E. M. Lifshitz, A Course of Theoretical Physics, Pergamon Press, Vol. 2, 1971) it is stated that onsistent.For example, the theory of relativity requires that the charge of the electron was a point-like, bu charge has an infinite energy.Obviously, it is necessary to charge cannot be point-like.The equation of motion for the force field canno duce an additional force, then e charge-is a localized formation.Th that classical electrodynamics is internally inc t the point reject the requirements of the theory of relativity, since the t written, as if we introffects of self-interaction would lead to the internal contradictions.Thus, the equations of motion for the electromagnetic wave can be expressed only by the order parameters in the form of the electric and magnetic polarization, but not by the both force fields, electric and magnetic fields.
On the other hand, quantum mechanics implies that the free electron-is the plane wave, which is also false, since the electron erefore, from the viewpoint of wave mechanics elementary particles have to be considered as stable wave packets with a well-defined spatial distribution.
The first attempt to associate the field character to the electron energy is related with the introduction of the classical radius of the electron charge in the form: are considered as fundamental and independent variables.However, this is not the case.Neither of these units is neither basic nor independent.The fact that from quantum mechanical expression for the electron energy The physical meaning of the Planck constant remained unclear despite the fact that this term Planck introduced more than a hundred years ago.However, from the point of view of the existence of the vacuum medium (which is based on the rigid three-dimensional crystal model), the physical meaning is easily recovered, if in the expression (9) for the electron energy the Planck constant is expressed in terms of the electron charge e and the fine structure constant  in addition, exactly the same relationship holds for the proton: These last expressions for the en and proton acquire a quite transparent physical meaning.Th get that energy consists of two parts: ergy of the electron e fact that the electric charge is related not only the energy of the electric field, but also the energy of the electric polarization, which induces the charge.As a result, we The first term determines the energy of the electric field, and the second term-the energy of the vacuum polarization, and the quantity  characterizes the dielectric susceptibility of the vacuum.
For certain classes of solutions, Equation ( 14) can be written as: where characterizes a localizat The last expression shows that under the condition r ion of the charge e .
1   the energy associated with the polarization becomes greater than the energy of the electric field.Comparing the second term in (15) with ( 12) and (13) for the energy of the electron and the proton, respectively, we see that these expressions are consistent, if we assume that the polarizability of the vacuum is the fi constant: ne structure 1 137     .e energy of th Thus, th e electric field is 137 times less th e ia and Wave Properties of Electrons an the energy associated with the polarization of the vacuum.
Dirac has raised the question of the need to understand the physical meaning of the fine structure constant.In this paper we show that the fine structure constant is a fundamental characteristic and determines the susceptibility of the vacuum.

A2. About the In rt
It looks like there is a myth about the equivalence of inertial and gravitational masses.Since misunderstandings ss, it makes sense to consider the inertia and the wave properties of electrons on the example of the hydrogen atom.Consider the Hamiltonian o an arbitrary potential as with the problem of equivalence of inertial and gravitational ma f a particle in from the conservation energy law we have:

 
, p     p then Equation (17) can be rewritten as follows: which yields the Hamilton motion equation: The ( 20) is valid for any particle and any extern l potential.In the particular case of an electron in t he nuclear field, the Hamiltonian has the form: Here one can get rid of the notion of the mass of the electron and go to the expression, reflecting the wave properties of the electron Since we are interested in the frequency spectrum of th 2) by , then select the frequency e hydrogen atom, then, in accordance with the theory of self-similarity, we must select the characteristic frequency of the problem, and then all the other compo-nents can be represented in a dimensionless form.Let  after which the Hamiltonian takes the form, which is displayed in the peer-reviewed paper: which implies that the entire frequency s hydrogen atom is determined solely by its principal electro quency pectrum of the nic fre 0,e  and the fine structure constant  , and  -is the in fundamental quantity that determines the susceptibility of vacuum on here, he Planck's constant.The velo term ma nor t . There is no mass of the electr city s of becomes also dimensionless and is expressed in the speed of light.This is because the Planck constant and e mass of the electron and th the proton are determined by the electron charge e , which actually determines the amplitude fluctuations of the order parameter in the form of electric polarization of the vacuum, and for a system of harmonic oscillators frequency oscillations does not depend on the amplitude of oscillations, which is reflected in the expression (24).The velocity becomes also dimensionless and is expressed in terms of the speed of light and can be expressed in terms of the group velocity of the wave packet: iltonian (24) are as follows (the primes in (24, 25) can now be om The equations of motion (20) for the electron in the nuclear field with the Ham itted): From the first equation, the wave vector k can be expressed in terms of the group velocity of the wave packet-v : after which the second Equation (26) transforms into a form which can be expressed in two different ways ) v which are reflecting the inertia and the wave properties of the electron.
From Equation (28) it follows so it can be seen that the acceleration in the direction perpendicular to th In this case, the particle inertia is proportional to the energy.However, in the direction along velocity   v v   , the acceleration is proportional to the factor    , which implies that the inertia is growing faster in the direction of motion than in the perpendicular direction.
The inertia of the particles is the easiest checked on the accelerator.In the ring accelerator, the centripetal force required to keep the particles on a specific trajectory, increases proportional to the factor 2 1 1 v  , therefore, in this case inertia is proportional to the energy.In a linear accelerator, the equation of motion for a particle is as follows: Thus, the inertia of the particles (inertial mass) is the magnitude of the anisotropic, while the gravitational m in time takes the form: ass (energy divided by 2 c ) is a scalar quantity.The wave properties of electrons can be easier analyzed using Equation (29), which after differentiation we arrive at the equation: Multiplying both sides of (38) by r and taking into account that r v     , we obtain the following eq uation: with help of (33), we obtain: The Bohr quantization condition should be added to Equation (40), which he wrote down in the form of quantization of adiabatic invariants: For the circular motion, the relation ( 40

Pl
. Therefore anck's constant has nothing to do with formation of stationary orbits in the hydrogen atom.Solving Equations (32) and (36) we obtain: 2 2 , 2 ; 1 Open Access IJAA

E. V. CHENSKY 460
As a result, the frequency spectrum atom that follows from the Ham form: of the hydrogen iltonian (16) takes the 2 0, Wherein the spectrum depends electron frequency and the fine structure constant-susce only on the intrinsic ptibility of vacuum,  .The term "the fine structure constant" is not appropriate, since both intrinsic electron frequency, and the enti ectrum of the hydrogen atom depend on the quantity re sp Here R is the Rydberg constant, the expression of which had received by Bohr.However, if we recall the relation Such a monstrous conglomeration of symbols in the expression (49) shows an absolute lack of u erstanding of the nature of the wave processes that occur in the hydrogen atom, a nd nd more over the wave processes within the electron itself.Now, coming back to the energy E n n   from tor  the discrete frequencies (46), we then arrive at the expression: And these relations for hoton and electron have completely different physical meanings.
der a simple example.If we connect the antenna to the generator of electrical oscillations with frequency ω for a time interval T, then this will result in the radiation of a wave packet of length L = сТ.Now, in order to study the frequency spectrum of the wave packet, by using a narrowband receiver, we see that th s will be distributed in a certain range The solution (54) is realized for exam any wave process.For ple, if a guitar string is fixed at points at a distance L , then it results in a wave vector quantization according to (55), with frequencies , where 1 c  the signal propagation velocity along the string, depending on the tension of the string.Any player knows that the frequency of the string vibrations depends on the tension of a string and distance between the fixing points of the string.The same situation arises in the piezoelectric resonator having a thickness L , its vibrat ons may be given i e form (54) with the frequencies i n th , where s c -the sound vel ity in the piezoelectric.Thus, the restriction of the signal in time leads to th uncertainties and restriction of vibrations in space leads to the quantization of the wave vector and the vibrations with the well-defined frequencies.Therefore piezoelectric resonators are used, for example, to stabilize the operation of an electronic clock.
A characteristic feature of linear vibration systems is that the frequency does not depend on the amplitude, therefore the s ular equation determining the spectrum of normal oscillations, does not contain the amplitude at all.
If the Laplace operator is present in the equation of motion (or a system of equations), then the solution can be conveniently represented in terms of the eigenfunctions of the Laplace operator (58) On the example of a one-dimensional string, we can see that the arbitrary force excites the entire spectrum of normal vibrations in the form (57).However, really only three normal modes in the form of spherical functions are associated with the electron: In addition, the spatial and f tions must be fulfilled: requency resonance condi- it follows then that A   .Thus, as conjectured by Planck, electron emits and absorbs light by quanta, but it does not follow from this that light is quantized, moreover, that any field is quantized, as stated by Einstein.But it is connected only specific field of the electron energy distribution in spa The introduction of vacuum parameters allows un ce.
us to derstand the physical mechanism of the appearance of the spin and magnetic moment of the electron.The fact is that the magnetic field configuration of the electron coincides with the magnetic field of the ring current.The magnetic moment associated with the charge, rotating on a circular orbit of radius r is equal to Comparing an expression (66) with the magnetic moment of the electron, that is equal to the Bohr magneton, We see that the magnetic moment of the electron charge is related to the rotation of the charge in a circular orbit with the speed of light with a size equal to the correlation radius .Consequently, the emerg ce r ence of the electron spin associated with the movement of fields in a circular orbit.
Closer examination shows that the charge rotates in the orbit with a radius 2 ce r which leads to the spin of 2  .The magnetic moment in this case is two times greater than that given by the form 66).This means that the magnetic moment of the electron consists of two components: a magnetic moment associated with the motion of the charge and the magnetic moment associated with the magnetization of vacuum.

A3. The Formation of the Energy Spectrum of the Massive Body ula (
Consider the process of formation of the energy spectrum of massive bodies, consisting of a certain set of quantum particles.Ignoring the interaction between particles the energy of a can be represented as massive body the sum of the energies of each of the particles: Convenient to go to the four-dimensional coordinate system of the same dimension , , , , x y z t where t ct  .In this case, the velocity of the particle d dt  v r is a dimensionless quantity and is expressed in units of the speed of light, then the energy of elementary particles can be written as: For massive body can be considered that the velocities of all particles are the same and then i v v  .The total energy and total impulse can be written as: Using the defi Despite the fact that (72), (73), (75) have a relativistic nitions of zero energy and total momenview, speed in them has a different physical meaning and tum of a massive body (72) and (73), we can write the expression: is defined as the velocity relative to the absolute coordi- Whence it follows that the energy spectrum of a massive body has the form: nate system tied to the medium-p presented as the model of the three-dimensional rigid hysical vacuum which crystal lattice structure.


 and parameters of time , e n   for electron and nucleon oscillations, correspondingly.Energy of elementary particles has been expressed in terms of the fundamental vacuum parameters, light velocity being equal to sense to specify a dimensional value for the electric polarization in the terms of the electron charge: we can see that the characteristic dimension of the polarization charge is a definite val ual to the correlation radius or the Compton length of electron: can see that the vacuum polarization results in decrease of the source energy by 0 U , both electronic and nucleonic m e fo for both electron and proton, covers the entire infinite space and oscillates synchro-The solution (33), howev ontains a substantial disadvantage: such wave packet cannot move in pace, it is a typical standing wave.Impossibility of motion is ca s used by the fact that the phase velocity of different har- Now we show in what way the inten the electric and magnetic polarization provides the solution of the soliton type.We add the interaction energy of currents t raction betwee o the Hamiltonians (7) and (35) in the form: connection with this, we must change the concepts of mass and matter.
fact, that rela-ver into cons 5) and (6) define the spectrum of a particle, we can reduce combined Equations (54) to the form: the electron mass, but by the space and frequency resonance for the wave packets; scattering being submitted to the same formula (55) with the Compton length   It follows that the scattering characteristic is defined neither by the Planck constant no , upon this equation, Albert Einstein affirmed that the inertial mass and the gravitati uivalent.This statement, however, is incorrect.An accurate eq (63)It follows, that particle inertia depe of e intrinsic (internal) energetic properties of a particle are lost in the equation of motion (63).This the obtained equation to any relatively compact object.It ca ectron, a p all the g in min ng mass are eq uation of motion (62) is transformed to: direction motion.It is interesting to note that th means that we can apply n be a planet, a satellite, an el roton, a photon, a neutrino-same.Bearin d (60), we reduce (61) as follows: equation we obtain the integral of motion in two different forms: (57).In a centrally symmetrical field motion develops in a plane crossing the centre of a massive body; therefo consider an arbitrary motion relative to a heavy centre.Let us assume that at time t = 0

r
In the polar coordinate system Equations (65) becomes y y y x x y y r

Figure 1 ..
Figure 1.The paths of a photon at differe tions.Curve 1 exhibits the photon leaving for infinity at the input condition nt initial condi- situation is described by the equation of motion (73) where we can consider the value of  as a

.
This causes gravitational instability of the system relative to the long-wave density fluctua .As fluctuations develop, slow ose a small part the surrounding ace and transformed into clusters of matter in form of stars and galaxies.Fast relati in creating an additional gravitational field.We denote clusters of a cool matter in form of stars and galaxie The remainder relativistic particles in form of ic rays, photons and neutrino create additional nonneous matter density due to the trajectory distorlativistic particles.Thus, the tot ensity is equal to the gravitational attraction turns out to exceed the electrical repulsion.Consequently, the gravitational collapse may occur when the particle energy amounts to value of energy expected at the accelerator in CERN is that is eleven orders less e critical value.
It is easy to see that the specific length  can be exc pressed via Planck length as follows: electron mass growth within recent 15 billion years, inducing red shift; on the contrary, pro-ton mass decreases, responsible for emission of radiation by planets.
however, have shown that the different length is associated with electron, which Compton obtained from the scattering of photons by the free elec- the Compton length can be expressed in terms of the characteristics of the vacuum environment the vacuum c and 0e  , in turn, are expressed in terms of the fundamental parameters of vacuum:

2
)Equation (35) is also displays anisotropy of properties of the electron.When consider along

2 
. We obtain a well-defined frequency to each eigenfunction, as a result, we have the spectrum of normal vibrations     .In the Cartesian coordinate s em, the eigenfunctions can be plane waves cylindrical coordinate system, eigenfunctions can be Bessel he spherical coordinate syste e employed spherical cylinder functions.The amplit mode is arbitrary and depends on external conditions.For example, the guita functions, in t m can b ude of each normal rist finger deflects a string to some distance from the equilibrium position.The initial deflection can be expanded in the eigenfunctions (54): the string was released, every normal mode begins its own motion the electron is considered as an elementary excitation of the vacuum, the dynamic properties of the elementary particles must be determined directly by the dynamic properties of vacuum.Let us make rough estimates.Let the vacuum has a dielectric susceptibility equal  , then the energy associated with the creation of the electric polarization is: equal to zero.Such fields can be excited only in the event that the external force itself satisfies the Laplace equation.In fact, ho tru u g interac we need to find out w plays the role of "guitarist" that plays on the vacuum fields.At this point we are led to the introduction of the crystal s ct re of the vacuum with particles having an intrinsic field and the correspondin tion energy: self-energy of the field for the solutions in the form (59) is infinite, and therein lies the problem of divergence for point charges.The introduction of the gradient energy with the parameter length e  and the kinetic energy of the field with the parameter of time e  leads to a blurring of the polarization charge to the size equal to the correlation radius 0e polarization charge is then determined by the relation q g   .Assuming q e  , we get g e   the Planck constant is directly related to the charge of the electron and reflects the polarization and dynamic properties of the vacuum fields, however, is by no means a universal fundamental constant.Vacuum fundam ntal .Charge, mass, energy and momentum of electron and proton, and the Planck constant are indeed expressed i vacuum e an arb n terms of the fundamental parameters of low from this that if we tak itrary scalar field (for ex y amplitude, and the quantum of light can have arbitrary momentum and the corresponding energy , but it does not folample, photon field) in the form   exp ikr , then the momentum can be quantized  p k  and then proceed to the quantum field theory.There is no physical meaning to this.In a vacuum, as a linear system, the electromagnetic oscillations can occur with an ; by an , but in the emission and absorptio conservation of energy and momentu electron the laws of m must be fulfilled: of a particle, also has dimension of energy.The speed of the particle is determined by the expression:Of the last expression can be expressed momentum of a particle and energy as follows: and we express it in terms of light velocity.Approximate expressions correspond to the case of a low velocity 1 From (52) it follows that the Schrödinger equation only contains one dimensionless small parameter  of a physical vacuum susceptibility.The fundamental function  of a free electron in Cartesian coordinates is equal to

Table 1 . A specific luminosity of a number of objects.
,