Sergey Fedosin. The physical theories and infinite hierarchical nesting of matter, Volume 2. – LAP LAMBERT Academic Publishing, pages: 420, ISBN-13: 978-3-659-71511-2. (2015).
In contrast to the first volume of the book "Physical Theories and Infinite Hierarchical Nesting of Matter", where the substantial model of particles mainly are considered, in the second volume we have focused on the construction of field theories and its application to various problems.
Since the problem of the origin of the magnetic field in cosmic bodies is still unsolved, in § 1 we presented the electrokinetic model as the alternative to the well-known model of hydromagnetic dynamo. The essence of the new approach is that we predict the oscillation regime in the charge separation within the convective shells of planets and stars. This occurs due to the phase shift in the feedback between the processes – with the maximum charge separation the electric field gradient at the center of the convective shell reaches its maximum magnitude and the matter layers with the charges with different signs are formed here. Under the action of thermal convection the charged layers of the one sign go up to the surface and not only discharge the charged layers of the opposite sign, but also recharge them. If we add to this the rotation of cosmic bodies, we obtain the corresponding periodic change of the sign of the magnetic moment and the magnetic field of these bodies. Since the magnetic field arises from the rotation of the differently charged lower and upper parts of the shells, then in the electrokinetic model there is no the problem of the magnetic field attenuation. This problem is typical for the models, such as hydromagnetic dynamo, in which the field should be created by electric currents in the matter with the resulting ohmic losses and weakening of currents.
As it is noted in , the metric is a mathematical object that characterizes the gravitational field in terms of its influence on the processes of spacetime measurements. Using metrics in § 2 we also present the acceleration field of any kind, as it is assumed in the metric theory of relativity (MTR). If the field has energy, momentum, quantization and other physical parameters, then the metric is a perfect object of geometric type, depending on the field properties. In no reference frame the energy of the particles of the ether or the physical vacuum, which are responsible for emerging of the field is equal to zero. If these particles have high penetrability, their energy is hardly noticeable and is seen only in large or extremely dense objects. Near the bodies the trajectory of test particles and waves is bending due to the violation of isotropy of the ether medium near bodies, which is described as the curvature of spacetime metric.
Based on this picture it is possible to formulate the axioms of MTR, generalizing the foundations of special (STR) and general theories of relativity (GTR). A concrete example of MTR application is the definition of the metric inside a uniformly accelerated reference frame. As it turned out in the case, the metric is the function not only of the coordinates, but also of the time. Another previously unknown feature is the reduction of visible transverse dimensions of accelerated bodies, and also not slowing down but acceleration of the rate of time under certain conditions of motion. With the help of the metric in the accelerated reference frame it is possible to obtain an exact solution of the problem of twins, one of which is fixed, and the other travels and comes back. Comparing the indications of the clocks of the twins shows that the result depends on the type of motion of the second twin, on the ratio between the stages of the way, where the motion occurs either at constant velocity or with acceleration. If in the framework of STR or GTR it is predicted that the time at the clock of the second twin is always less than of the first, then in our case the opposite situation appears to be possible. One of the consequences of this approach is proving that in contrast to the speed, the acceleration manifests itself in an absolute manner. In this case, a natural question arises about the existence of an isotropic reference frame relative to which the acceleration is manifested as the acceleration relative to the fluxes of gravitons.
In § 3 we refer to the construction of the axiomatic foundations of the theory of gravitational and electromagnetic fields and the theory for description of the matter. In Minkowski space the theory of gravitation is Lorentz-invariant theory of gravitation (LITG) and in Riemannian space LITG turns into covariant theory of gravitation (CTG). In LITG the gravitational field not only obtains the complete formula for its energy, but also the formula for the momentum and becomes a real Lorentz-invariant field. In particular, just as the charge rotation produces the magnetic field, so the mass rotation creates in the space the torsion as a separate component of the gravitational field. The torsion is necessary because otherwise it is impossible fully to describe the force of gravitational interaction between two masses in different reference frames. The summary of formulas for the torsion field is presented in § 5. From comparison of LITG, electrodynamics and relativistic mechanics with the help of STR we discover the essence of the rest energy of the matter. This energy is the absolute value of total energy of the matter in the strong gravitational field and in proper electromagnetic field in accordance with the virial theorem.
What should we now do with the Hilbert-Einstein tensor equations in GTR, if we assume the gravitational field as real in STR? How will the content of these equations change? Here it is necessary to take into account the same method, which is widely used to include the electromagnetic field in GTR. Namely, all tensor quantities should be written in the required covariant form, and only after that substitute into the tensor equations for calculating the metric. Doing it for the gravitational field in CTG, we can find the metric which changes under the joint action of the electromagnetic and gravitational fields. Now it is impossible to consider the energy-momentum equal to zero outside a single gravitating body, as it is done in traditional GTR, because around the body there is always a gravitational field, both the proper one and from other sources. Interaction of bodies appears to us as the combined effect of real physical fields – electromagnetic and gravitational.
In § 4 we compare the form of the metric in GTR and CTG outside a single massive body taking into account the contribution of the energy-momentum of the gravitational field. One conclusion is that the solution of the Hilbert-Einstein equations for the metric does not allow us to uniquely determine all the required coefficients for the components of the metric tensor. This result also follows from the solution for the metric inside the bodies in § 5 in the weak field limit. Consequently, to determine these coefficients we should involve the equations of motion of particles and wave quanta and compare them with the formulas of classical mechanics. But if in GTR the equation of motion is the same for particles and quanta due to the assumed validity of the equivalence principle, then in CTG the equation of motion for particles differs from the equation of motion for wave quanta.
The latter follows from the difference between the properties of particles and wave quanta. For example, in the propagation of the sound wave in the medium the particles of this medium are only briefly involved in the transfer of the wave and on the average they stay in the same place. In the stationary gravitational field the particles of the medium (ether) are influenced by the gravitational pressure, which can be different at different points in space. This can lead to changing of the wave speed in the space but not in the time, so that in this case the force is acting on the wave quantum in a special way. Besides for the electromagnetic waves we assume the condition that the interval is equal to zero, . With this in mind in CTG we obtain that the equation of motion for wave quanta (468) coincides in the form with the equation of motion in GTR (408). For particles in the equation of motion in CTG (407), the density of the gravitational force additionally appears which is determined by the tensor of the gravitational field strengths and the momentum density of the matter. The more general equation (324) also includes the electromagnetic force acting on the particle or the charged matter unit.
Such phenomena as gravitational and electromagnetic forces, short-range interaction of forces and the delay in their appearance, the transfer of gravitational and electromagnetic waves in space for long distances, the constancy of the speed of light and its independence on the sources of emission, the displacement currents, the relation between the wave and particle properties of the particles (wave-particle duality), the principle of superposition of fields, the mass and the inertia of bodies, the principle of inertia, the principle of relativity, the principle of equivalence of inertial and gravitational masses, the principle of local equivalence of gravitational and non-gravitational forces, the correspondence between the mass and the rest energy of bodies – all these and similar phenomena have something in common in the basis. We assume in § 5, that this common basis is the graviton ether, which consists of diffuse and dynamic components. According to the evolution of particles of the matter and fields, the matter produces the components of the ether, revealed as the action of the electromagnetic and gravitational fields, and the ether in turn by means of the forces from the fields leads to formation of larger particles of matter. The relationship between gravitation and electromagnetism, except the similarity of their field equations and of the influence transfer through the ether, can be seen in the fact that according to CTG they participate to the same extent in determining the metric in the equation (258) and in the equation of matter motion (324). In addition, in [7, § 14], in the analysis of equilibrium of the atoms in the molecules, we assume that the fast-moving electron matter in the atoms can compensate for the gravitational force, deflecting the fluxes of gravitons from the initial direction or scattering them.
The difference in the properties of particles and field quanta in CTG leads to the fact that for them the coefficients in the metric tensor are different. The metric is the function of the type of test objects and their properties. Since the metric tensor characterizes the spacetime, then the spacetime properties for particles and field quanta do not coincide completely. In particular, as shown in § 6, the dynamic time becomes characteristic for particles, generalizing the definition of time in moving inertial reference frames of STR to non-inertial reference frames. Due to the difference of the dependence of velocities of wave quanta and particles in the gravitational field, the rate of clock, determined by means of waves in periodic processes, specifies the time which differs from the dynamic time of particles.
In order to determine the constant coefficients appearing in the metric we can compare the equations of motion of CTG with the results of gravitational experiments. For this purpose, in § 6 we analyze such effects as the shift of the perihelion of planets, the deflection of light beams near massive bodies, the gravitational time dilation and the gravitational redshift. From the point of view of CTG the effect of "Pioneers" is explained as the result of using a more accurate equation of motion. Spin-spin and spin-orbit interactions of bodies are treated in CTG with the help of gravitational torsion field included in the tensor of field strengths. In the orbital rotation of test bodies around the Earth and in the transfer of test bodies with the spin in the field of the Earth, besides the energy-momentum of the gravitational field we must also take into account the metric for the body, which has a spin. Thus in CTG there is a need to solve the problem of finding the metric around a rotating body, taking into account the energy of the gravitational field and of the torsion field in the surrounding space. Apparently, this metric should have the form of the Newman metric  for a rotating charged body.
Analyzing the equivalence principle we see incompleteness or inaccuracy of the equation of motion of GTR (530), since it is impossible to describe with the help of it the reactive motion of a test particle. Meanwhile, the equation of motion of CTG (531) contains both the gravitational force and the possibility of transition to the classical Meshchersky equation for a body of variable mass.
Using the stress-energy tensors for the matter and the gravitational and electromagnetic fields allows us to write the equations of thermodynamics explicitly in the Lorentz-invariant form. As a result the entropy, the amount of heat, the chemical potential, the work and thermodynamic potentials can be represented as tensor functions of microscopic quantities, including the electric and gravitational field strengths, the pressure and the compression function. This allows us in § 7 to find out the meaning of the entropy as the function of the system state – it is proportional to the ratio, taken with the negative sign, of the absolute value of the ordered energy in the system to the heat energy, which is chaotic by nature. The ordered energy means the energy of directed motion of the matter, the compression energy from pressure and the potential energy of the matter in the gravitational and electromagnetic fields. When the system achieves equilibrium, part of the orderly energy inevitably is converted into thermal form and the entropy obtains a positive increment.
The global flux of negentropy emerges at lower scale levels of matter and is transferred to higher levels of matter by means of energetic field particles (ether particles), that is by gravitons in the form of different types of photons, neutrinos and relativistic particles. These particles are constantly ordering the matter, creating the rest energy of the matter, moving it from the equilibrium state and reducing its entropy. Emerging non-equilibrium systems, in turn, are the source of emission of new field particles which are more massive and have the ability to transfer the negentropy to subsequent matter levels. This is the way how the development of the world occurs on all conceivable levels of matter. Besides this transfer of order and negentropy there is also a reverse flux, accompanied by increasing entropy in different systems and at different scale levels of matter . For example, the matter is not only produced, but also is destroyed in a number of processes (collision of particles, scattering of quanta, the death of living organisms, etc.). The fluxes of ordering and disordering, negentropy and entropy are not only the sources of development, but also cause the existence of each other as the dialectical opposites.
As one of the practical applications of physical ideas we consider the use in economic theory of the formula, similar to the formula for the density of distribution of the photon gas by energies. Distribution of the annual per capita income in different countries has a rather complex structure. As it turns out, it can be explained by the superposition of the distribution curves for several social groups with different incomes. As an example, in § 8 we analyzed the income distribution in the US economy and determined four major groups of population. The resulting formulas, in contrast to the previously used, contain only a few parameters and are given in explicit analytic form. This allows us to carry out all the necessary mathematical operations on the statistical data on incomes and expenses, making easier the presentation and the research of the economy state.
The book is translated by Slesarchuk Sofia Valeryevna.
I dedicate this book to Fedosina Lubov Mikhailovna.
After preparing a number of new articles it became necessary to connect the obtained results with this book. This has been realized in the form of the Commentaries to the book "Physical Theories and Infinite Hierarchical Nesting of Matter", attached to it as a separate edition. There are 20 commentaries on 156 pages. At the same time corrections to the book were made, the list of references was increased.
Sergey G. Fedosin