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).

**Afterword **

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 [158],
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 [136]
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 [89]. 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.

**Additions**

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

Source: http://sergf.ru/con6en.htm