Sergey Fedosin. The
physical theories and infinite hierarchical nesting of matter, Volume 1. – LAP LAMBERT
Academic Publishing, pages: 580, ISBN-13: 978-3-659-57301-9. (2014).

**CONCLUSION**

At each stage of its
development the science faces intriguing and incomprehensible phenomena,
unresolved questions, the facts which do not fit into the framework of old
theories. As it is indicated in [143], the
following questions still remain a mystery:

1. The nature of gravitation.

2. The nature of ** the
medium**, the "empty" space (ether, physical vacuum).

3. The nature of electromagnetic
wave propagation.

4. The nature of electricity and
magnetism. Theoretically "open" magnetic monopoles are still being searched
for.

5. The nature of limiting of the
speed of light in ** the medium** and in the substance.

6. The nature of quantization of the
orbits of electrons in atoms.

7. The nature of the wave-particle
phenomenon.

8. The nature of the structure of
"elementary" particles.

9. The nature of nuclear forces.

10. The nature of the electric
charge and the mass.

11. The integration of all
interactions on some basis.

This list could be
continued, proceeding to more specific issues almost in all areas of modern
physics. For example, in [144] the
committee on the physics of the Universe in order to understand the relation,
assumed between quarks and cosmos, has presented a list of tasks for further
research:

1. What is the dark matter like?

2. What is the nature of dark energy?

3. What was the origin of the
Universe?

4. Is the Einstein theory of
gravitation complete?

5. What are the masses of neutrinos
and how have they influenced the evolution of the Universe?

6. What is the
structure of "cosmic accelerators" like and which particles do they
accelerate?

7. Are protons stable?

8. What are the new states of matter
at very high densities and pressure?

9. Are there any additional
spacetime dimensions?

10. How did the elements from iron
to uranium appear?

11. Do we need a new theory to
describe the behavior of substance and emission at high energies?

One of the main goals
that were set by the author of this book was the use of syncretics as new
philosophical logic, the philosophy of carriers, the similarity theory and the
theory of infinite hierarchical nesting of matter to solve the acute problems
of modern physics. The classical and relativistic mechanics, special and
general theories of relativity, the theory of electromagnetic and gravitational
fields, the theory of weak and strong interactions have been analyzed from a
new perspective. In many cases the result was the models of phenomena clearly
showing their structure and the mode of existence or interaction.

A typical example is the
model which describes the structure of bead lightning in § 1, and is based on
the electron-ion model of ball lightning, according to [2], [3], [4], [145], [146]. An
interesting example of the similarity of atomic and stellar systems was
quantization of specific orbital and spin angular momenta of the Solar system
planets found out in [4] and [9]. In § 2 we
showed that the specific orbital angular momenta of the moons of such planets
as Jupiter, Saturn and Uranus are quantized. To a number of dependences
characterizing the Solar system, we have added one more
dependence. According to it the average surface temperatures of planets
depend in inverse proportion on the square root of the distance between the Sun
and the planets.

The cosmic theme was
continued in § 3, analyzing the evolution of the "Earth–Moon" system. The results show that the Moon
could probably appear at the distance of 29 Earth radii from the Earth at the
same time when the Earth itself was formed. The calculations are consistent
with the energy release in the lunar tides and assume synchronization of the
proper rotation of the Earth and the orbital rotation of the Moon in 2.6·10^{10} years.

The analysis of the
action function in § 5 shows that it is not only useful for finding the
equations of motion based on the principle of least action, but actually
influences the properties of bodies. This follows from the fact that parts of
the action function are the gauge field function used for potential calibration
as well as the function of energy, depending on the velocity of the substance.
If these functions change due to changing of the potentials and the velocity,
this leads to slowing down of the processes and time, the phase shift in the
considered reference frame relative to the control reference frame. Besides the
action function also contains the terms with the field energies, depending on
the field strengths. This means that not only the potentials but also the field
strengths are involved in changing the properties of the bodies.

Using the theory of
infinite hierarchical nesting of matter [36] in § 6 the existence in cosmic space of the so-called "new"
particles (nuons) is substantiated. These particles
belong to neutral leptons, and their analogues among the stars are white
dwarfs. Since the substance density of nuons averaged
over space is fairly close to the average substance density of nucleons in
cosmos, so nuons play the role of dark matter,
affecting the motion of stars and galaxies. Due to their large number and
relatively large sizes in comparison with nucleons, the cross section of nuons is of such kind that they are able to create redshift
of the emission from distant galaxies. Nuons not only
reduce the energy of electromagnetic quanta which are propagating in space, but
also scatter them partially. This leads to weakening of the emission intensity
with the distance, which has been recently detected by comparing the amplitude
of the outbursts of supernovae of the same type with different redshifts, so that the solution of the problem does not
require involving exotic dark energy. Besides nuons
are one of the sources for thermalization of
electromagnetic emission which is pervading the Universe and is converted into
isotropic microwave background radiation with the effective temperature of
about 2.725 ± 0.001K. Interpretation of the effect of redshift due to the loss
of emission energy on nuons allows us to explain the
observed fact of quantization of the redshift values in nearby galaxies. Since
the losses of the emission energy depend on the distance traveled, then the
recurring periodicities of the redshift values reflect almost equal average
sizes of typical galaxies, separations between the neighboring and binary
galaxies, as well as average distances between the clusters of galaxies.

It is well known that
the Newton law and the general theory of relativity (GTR) only describe
gravitation, but do not give specific explanation of it. In § 7 on the basis of
[9] and [147] we developed the theory of gravitation in the concept of gravitons,
proceeding from the representations of the Fatio – Le
Sage kinetic theory. This leads to the derivation of Newton law and the
definition of the basic characteristics of fluxes of gravitons – the density of
their energy in space and the penetrability in the substance. The gravitational
force is responsible for the shape and the integrity of cosmic objects, while
gravitons in the form of relativistic particles, photons and neutrinos are
generated by the substance at all levels of matter. At the level of stars the
emission of particles and photons is most active near neutron stars and at the
atomic matter level – near nucleons. As we move deeper into the matter the
energy density and the concentration of particles in the fluxes of gravitons
increase, but their free path in the substance decreases. This results in the
complex structure of gravitons existing in the space, as well as in the
impossibility of black holes as objects absorbing any substance and not
releasing anything out. If the latter statement would be true, we should expect
black holes at the deepest levels of matter. But then black holes would absorb
all the minute substance and at our level of matter there would be neither
gravitons nor gravitation.

One of the most successful
approaches in physics is the principle of least action. The essence of it is
that when the system passes from one state into another, among all the possible
ways that one is realized at which the function has the least stationary value.
There are two variants of the principle: in the form of Hamilton–Ostrogradsky with the additional condition that the
possible ways are passed during the same time; and in the form of Maupertuis–Lagrange, with the condition of conservation of
the initial energy. We want to focus on why performing this principle is
possible. Let us take, for example, bodies which are interacting by means of
the gravitational field. How do these bodies determine how they should move and
along which trajectory? It is obvious that the uniqueness of motion is achieved
due to the action of a great number of particles. An example is the gas
temperature which is stable because it is the average characteristic of the
kinetic energy of a large number of molecules. For emerging of gravitation, as
we assume in accordance with § 7, there are numerous fluxes of gravitons, which
cause attraction of bodies. That is huge multiplicity of particles that creates
the effect of the gravitational field and ensures the motion of bodies
according to the principle of least action. Apparently, a similar situation
exists with regard to the electromagnetic field. Both fields together are
fundamental long-range fields and they generate the basic forces that we
observe in the nature. As a consequence of the principle of least action, we
should consider other less general principles that are performed under
additional conditions, such as the principle of minimum energy dissipation by
N.N. Moiseyev [148], the principle of least entropy production by I.R. Prigogine, and the
principle of minimum energy dissipation at the boundaries by L. Onsager [149].

In § 8, we state
difference of mass-energy of the gravitational field of a spherical body in two
reference frames, in one of which the body is fixed, and in the second it is
moving at a constant velocity. The first mass-energy is calculated through the
gravitational energy of the static field as mass-energy .

If we integrate the
vector of the momentum density of the gravitational field of the moving body
over the entire volume, occupied by the field, then the momentum of the field
will be proportional to the velocity of the body and the mass-energy of the field . Inequality
of the gravitational mass-energy and the inertial mass-energy means the probable violation of the equivalence
principle, as applied to the mass-energy of the gravitational field, which can not be explained in GTR in the weak field
approximation. From the point of view of the Lorentz-invariant theory of
gravitation (LITG) [9], the difference between the mass-energies
is associated with the existence of an isotropic reference frame, in which the
fluxes of gravitons are isotropic [150]. Any motion
of the body relative to this reference frame leads to distortion of the fluxes
of gravitons, acting on the body, and to emerging of wave disturbance in the
fluxes of gravitons, which is moving at the same velocity as the body. The
mass-energy of such disturbance can then be equated to the difference between
mass-energies and . According
to extended special theory of relativity we show that the Lorentz
transformations are conditional and that other transformations, containing the
absolute velocities of reference frames relative to the isotropic reference
frame, are possible. One of the consequences of this is that the observer
moving with the body relative to the isotropic reference frame and using the
principle of relativity, can calculate only the mass-energy and does not see the increased mass-energy . The
difference between the mass-energies and can be understood as the additional energy of
the gravitational field arising from the work required to bring the initially
fixed body in some reference frame into the state of motion.

According to GTR the
gravitational field is very special – it is created by all possible sources of
mass-energy, from the substance to the electromagnetic field, but it does not
necessarily produce either substance, or any other field. This follows from the
geometrization of the gravitational field and its
representation by the curvature of spacetime and the equivalence principle.
This approach is a necessary measure, since in GTR there is neither the model
of the gravitational field, nor the mechanism of its action. Accordingly, the
main task is the description of the gravitation effect without going into the
essence of the phenomenon.

The most obvious
weakness of this approach reveals in the fact that the gravitational energy
density in GTR is not a real tensor but only pseudotensor. This is natural –
the energy density of the physical field is always a tensor and can be
transformed into any reference frame, while the geometric analogue of energy can not be directly transformed from one frame to another,
as it requires to know beforehand the geometry of the
new reference frame. The problem with the energy actually means the problem of
its localization – in different reference frames in GTR,
it is concentrated in space differently.

In contrast to this in
the covariant theory of gravitation (CTG), which is the continuation of LITG
for the case of Riemannian space and arbitrary reference frames, gravitation is explained in the model of
gravitons and is a real physical force. The metric in this case is not
identified with the gravitational field, but characterizes the degree of
influence of the matter and fields on the deviation of the results of spacetime
measurements from their values in inertial reference frames. In § 9, according
to the results of [151] we show the similarity of the equations of
electromagnetism and gravitation, and construct a unified electromagnetic and
gravitational picture of the world, which conforms to the principle of
relativity.

If in the macroworld the key role is played by ordinary gravitation,
then in the microworld strong gravitation is
responsible for the integrity of elementary particles. By introduction of the
strong gravitational constant: m^{3}∙kg^{ –1}∙s^{–2},

where and are the charge and the mass of the electron, is the vacuum permittivity, is the mass of the proton, in § 10 we managed
to describe the force and the energy of gravitation, to express the
gravitational torsion field from the motion of nucleons. This made it
possible to specify in the mathematical form the conditions of the equilibrium
of nucleons, to determine the structure of the simplest nuclei, to present the
nuclear forces as the combination of strong gravitation, torsion field and
electromagnetic forces. It is shown that in the massive nuclei the saturation
mode of specific binding energy is realized when adding new nucleons stops
increasing the gravitational potential of the nucleus and the gravitational
force, and the subsequent increase of the number of protons leads to decreasing
of the specific binding energy of the nucleus due to the additional positive
electrical energy.

In § 11, based on the
similarity of the properties of nucleons and neutron stars, the model of the
internal electromagnetic structure of the neutron and the proton is
constructed, taking into account the configuration of their magnetic field,
composition and charge of the substance of nucleons, the possibility of
transformation of the particles into each other in the reactions of weak
interaction. The analysis of reactions involving nucleons, pions,
muons, electrons and neutrinos leads to the
conclusion that the muon and electron neutrinos (antineutrinos) are composed of
the corresponding beams of electron neutrinos (antineutrinos), but belong to a
deeper level of matter. The weak interaction is the result of the natural
transformation of the substance of elementary particles, but not some special
force. The considered approach follows from the theory of infinite hierarchical
nesting of matter [36] and allows us on the unified basis to present the
evolution of matter in time and space. In particular, this means that neutron
stars will eventually experience transformation of their substance, similar to
the reactions of weak interaction, for example transforming into magnetars as
in charged and magnetized stars. The structure of nucleons is supplemented by
the picture of their electromagnetic and gravitational fields at limiting
rotation of the particles in § 13. This allows us to estimate the radius of the
proton by comparing the spin and the angular momentum of the gravitational and
electromagnetic fields of the proton.

Introduced by the theory
of elementary particles and quantum chromodynamics, quarks and gluons are
considered as the basic building material that makes up the mesons and baryons.
The properties of quarks in the theory are chosen in such a way that their
combinations would correspond to the properties of elementary particles. As for
leptons, they stand apart from hadrons and can not be
modeled with the help of quarks. What are leptons made of – it still remains
unknown. The analysis of the concept of quarks was made in § 12, where it was
shown that quarks could be presented in the form of different sets of – phase and – phase of
hadronic substance. These phases have different charges and magnetic moments
and are the constituent parts of the substance of nucleons, being located
either in the nucleus or in the shell of the particles. Reducing the properties
of quarks to the typical phases of hadronic substance means that quarks are not
independent particles but rather a special kind of quasi-particles. The similar
conclusion follows in respect of the intermediate vector bosons of electroweak
interaction with their energies of the
order of 80 – 90 GeV. These bosons are detected by
symmetrical tracks of high-energy leptons arising from collisions of
counter-propagating beams of protons and antiprotons with the energies of the
order of GeV. However, at
these energies the particles of the substance of colliding nucleons can reach
almost the maximum possible speed , where is the speed of light, is the coefficient of similarity in velocities
for degenerate objects. The speed is determined with the help of the theory of
similarity of matter levels [152]. In this case, instead of appearing of vector
bosons, we can simply state that the
boundary is reached, at which the substance of elementary particles starts
interacting with velocities close to the maximum velocity for this type of
substance.

As for the weak
interaction, the possibility to model it in the framework of the electroweak
quantum formalism with the help of vector bosons, as the carriers of
interaction, does not mean the construction of the essential mechanism of the
phenomenon. Indeed, in § 11 the weak interaction is reduced not to the forces
but to the transformation of the substance of elementary particles which occurs
in it at a deeper level of matter. In the interaction of pions
and nucleons the gravitational and electromagnetic forces are significant,
leading to appearing of nucleon resonances or , depending
on the order of addition of the orbital angular momentum and the charge of
particles. And the analysis of Regge hadron families shows that they
can be explained taking into account the spin quantization and the state of the
particles’ substance, retained by the strong gravitational field.

In addition to nucleons,
another basic constituent part of the substance is electrons the properties of
which in the atoms determine the variety of chemical substances. However
quantum mechanics and the theory of elementary particles due to the
probabilistic and statistical methods can not give
exact substantial models of the electron and the elementary particles. In § 14
we found the feature of the electron, consisting in the absence of its proper
radius as of an independent particle. This follows from the weakness of the
gravitational force which is not able to keep the electron substance from the
repulsion force of its proper electrical charge. From the evolution of
substance at the level of elementary particles we can understand that the
electron appears as the necessary consequence of achieving electrical
neutrality of the hydrogen atom (or another atom), when around the positively
charged proton (the nucleus) a negatively charged electron cloud is formed.

Since this electron
cloud can not have proper static magnetic and
mechanical moments, which are assumed in quantum mechanics for the electron
spin in order to explain the spin and the spin magnetic moment, we introduce a
dynamic concept. This means that all phenomena which are attributed to the spin, occur only at the moment of transition of the electron
from one energy state to another, since in the stationary states there is no
spin. The main reason of emerging of the spin is deflection of the center of
mass of the electron cloud in the atom from the nucleus, which takes place, for
example, after interaction of the electron with the photon. In this case the
spin is part of the total angular momentum of the electron cloud associated
with rotation of the center of mass of the cloud around the atomic nucleus.
Different directions of rotation of the substance in the cloud, taking into
account the orbital motion of the nucleus relative to the center of mass of the
electron, result in fine splitting of atomic energy levels. While the electron
cloud as a whole is shifted relative to the nucleus and is rotating, the
electromagnetic emission takes place and the loss of energy by the atom. Then
the atom achieves the equilibrium state with the simultaneous disappearance of
the spin.

Based on this picture,
we can get rid of the famous paradox of quantum mechanics, according to which
in the ground state of the atom the electron can not
have the orbital angular momentum, but it has the spin angular momentum. If the
spin is a dynamic phenomenon, this should be just the opposite way – in the
ground and in the s-states there is no spin, but there is the orbital angular
momentum which it ensures the magnetic moment, which had been previously
considered to be the spin magnetic moment of the electron. The orbital angular
momentum does not allow the electron cloud to fall on the nucleus,
and due to the axisymmetric configuration of the
cloud there is no emission from it and the rotational energy is not lost. A
number of other effects, that are assumed to be associated with the electron
spin, obtain new explanation. In particular, the fine splitting of the atomic
energy levels and the multiplicity of atomic spectra are derived as the
consequence of combining the contributions of magnetic energies in the nucleus’
field from all the excited electrons of the open outer shell of the atom.
Taking into account the energy of the magnetic moments of electrons in the
proper magnetization field of the studied samples leads to the fact that in magnetomechanical phenomena such as Barnett and Einstein-de
Haas effect with ferromagnetic samples the Landé
g-factor of electrons is as in the classical case, but not , as
it is expected for the spin.

Successive consideration
of the structure of the electron cloud in the atom allows us to determine the
probable nature of the annihilation of electrons and positrons, to take into
account the contribution of strong gravitational field in the balance of forces
and energies of the electron, in the process of photon emission. The analysis
of the stationary states of the atom shows that there is a balance between the
fluxes of electromagnetic and gravitational field energies and the flux of the
kinetic energy in the substance of the electron cloud. This leads to
quantization of energy and the angular momentum of the electron states and to
discreteness of atomic spectra. Representation of the structure of electron
clouds in the form of discs allows us to calculate the parameters of the helium
atom and to relate the emergence of the Pauli exclusion
principle to the electromagnetic induction in neighboring electron
clouds and to the Lenz's law. Among other conclusions we can mention the
attainability of wave-particle duality only at energies comparable to the rest
energy of particles and the explanation of high energy cosmic rays as the
consequence of the existence of the positive electrical charge in magnetars.

We shall say a few words
about the uncertainty principle and the principle of complementarity
in quantum mechanics. In our opinion, the uncertainty principle on the one hand
is the consequence of the fact that physical quantities associated with
elementary particles must be measured with the help of the same elementary
particles or rather energetic field quanta. Of course, this implies that
measuring the position of the electron with the help of the photon we can not determine the exact momentum of the electron,
changing while interacting with the photon. If we can make of two physical
quantities and the product with the dimension of the quantum
of action, then these quantities can be included into the uncertainty relation
of the form: , where and are the mean square deviations of physical
quantities from their average values. Due to the uncertainty principle, the
more exactly some quantities are determined, the less exactly are known at this
moment other quantities associated with them. Therefore, each time under these
conditions our knowledge about the system is incomplete, some information is
lost.

On the other hand, the
wave functions of elementary particles and the probability of events with them
strongly depend on the type and the energy of the ongoing and sometimes not
accounted interaction. Therefore, in quantum mechanics the initial conditions
are considered and the probabilities of final events are searched for, avoiding
the description of intermediate processes. Impossibility of continuous
description of a phenomenon in terms of physical quantities and the use of the
wave function as the event probability amplitude are also the cause of the
uncertainty principle, since between the initial and the final states of the
system unaccounted deviations of physical quantities from the average or
probabilistic values are admitted. In the probabilistic approach of quantum
mechanics, inevitably there are average values and deviations from them, and
some measurements can give close but different results. Thus, the uncertainty
principle reflects the degree of our unawareness of the course of intermediate
processes and also takes into account the lack of measurement tools that would
not allow distortion of the measurement results.

As a result of
incomplete knowledge of intermediate processes and physical quantities the
principle of complementarity appears. The fact is
that in the initial and final states, we can prepare different sets of
conditions to observe different physical variables, and to make the
corresponding probabilistic predictions. The complete available knowledge of
the system is achieved when we examine all the possible initial conditions for
the considered sets of physical variables and conduct corresponding experiments
to prove the theoretical predictions. The results will complement each other,
giving the general picture. The principle of complementarity
is also reflected in the fact that the mathematical description itself and the
formulas for finding the experimental results depend on the sets of the
considered physical variables. All this implies that determinism in quantum
phenomena does not disappear. But the available theoretical and experimental
tools of quantum mechanics are not able to show us this determinism in the
usual form. We observe a special variant of determinism, partially accompanied
by indeterminism, which is limited by the uncertainty principle and the
principle of complementarity with each set of
selected physical variables.

We shall note one more
feature of the uncertainty principle. It is related to the fact that this
principle works only within a certain level of matter, since each level of
matter has its own characteristic angular momentum. For example, at the level
of elementary particles the characteristic angular momentum is of the order of
the Dirac constant J∙s. At the stellar level of
matter the objects such as neutron stars have the characteristic angular
momentum equal to J∙s according to (345) and somewhat less
magnitude J∙s for planetary stellar systems according to
(10). For the objects such as neutron stars the uncertainty relation is:

.
(557)

It means that measuring
the location of the star with the help of other stellar objects with the spread
of their momenta to the quantity we have uncertainty about the coordinate showing the degree of inaccuracy of our
knowledge about the location of the star. The uncertainty relation (557) must
be satisfied in all interactions between stars, but we can show that it stops
working for internal components which could make up the star. Thus, according
to the quark hypothesis nucleons consist of three quarks (in fact, in § 12 we
showed that all quarks, and hence all hadrons, can be presented as combinations
of the substance from the nucleon nucleus in the form of – phase of
the substance, and of the substance from the shell of the nucleon in form of – phase of
the substance).

We shall suppose further
that because of similarity relations between the nucleon and the neutron star,
the star consists of three objects similar to quarks. Substituting in (557)
instead of the diameter of the neutron star of the order
of 24 km, we find N·s. From this by dividing it by the mass of the object kg, we can obtain for the mean square
deviation of the speed of this object inside the star: m/s. This value is an order of magnitude less
than the speed of light and seems acceptable. But in fact the neutron star is
not composed of three objects, but of number of neutrons – their number reaches . If we
apply (557) to these neutrons, then in view of their low mass, the spread of
speeds of neutrons will be much greater than the speed of light. Therefore, the
relation written for the objects of the stellar level of matter (557) can not be directly applied to such objects as elementary
particles, since beforehand in (557) we must substitute by .

In this case, we can
assume that the approach of quantum chromodynamics, in which quarks and gluons
are placed inside the hadrons, and the quarks are attributed the spin equal to , is
incorrect. The situation becomes even more complicated when elementary
particles are assumed to consist of a set of partons
or preons with the same spin . In our opinion
this approach is incorrect because the less is the mass and the sizes of the object, the less is its characteristic angular momentum. For
each level of matter there is its proper characteristic angular momentum and
its uncertainty relation, and the use of the same Dirac constant for all objects regardless of their belonging
to the level of elementary particles leads to an error.

The author hopes that
this book will be a good introduction to the range of problems and the solution
of the fundamental questions that are arising in the natural science nowadays
due to the theory of infinite hierarchical nesting of matter. We shall remind
that in fact some predictions of this theory have been already proved – the
minimum mass of main sequence stars equal to 0.056 solar masses by discovery of
brown dwarfs, and the typical parameters of dwarf galaxies with the mass of
4.4∙10^{6} solar masses and the radius up to 371 pc [153], [154]. From
the possibility of locating all the known objects in the form of points at the
infinite scale ladder of matter in this theory also a new degree of freedom
(scale physical dimension) follows, in addition to three spatial dimensions and
time [155].

Sergey G. Fedosin

Source: http://sergf.ru/con5en.htm