**Pavlo DANYLCHENKO**

Full version of the article PDF ( 295 kb), DOC ( 211 kb).

The existence of singularities in GR is
considered by Einstein [1] and later by the most authoritative specialists in
this branch of physics (Ivanenko [2], Möller [3, 4], Hawking [5]) not only
as the most apparent difficulty of this theory, but also as the sign of
limitation of its application region. Being based on this and on the evidence
of mathematical inevitability of existence of
singularities in GR [6,7], many attempts of radical upgrade of GR applying to
big densities of matter are undertaken. We have chosen another way to solve
this problem.

The process of expansion of the Universe as whole can
take place only, if it takes place in every single point of its infinite space.
The presence of this process may be caused only by evolutionary variability of
the properties of physical vacuum and, therefore, by “adaptation” of matter
elementary particles to continuously renewed terms of their interaction.
Therefore, apparently, distances between quasi-motionless in Weyl FR galaxies
(according to Weyl hypothesis [8-10], in this FR, which doesn’t co-move with
matter, they take part only in small peculiar motions) elongate in FR,
co-moving with evolutionarily self-contracting matter, not because of the
expansion of cosmic space into “nowhere”, but because of the continuous
shrinkage of length standard in Weyl FR. The last is caused by gauge change
(which is unobservable in principle in matter FR because of invariance of
people’s world to scaling transformations in microworld [11]) of values of spatial parameters of
elementary particles, evolutionarily self-contracting in Newton-Weyl absolute
space. This is the cause of continuous decreasing of dimensions of all Universe
objects in Weyl FR. The fact that process, which takes place in megaworld, is
caused by the processes, which take place in microworld, is in good agreement
with existence of many correspondences in correlations between atomic,
gravitational and cosmological characteristics – Eddington-Dirac “large
numbers” [2, 12, 13] and doesn’t contradict with modern physical notions.
That’s why we can consider the expansion of the Universe, in analogy to daily
solar motion on the celestial sphere, only as phenomenon that is observed in
some selected FR. Already ancient Greeks (Aristarchus of Samos (ca.310 – ca.230
BC) and Seleucus of Seleucia (ca.190 - unknown BC)) presumed, that in fact
Earth revolves on its axis and around the Sun. But it took near two thousand
years to make this the apparent truth for all. We can only hope, that
phenomenon of Universe expansion won’t have such fate.

Because
of motion relativity, at the first sight it seems that there is no difference
if space expanses relatively to matter or matter self-contracts in space. But
in fact the difference between these processes is present and this difference
is very essential. World points, in which points of empty intrinsic space of
self-contracting body move in Newton-Weyl absolute space with supraluminal
velocity, are found beyond the limits of space-time continuum (STC) of this
body. At that, empty intrinsic space becomes self-limited by observer horizon.
Furthermore, inequality of relativistic shrinkages of dimensions and
relativistic time dilations in different points of intrinsic space, which is
caused by inequality of velocities of these points, leads to onset of curvature
and physical inhomogeneity of intrinsic space of self-contracting body
correspondingly.

The spaces, in which contraction takes place, don’t
have all this and may be unlimited and infinitely large. Therefore, if cosmic
space expands relatively to matter, then observer horizon will limit Weyl FR
space. And if, as we consider, matter contracts in cosmic space, then observer
horizon will limit space of FR, co-moving with matter. In conventionally empty
space of self-contracting body, viz in its distant regions, points of which
move in Weyl FR at velocities higher then velocity of light, there are no
physical bodies, dragged by this space, On the contrary, all astronomical
objects, conventionally motionless in Weyl FR, are dragged by expanding cosmic
space. And at as long as desired distances from observer they can move, according
to Hubble relation, at as high as desired velocities. However, velocity of
physical object can’t exceed velocity of light in the point, where it's
located. Therefore, at as long as desired distances from observer improper
values of velocity of light must be as large as desired. This, however, doesn’t
follow from GR gravitational field equations. Otherwise, observer intrinsic
space must be finite. And this is possible in case of Friedmann singular model
of expanding Universe with its finite past, as well as in case of presence of
observer horizon in matter intrinsic space. In case of eternal existence of
Universe in the past, (this doesn’t allow existence of cosmological
singularity) there are no other known physical mechanisms, which form observer
horizon of intrinsic space of any astronomical body, except relativistic
shrinkage of dimensions and relativistic time dilation. Therefore, phenomenon
of Universe expansion can be caused only by gauge process of evolutionary
self-contraction of matter in cosmic space.

Such gauge (for intrinsic observer) matter
self-contraction, which becomes apparent in relativistic shrinkage of moving
body dimensions, has been recognized as physically real for the first time in
special theory of relativity. In GR it is caused by the influence of
gravitational field on matter and may be rather substantial in the process of
relativistic gravitational collapse. But if such gauge self-deformation of
matter is possible in absolute space in case of transposition of body in space along
the force lines of gravitational field, then why it can’t be possible in case
of “transposition” of body only in time? After all, because of unification of
space and time in single STC (Minkowski four-dimensional space-time) coordinate
time is equal to spatial coordinates in GR. In this case, gravitational field
may be considered as demonstration of presence of time delay of the process of
gauge matter self-contraction in the points more distanced from the center of
astronomical body and as demonstration of presence of matter influence on the
properties of physical vacuum via negative feedback. This feedback is realizing
via changes of eigenvalue of molecules volume as well as of eigenvalues of
densities of energy and enthalpy of matter. At the early stages of Universe
evolution, when its whole space was filled in with matter, eigenvalue of
molecules volume gradually increased and eigenvalues of densities of energy and
enthalpy of matter gradually decreased. The same takes place in case of advance
from the center of astronomical object to its boundary surface, in other words
– in case of advance in space, but not in time.

Let’s examine Schwarzschild internal solution for
ideal liquid, which is gauge-self-contracting in Weyl FR and, therefore, has
rigid co-moving with it FR. In this intrinsic FR of liquid, which is
inhomogeneously contracted by the gravity, linear element has static and
spherically symmetric form [10] and therefore it is determined by increments of
angular coordinates, increment of luminosity radius *r* of
spherical surface (value of which is determined by its area and in principle can vary non-monotonically along metrical
radial interval *r _{metr}* in nonempty space
with curvature) and increment of coordinate (astronomical) time

If we know function *b*(*r*) we can find radial distribution of improper (coordinate) value of the velocity
of light *v _{c}*(

It was shown by Lemaitre [10, 14] and
independently by Robertson [10, 15], that there is an appropriate
transformation of coordinates, using which we can proceed from rigid FR,
co-moving with matter, to not co-moving FR, in which dimensions of both macro-
and microobjects of body matter mutually proportionally vary with time. When
values of gravitational radius of this astronomical body, located far from
other astronomical objects, are negligible (*r _{ge}*≈0), we’ll have:

According to this, velocities of radial motion not
only of macroparticles of self-contracting body matter, but also of all points
of conventionally empty intrinsic space of gauge-self-contracting body are determined in Weyl FR by metrically
homogeneous time scale via Hubble relation:

*V*=*dR*/*dT*=–*H _{e}R_{k}*exp[–

And they absolutely don’t depend, as it was shown in
[16], on parameters of equations of GR gravitational field. Taking into account
relativistic time dilation, improper values of velocities of light in FR of
evolutionarily self-contracting body (*v _{c}*) and
in Weyl FR (

Simultaneity in
matter FR of infinitely far past on observer horizon (when distances between
interacting elementary particles of protomatter in absolute space were as long as desired) with every concrete event in any
point of matter intrinsic space causes the finiteness of metrical distance in
intrinsic space to its observer horizon [16, 17] (the possibility of this was shown earlier by Penrose
[20]). The fact, that observer horizon
covers all infinite absolute space explains impossibility for radiation to
reach this horizon and to come from horizon to observer within as long as desired but finite time interval.
Therefore, near the observer horizon of any body the delayed (by the clock of
the body) process of origination of matter is continuously “observed”, which
corresponds to Gold-Bondi-Hoyl theory [2, 21] only formally. If observer
horizon of matter intrinsic space is in fact a pseudohorizon of past, then
Schwarzschild sphere with luminosity radius *r _{s}* is a
pseudohorizon of future of matter [16]. Events, which take place on this
sphere, are simultaneous in physical body FR with every event on the surface and
in any other points of this body. Therefore, they can take place in
cosmological time only in infinitely far future. There is nothing inside the
“fictive” Schwarzschild sphere in that “moment” of cosmological time, and thus,
in any moment of intrinsic time of physical body. This, of course, is connected
with principal conservation of finite eigenvalues of matter dimensions, when
its dimensions are as large as desired or as small as desired (hypothetically –
conventionally “zero” in infinitely far future) in absolute space, and, thus,
with the fact that luminosity radius in principle can’t obtain (analogously to
absolute temperature) not only infinitely large value but also zero value.

The presence of
negative feedback between eigenvalue of dimension (stabilizable output
parameter) and length unit, which is being determined in absolute space by the
material length standard, becomes apparent here. This negative feedback prevent from
catastrophical decrease not only intrinsic dimensions of self-cooling astronomical
objects, but also rates of physical
processes in matter (which is possible because of the decrease of absolute
value of the velocity of light) and, thus, guarantees the stable existence of
matter. Moreover it causes the self-organization and stable existence of
spiral-wave structural elements (matter elementary particles) in physical
vacuum, which gauge-evolves (becomes older) and is the pseudodissipative medium in Weyl FR. Analogous phenomena take place in thermodynamics (Le Chatelier –
Brown principle), in electromagnetic phenomena (Lenz rule) and in the process
of motion (relativistic shrinkage of length [18]). The character of any
physical law or phenomenon is being determined by the presence of explicit and
implicit (hidden from observation in principle) negative feedbacks, which are
formed between parameters and characteristics of matter in the process of its
self-organization and are aimed at the maintaining of stability of steady phase state of matter. Revelation of
global topology of direct communications and feedbacks between parameters and
characteristics of matter is the supreme aim of physics.

The postulation of Universe stationarity in Weyl FR
(as well as in Gold-Bondi-Hoyl theory) causes principal impossibility of
finiteness of its cosmological age in future, as well as in the past. Thus the
possibility of birth of Universe from “nothing” and its expansion into
“nowhere” is excluded. Conception of Big Bang of Universe is based on using in
cosmology instead of metrically homogeneous scale exponential scale of
cosmological time *t**′*=*t**′ _{k}*–(1/

Because of this, such conception substitutes
infinitely long evolutionary development of the Universe by revolutionary
event, which took place “not known where and not
known inside of what”. Rejection of it, however, doesn’t deny the
possibility of hot condition of matter at early evolutionary stages and other
results in Universe evolution research, achieved by cosmology (only some remaking sense of this results is required).
Moreover, this rejection leads only to metrical transformations
of STC, which have no influence on sequence of cause and effect in evolutionary
physical processes.

According to physical notions stated here,
exponential slowing down of all physical processes by used now in cosmology
time scale is provided. Thus, exponential slowing down of matter
self-contraction in the Newton-Weyl absolute space is provided too. And this is
equal to exponentially quick Universe expansion in FR, co-moving with matter.
Therefore, these notions are in good agreement with inflationary cosmology
[22], based on the scenario of inflatory Universe.

Since (*b*′)* _{e}*>0, when
values of functions

According to
relation for lower limit of values of difference between cosmological ages of
simultaneous events in nonempty space of any physical body, finiteness of
intervals of cosmological time between simultaneous events in FR, co-moving
with body, takes place also only in case of presence of spherocylindrical
metrics of internal intrinsic body space. From all these follows the absence of
both gravitation inside such “body” and radial pressure drop in its ”matter”,
elementary particles of which, because of
equality of their hamiltonians to zero, have radiated all their energy with
quasi-particles and, therefore, have proceeded from actual state into virtual
and in fact have destroyed themselves (for external observer). Energy of such
“dead” black hole is concentrated only in electromagnetic radiation, which
propagates in Weyl FR at Hubble velocity. And, therefore, only “dead” black
hole can correspond to GR gravitational field equations if values of functions *a* and *b* are
nonnegative.

Let’s examine also
compatibility of existence of black holes with presence of Weyl FR. The
observer horizon of rigid body in its intrinsic FR is motionless. However, it
moves in Weyl FR at the velocity of light. Therefore, matter, which has
inertia, can’t be on this horizon in principle. There necessarily must be a
layer of empty space between the surface of the body and its external observer
horizon (which, as it was shown before, is a pseudohorizon of past). However, any as “photometrically” thin as desired layer of external conventionally empty part of intrinsic
space of physical body contains whole Universe. In other words, both on and
outside observer horizon of as massive as desired physical body no other
physical objects can be in principle. Ultralow gravitational
field strength, which is created near its observer horizon by astronomical body
with as small as desired mass, doesn’t prevent other astronomical objects near
this horizon from spontaneous motion near this horizon. And, if observer horizon of body is ”passing by” these
astronomical objects in absolute space, then in intrinsic space of this body
the distancing of these objects from observer at velocity of light would be
observed. Therefore, no physical body can be self-isolated from Universe
by singular surface, which is located in empty space or at least contacts with
this space.

So, according to
physical notions taken here, such hypothetic astronomical objects as black
holes can’t exist in principle. Impossibility of motion of surface of
evolutionarily self-contracting in absolute space astronomical body at velocity
of light in this space is imposing substantial restriction both on the value of
luminosity radius of this surface in intrinsic space and on the value of body
gravitational radius. So, for example, for hypothetical
incompressible ideal liquid, which can contract
only in the case of change of velocity and also in nonrigid FR and Weyl FR, in
its whole volume both eigenvalues of mass density and, improper (coordinate)
values of enthalpy density are identical. Taking this into account we can show
that improper value of velocity of light on the boundary surface of such liquid is minimal for the maximal value of surface radius, for which value of pressure becomes infinitely large and, consequently, gravitational
singularity originates in the center of gravity of the liquid. Further growth
of *r _{e}*, and so growth of liquid mass for such
(normal:

Like in all other
solutions of equations of GR gravitational field, in
this solution integration begins only from zero value of luminosity radius of
body. Therefore, upper layers of matter (even when they’re as massive as
desired) have no direct effect on the curvature of intrinsic space of body in
lower layers of matter, while lower layers of matter have direct effect on the
curvature of this space in upper layers. For hypothetic incompressible liquid
function *a*,
which determines curvature of its intrinsic space, in the points of lower
liquid layers doesn’t depend on the presence of liquid higher than these layers
at all. In fact, the pressure of upper layers of incompressible liquid has no
effect on distribution of eigenvalue of its density in lower layers. This is
not only a paradox, but not always may be a physical reality. Upper layers of
matter, when their mass is very big, must have direct effect on curvature of
the space of body in lower layers via some integral characteristics. This is
possible if in intrinsic spaces of extraordinarily
massive astronomical bodies physically realized values of luminosity radius are
limited not only from the top, but also from the bottom. This limitation from
the bottom of value of luminosity radius of body with strong gravitation field
may be connected with existence of metrical singularity (1/*a*_{0}=0) inside of body. It takes place in the case of nonmonotone radial
change of gravitational field strength in absolute and co-moving spaces. For
such spatial distribution of gravitational field strength with decreasing of
value of metrical radial distance *r _{metr}*
luminosity radius

Covariance of GR gravitational field
equations relatively to coordinate transformations allows us to receive their
internal solution for ideal liquid also in Weyl FR. In this FR nonzero
components of metrical tensor are being determined by
parameters, which have the following physical sence. Eigenvalue of radial coordinate *r*(*R*,*T*) is
determined by intrinsic length standard in world point with following absolute
coordinates and is identical to the value of luminosity radius in intrinsic FR
of the liquid. Relation *N*(*R*,*T*)=*r*/*R*
determines inequality of dimensions of identical matter objects in different
points of Euclidean world space (space of Weyl FR), and, therefore,
characterizes metrical (scale) inhomogeneity of this space for matter. Average
statistical relative value of frequency of interaction of matter elementary particles
*f*(*R*,*T*)=*NV _{c}*/

From the equations
of gravitational field, which are determined in coordinates of
pseudoeuclidean Minkowski space of Weyl FR, and, taking into account rigidity of intrinsic FR of ideal liquid, we can receive dependences of
coordinates of world points of liquid in Weyl FR from their coordinates in FR,
co-moving with liquid. Limiting minimal value of luminosity
radius *r*_{0}
corresponds in these dependences to spherical
surface, in the points of which there is no gravitational field strength, and
the following conditions are fulfilled: *f*_{0}=*H _{e}r*

The absence in
Weyl FR of so called “antigravity” [27], which take place in intrinsic FR of ideal liquid due to nonzero value of
cosmological constant, justifys total removability of “antigravitational” field
by the transformation of coordinates. Proportionality of the velocity of radial
motion of the points of ideal liquid to cosmological constant justifys the fact
that the phenomenon of Universe expansion is caused only by evolutionary
self-contraction of matter in Newton-Weyl absolute space.

Because of presence
of principal possibility of function *R*(*r*)
two-valuedness in this internal solution (the same as in external solution
[16]), function *r _{metr}*(

Such singular solution of GR gravitational
field equations corresponds to hollow spherically symmetrical body with mirror
symmetrical intrinsic space and many centers of gravity in the points of median singular surface, which is concentric to
external and internal boundary body surfaces. When value of *λ *is zero, such
configuration of intrinsic space consists of two asymptotically Euclidean
half-spaces, connected by narrow gullet. This configuration is obtained by
Fuller and Wheeler [28, 29], being based on geometrodynamic model of mass. When
value of *λ *is nonzero, internal empty space of massive astronomical body is limited by
fictive sphere of the pseudohorizon of future. In this internal empty space,
which is as it were «turned inside-out» by extraordinarily strong gravitational
field, instead of the Universe expansion phenomenon, phenomenon of contraction
of “internal universe” is “observed” and also internal planet system may be
formed. In intrinsic FRs of these planets internal boundary surface of this
astronomical body will be observed as convex (the same as external boundary surface).
This is because of the fact that luminosity radiuses of their orbits will be longer than
luminosity radius of this surface. Only absence of distant stellar systems in
internal empty space will give the opportunity to differ it from external
space.

The value of luminosity radius in the center of
gravity is determined unambiguously, if the configuration of STC of liquid is
ordinary (*r*_{0}=0 when *a*_{0}=1), and becomes indeterminate from GR
equations, if the configuration is extraordinary (1/*a*_{0}=0). Because of this, one should agree with the
statement of Hawking [5]: “GR itself (without use of additional laws, obtained
in classical physics) doesn’t provide field equations with boundary conditions
in singular points. And, therefore, it becomes incomplete near these points.”
Absolute stability of thermodynamic equilibrium condition of matter, which is
held by gravitational field and is self-contracting in Weyl FR as whole, may be
guaranteed in case of invariability of entropy and external pressure only when
the following condition is fulfilled. Spatial distribution of function *r*(*r _{metr}*) must correspond to the minimum of lagrangian of
enthalpy of whole matter of liquid body in Weyl FR. This value of lagrangian is
equal to enthalpy of liquid in FR, co-moving with it, and is determined by the relation, which
takes into account direct influence of both upper and lower matter layers on
the values of functions

When quantity of
matter doesn’t exceed its critical value, function, which determines the dependence of integral improper value of the
enthalpy of whole matter on the values of *r _{e}* and

For
incompressible ideal liquid the value of minimal luminosity radius is indeterminate. This shows the degeneracy of such state for ideal
liquid. Because of this, equilibrium state of incompressible liquid will be
absolutely stable for any values of *r*_{0}. And thus, as large as desired quantity
of incompressible liquid may be contained inside of hollow body, when the value
of *r _{e}* is as small as desired. This, of course,
is physically unreal, the same as existence of incompressible liquid.
Therefore, such result may be considered as one more sign of degeneracy of
state of ideal liquid, and, thus, as apparent confirmation of validity of
selected by us criterion for determination of minimally possible value of
luminosity radius of body when it has hollow topological form.

So, avoidance of physical realizability of
cosmological singularity in GR is possible. It is necessary and enough for this
to postulate the counting of cosmological time in Weyl FR and not to exclude
(the most of physicists agree with this [2, 27]) cosmological *λ*-term from gravitational field equations. And thus, it is necessary to admit physical reality of infinitely long gauge
process of matter self-contraction in absolute space of Weyl FR.

Avoidance of
physical realizability of gravitational singularity for extraordinarily massive astronomical body is also
possible. It is necessary and enough for this to supplement gravitational field
equations with condition of reaching the minimum of enthalpy of the whole
matter of body and to admit physical reality
of mathematically inevitable hollow topological form of body and configuration
of STC with “turned inside out” internal half-space, which corresponds to this
topology.

Equations of GR
gravitational field describe only equilibrium motion in Weyl FR of the points
of whole matter (ideal liquid) and its intrinsic space, which is rigidly
connected with this matter. Free (inertial) motion of the test particles in the
hollows inside the liquid or in an empty space above it will depend in Weyl FR
not only on the strength of gravitational forces, which are determined by the
metrical tensor of STC of liquid and are proportional to hamiltonians of these
particles, but also on the strength of pseudodissipative pseudoforces, which are determined by the
cosmological
*λ*-term of GR equations and
are proportional to linear momentums of these particles. The presence of these dissipative
pseudoforces in empty space is caused only by the evolutionary decrease of the
value of absolute velocity of light [16, 17]. Therefore, hamiltonian of
free-moving test particle in Weyl FR (as well as in nonrigid FR of matter) does
not conserve. And, consequently, inertial motion of this particle realizes in
Weyl FR along the non-stationary geodesic lines of the STC of liquid and is
hyperbolic even in case of hypothetical absence of gravitational field [16,
17]. Analogously, because of evolutionary decreasing of kinetic energy in Weyl
FR the Earth moves in the space of this FR (in Newton-Weyl absolute space) not
along the circular orbit, but along the logarithmic spiral. Unlike in Weyl FR
and in nonrigid FR of naturally self-cooling body, in rigid FR of matter the
strength of pseudodissipative pseudoforces is
equal to zero, as well as the improper values of velocity of light on its
observer horizon. This is connected with the principal unobservability in
matter FR of evolutionary changes of values of the velocity of light and of
spatial parameters of matter elementary particles. And, therefore, hamiltonian
conservation in rigid FR of matter takes place only because of gauge-invariance
of eigenvalues of matter space-time characteristics. Thus, physical vacuum is
an active medium with energy pseudodissipation in Weyl FR.

While in
cybernetics and thermodynamics the most fundamental factor is the presence of
negative feedbacks, which guarantee the stability of correspondingly complex
systems and matter equilibrium states, in synergetics (the theory of
dissipative systems) the most fundamental factor is the self-organization of
spiral autowave structures in active mediums with energy dissipation. Spiral waves are the main type of elementary self-sustained structures in homogeneous excitable mediums [30]. The physical vacuum is exactly such medium. Therefore, matter elementary particles
inevitably had to be self-organized in it exactly only as spiral waves. The
following main regular properties, which are inherent for matter elementary
particles and for spiral waves, also denote this:

1)
wave-corpuscle nature
of the elementary particles (they, like the nuclei of spiral waves, have spatial coordinates);

2)
cooperative behavior
of elementary particles, as well as of spiral waves;

3)
presence of
inertial motion (for elementary particles, as well as for spiral autowave structural
elements);

4)
presence of annihilation
after collision
(for elementary particles and antiparticles,
as well as for diverging and converging spiral waves);

5)
presence of
uncertainty in time and space of execution of quantum of action (it’s impossible in
principle to determine the beginning and the end of any spiral turn, which
transfers the quantum of action, and, therefore, it’s impossible to determine
precisely the coordinates of world points, in which action executes);

6)
possibility to
interpret final local sinks of spiral waves as negative electric elementary
charges, and to interpret their initial local sources as positive electric
elementary charges;

7)
the fact that
electron has intrinsic angular momentum (spin), which is not connected with its
rotation (radial propagation of turns of spiral wave
is analogous to the effect of rotation of rigid logarithmic spiral);

8)
the fact that spin of elementary
particles may take on positive and negative values
(analogously to right- and left-hand spirals);

9)
the fact that
electrons in atom transform itself into
stationary and progressing orbital
waves (analogously to transformation of spiral
waves into simple vortex rings);

10)
impossibility of existence of single quark, as well as of single twisted vortex ring
[30];

11)
presence
of asymptotical freedom for quarks, as well as for twisted vortex rings, which are linked
(interaction forces appear only in case of attempt to separate quarks or
twisted vortex rings);

12)
resemblance of topological limitations (restrictions), which greatly reduce the number of permissible elementary
particles and three-dimensional spiral structures [31-34];

13)
very short lifetime of elementary particles,
as well as of three-dimensional spiral structures, which can’t be
self-organized in structures of higher hierarchical level.

However, we need to find the answers on the following questions. Which
of the known elementary particles are not fictive and,
therefore, can be spiral autowaves? Space-time
modulations of which parameters of physical vacuum can be three-dimensional spiral structures that correspond to elementary
particles?

When we
attribute to gravitational field the properties, such as has electromagnetic
field, we can consider it as equal in rights with electromagnetic field and,
therefore, – as something independent. But the
well-known facts denote contrary. All four fundamental fields – strong, weak,
electromagnetic and gravitational are based on electromagnetic properties of
physical vacuum and matter and they are specific reflections of these
properties on the various hierarchical levels of matter self-organization.
Despite the presence of variety of resemblances of properties of fundamental
fields, topological and other principal differences don’t allow us to make
total unification of all fundamental intercouplings (interactions) between
matter elementary particles. For example, gravitational potential in matter FR is the function of improper (coordinate) value of velocity of propagation of electromagnetic waves in vacuum, the
value of which is uniquely determined by the values of permittivity and magnetic permeability of physical vacuum.
Furthermore, the gravity reveals itself in macroworld only because of the presence of Van-der-Waals
forces of electromagnetic interactions between the molecules of hydrogen. After
all, only due to these forces molecules of hydrogen and initial helium began to mutually self-contract
in absolute space. In case of hypothetical absence of electromagnetic
interaction, separately self-contracting molecules of matter would remain
absolutely uniformly distributed in cosmic space and, therefore, gravitational
macrofields that reflect physical macroinhomogeneity of cosmic space would never be originated. This is the cause of absolutely different
mechanism of action of gravitation. For
electromagnetic interaction the change of linear momentum of elementary
particle is realized merely because of the transfer of additional momentum from
the free photon, adsorbed by it. Otherwise, the change of linear momentums of
elementary particles in gravitational field is caused by principal
nonconservation in physically inhomogeneous space of momentums of virtual
particles and quasiparticles, which realize interaction between neighbouring
stable particles as well as between these particles and the “cloud” of virtual
particles [18]. Therefore, there is no necessity in the existence of specific quasiparticles (gravitons), which transfer momentum and energy
during the process of matter motion in gravitational field. The existence of
gravitons is impossible in principle, as it is shown in [17].

Weak
interaction of elementary particles also has electromagnetic nature. In fact, it is realized via exchange of virtual particles, which have not only mass,
but also electric charge and in the process of their accelerated motion can generate
ordinary electromagnetic waves. The possibility of unification of weak
interaction with electromagnetic interaction into electroweak interaction also
denotes this.

Strong
couplings between quarks (between twisted vortex rings, according to 10) and
11)) are, apparently, absolutely topological couplings, such as couplings of
chain links or couplings of nested structure elements. It wouldn’t have been logical, if the nature hadn’t used such simple
mechanism of intercoupling of elementary particles. That’s why there is no necessity in the existence of gluons, forced to “glue” quarks together.

Molecules of
matter of real physical bodies execute heat oscillatory motions. Therefore,
individual motion of molecules of hyperbolically accelerating body is not
hyperbolic in fact. And, consequently, the values of strengths [18] of gravitational field, which appears in
FR of hyperbolically accelerating body, are only the average statistical values.
In the places of dislocations of the molecules of moving body space-time
modulation of the values of strength of graviinertional field, as well as of
the values of frequency of interaction of matter elementary particles, which
determines rate of course of proper quantum (standard) time of matter, takes
place. Therefore, intrinsic space of accelerating body is not only physically macroinhomogeneous, but
also physically microinhomogeneous.

Because of high
value of density of matter in atom nucleus average statistical relative value
of the frequency of interactions *f* in the points of dislocations of protons and neutrons much lower than
at the periphery of atom. As it follows from the solutions of GR equations, the decrease of the improper value of the velocity of light has the influence on the frequency
of interaction of elementary particles, and this influence is partially
compensated by the decreasing of the distance between the interacting particles
in absolute space. This compensation is like the
compensation, which is realized by relativistic length shrinkage of moving body
[18].
Therefore, physical microinhomogeneity of intrinsic space of matter, which is identical with Salam strong gravity [2, 36], is always followed also by
metrical microinhomogeneity or in another interpretation by the microcurvature
(roughness) of this space. Already in 1870 Clifford in his paper “On the spatial
theory of matter” denotes the possibility of this: “I consider that small
regions of space are analogous (by their nature) to the little hillocks on the
surface, which is plain on average. So ordinary geometrical laws are
inapplicable here” [37-39]. Being based on Clifford-Einstein spatial theory of
matter, Wheeler elaborated the geometrodynamical theory of small-scale
structure of space-time. This theory consider matter elementary particles as
geometrodynamical excitons [39, 40]. The
presence of physical and metrical (scaling) microinhomogeneities of space in
the places of high matter concentration (in atoms nuclei) has profound physical
meaning. This is the demonstration of the presence of negative feedback between
the values of measuring physical parameter (dimension) and the values of the
unit of this parameter (dimension) in Weyl FR. This feedback prevents
catastrophical change of the parameter (dimension) in internal FR of matter and
makes unreachable for it both zero value and infinitely high value. Because of
this, nuclei of atoms as well as astronomical bodies have individual
pseudohorizons of past and future, which assign correspondingly maximal and
minimal physically realizable values of the luminosity radius in their
intrinsic FRs.

In such physically
and metrically microinhomogeneous space improper values of energy and linear
momentum of elementary particles have to be determined with using of additional
conform transformations or renormalizations, which would take into account
these microinhomogeneities and their variation under the influence of
destabilizing factors. Such renormalizations of physical parameters are being
made during the process of finding of approximate solutions of the equations of
nuclear and quantum physics via the method of perturbation theory. These true
values of energy and linear momentum will be substantially smaller than their
eigenvalues, which don’t differ from their values in hypothetical physically
and metrically homogeneous space. In spite of the small mutual difference between the eigenvalues of effective cross-sections of neutron and proton, and, consequently, between their
values in rough internal space of the matter, in the Euclidean space of Weyl FR
the value of effective cross-section of neutron is much smaller than the value
of effective cross-section of proton. This is caused by the fact that the
intrinsic space of neutron is more curved, and, consequently, by more
considerable increase in density of flux of scattered particles in Weyl FR
during their approaching to neutron (than for the case of approaching to
proton). Therefore, during the process of neutron transformation into proton
the work on neutron expansion in self-gravitational field is being executed in
Weyl FR. In matter FR the execution of this work
is aimed to increase the eigenvalue of energy via the increase of local improper value of the
velocity of light, which is substantially higher for proton than for neutron.
The fact that we don’t take into account the changes of local improper values
of the velocity of light in the process of neutron β-decay is the cause of pretended energy deficit. This
deficit is being determined as the difference of not real but effective energy
values in initial and final states of elementary particles. Nonconservation of
the linear and angular momentums in the process of β-decay is caused
by the substantial physical microinhomogeneity of the space in atom nucleus.
And, therefore, the existence of additional particle, which takes away part of
energy and linear and angular momentums, is not required. Bohr hypothesis about energy nonconservation in
subatomic physics [41, 42] have to be considered as applied for effective
values of energies of elementary particles (for “projections” of real values of
energies on conventional metrically and physically microhomogeneous space of
macroscopic FR).

Unlike eigenvalues, improper values of energies of different neutrons (protons) are unequal in Weyl FR even for the same atom.
The dispersions of improper values of neutrons and protons energies are caused
by the substantial physical microinhomogeneity of the space inside the atom
nucleus and by continuous oscillatory variations of gravitational energies of
neutrons and protons during the process of interaction of their quarks with the
quarks of neighboring neutrons and protons, which are in actual as well as in
virtual states. Analogously to the dispersion of kinetic energies of thermal oscillatory
motion of molecules, it also obeys the certain statistical regularities.
Therefore, like the spectra of frequencies and energies of the photons of
thermal radiation, spectrum of the energies of electrons in the process of
neutrons β-decay is continuous (unlike the case of
the change of quantum-mechanical state of elementary particles, when the
spectrum is discrete). Generally the dispersion of the energies of electrons
during β-decay process is being explained by the
dispersion of energies of antineutrinos, which are the thing in itself (like
the black box in cybernetics) and as if they are radiated together with
electrons. However, there is no intelligible explanation of the fact that
antineutrinos itself have continuous spectra.

Of course,
the using of individual average value of frequency of interaction of concrete
elementary particle *f* in GR (or using of local improper value
of the velocity of light *v _{c}*, which is
equivalent to

Therefore,
in spite of the equality of total energies (improper values of energies) of
electron and muon, which had been transformed into this electron with
conservation of total energy, effective values of energy and mass of electron
in hypothetically microinhomogeneous and smooth (without microcurvature) space
are approximately 207 times less than effective values of energy and mass of
muon. And this takes place, despite the partial compensation of the effect,
which is caused by more substantial physical microinhomogeneity of internal
space, by the effect, which is caused by more substantial (than for electron)
microcurvature of internal space of muon. Being based on hyperbole (excessive
exaggeration) of this effect one can build geometrodynamical model of mass “without
mass” (Wheeler geon [29, 40]). In fact in this model one associates nonzero
effective (eigen-) value of energy of elementary particle with zero value of
its total energy (because of *v _{c}*=0). The possibility of such hyperbole is the ponderable argument in
favour of the conception of neutrino fictitiousness. It becomes apparent that
in fact we register not neutrino but only the
indirect consequences of nuclear reactions, in which as if they had to be
originated. After all, phase changes of collective space-time state of
matter and its gravitational field propagate with supraluminal velocity [18] and can be registered in any point of
space even without coming of hypothetical neutrinos to this point.

So among all well-known noncomposite fundamental particles of matter only electron with positron, muons and quarks with antiquarks can be for sure nonfictive. And photon is the only one fundamental quasiparticle, existence of which is irrefutable. Being based on electromagnetic nature of all elementary particles and taking into account principal impossibility to register separate turns of spiral waves, we can assume the following: Electron with muon and quarks are space-time modulations of permittivity and magnetic permeability of unstructured physical vacuum in the form of spiral waves, which form correspondingly simple and twisted vortex rings in atoms [30]. In this connection, the topology of STC of muons, positively charged quarks and negatively charged antiquarks is like the topology of STC of hollow astronomical bodies. At such topology of quarks the twistedness of vortex rings is obligatory only for internal microsubspace of enveloping quark (antiquark) and for external microsubspace of antiquark (quark), which is confined in the internal microsubspace of any other enveloping quark (antiquark). Such nested structure, which consists of enveloping and confined quarks, corresponds to (-mesons. Due to untwistedness of vortex ring in external subspace of enveloping quark, (-meson can be transformed into muon. This transformation is the result of annihilation of twisted vortex rings of enveloping quark and antiquark, confined into it, which takes place in the internal microsubspace of this quark. Vortex lines of spiral waves of quarks, which form resonances and some other metastable particles, can not only form circle, but also can be tied in a knot [30, 33]. It is possible that closure of conventional vortex lines into rings, as well as closure of terrestrial orbit, takes place only in matter FR and is absent in Weyl FR.

Electromagnetic waves, which imbue these vortex rings and knots, are the waves of modulating oscillations of electric and magnetic strengths. These oscillations are superimposed on more high-frequency quasiperiodical carrier oscillations of these strengths. Carrier oscillations (as well as oscillations of permittivity and magnetic permeability) are realizing on de Broglie frequency of totality of all matter objects, on which collectivized turns of spiral waves surge at the velocity of propagation of front of matter intrinsic time in Weyl FR. Therefore, every of these turns corresponds to simultaneous (coincident) events, and thus, to certain collective space-time (microphase) state of whole matter, on which it executes quantum of action HYPERLINK "http://pavlo-danylchenko.narod.ru/docs/Nature_Eng.doc" [18]. This is in a good agreement in Einstein-Podolki-Rosen paradox [43, 44] with momenrary mutual coordination of changes of quantum-mechanical characteristics of previously correlated photons or elementary particles after mutual self-distancing of them on long distances. The presence of metrical (which causes curvature of matter intrinsic space) and physical (identifiable with gravitational field) macroinhomogeneities of Weyl FR space may be caused by increasing (from periphery to the center) of spatial density of collectivized turns of spiral waves. This increasing of density of turns of spiral waves is inevitable because of shrinkage of distances between peaks of solitons, which form these turns, as they approach to the center. Also this increasing causes origination of metrical and physical microinhomogeneities of space in the places of dislocation of atom nuclei.

Microcurvature
and physical microinhomogeneity of intrinsic spaces of protons and neutrons
also take place because of increasing (from periphery to the center) of density
of their individual spiral turns. But these localized inhomogeneities can’t be
determined via solving the equations of gravitational field. In fact, GR, as
well as mechanics and thermodynamics, operates only with average statistical
parameters and as well as SR (Heisenberg [45] paid attention on inadequacy of
description of space-time relations in microworld by SR) provides only
absolutely solid and locally uniform fullness of space by matter. Moreover,
microcurvature and physical microinhomogeneity of space strongly vary in the
process of interaction of elementary particles. Therefore, equations of quantum
physics, which implicitly allow for (or must allow for) microcurvature and
physical microinhomogeneity of space, have to be solved together with equations
of renormalization group. And this means that metrical correlations in
microworld are nontrivial (Zelmanov postulates that they are absent at all [26,
46]; Menger proposes to bring in statistical notion of distance between the
points [46]) and don’t allow us to formulate conservation laws in ordinary
form. So, in matter rigid FR spatial distributions of the values of
microcurvature and physical microinhomogeneity of its space are not stable in
time (unlike the distributions of macrocurvature and physical
macroinhomogeneity). And this leads to nonconservation of momentary values of
energy of photons, as well as of elementary particles. And, therefore, only
average values (mathematical expectations) of energy of elementary particles can conserve in microworld
[17]. Measure of inaccuracy in determination of this average value of energy: Δ*E _{min}*=

Vortex lines of converging spiral waves, which
correspond, according to 6), to negatively charged particles, are stable only
in the space or microsubspaces, in which *∂**r*/*∂**R*>0.
Vortex lines of diverging spiral waves, which correspond to positively charged
particles, are stable only in the space or microsubspaces, in which *∂**r*/*∂**R*<0. Only
in these spaces or microsubspaces their phase trajectories are winding up on limit
cycles. Therefore, positively charged quarks of absolutely stable particles
(protons and neutrons) are self-isolated from
external space by metrically singular surface and turns of their spiral waves
are draining to pseudohorizon of future of microsubspace, limited by this
singular surface. Because of this Schwarzschild-like radius of influence of
strong gravitation is of the same order of magnitude with dimensions of protons
and neutrons [2]. This singular surface is the sink of turns of spiral waves in
external space and also it is their source in microsubspace, limited by it.

In this
microsubspace singular surface is considered as convex surface, which contains
whole Universe. That’s why in the FR of positively charged quark of proton,
which is confined in singular surface, the Universe can be considered as
negatively charged baryon. And this is one of the reasons of utopian considering of elementary
particles as microuniverses [2].

In general case two different topologies are
possible. If positively charged quark have hollow topological form and is
quasiconcentric to singular surface, in which it is confined, in absolute
space, then in its FR the Universe will be confined in it. And when this
quasiconcentricity is absent the planetary model will be realized. As if
positively charged quark revolves around the negatively charged Universe.
Transition from one topology to another corresponds to the change of metastable
state of quark (to the change of the values of its quantum numbers) and not
obligatory have to be connected with absorption or radiation of any specific
particles or quasiparticles by it. Negatively charged d-quark of proton, confined in this
singular surface, in addition may be confined in the singular surface of one of
two positively charged u-quarks (as in multiple nested structure). Therefore,
these two u-quarks will be in nonidentical quantum states (will have
nonidentical “colour”). Because of this, d-quark itself can be only s-quark, which is additionally
confined in singular surface, which hides (“screens”) its strangeness, of any
other quark.

These singular surfaces can be spherical or
ellipsoidal (when spiral wave tends to degeneration into concentric waves of
pacemaker [30] in FR, in which elementary particle, formed by this spiral wave,
is motionless) or toric, or maybe – they can be closed surfaces of more complex
form in the case of formation of vortex knots. Confinement of
several quarks by the same singular surface makes requirement of twistedness of
vortex rings of spiral waves of these quarks not strongly obligatory (surplus).
That’s why we can’t exclude the possibility of self-organization of all or only
of some types of quarks in the form of simple vortex rings.

The description of antimatter microobjects,
which are contained in internal half-space of hollow body, is analogous.
Physical notions, shown here, amplify well-known theories of elementary
particles very well, but only in the case of inevitable remaking sense of these theories (and possibly – with
modernization of some of them).

According to all
this, elementary particles and matter, which consists of them, are stable only
in external empty space and in external half-layer of the hollow body. On the
contrary, antiparticles and antimatter, which consists of them, are stable only
in internal empty space and in internal half-layer of the hollow body (see figure).

And, therefore, median singular surface of hollow body is a
natural barrier between matter and antimatter, which preserve them from
catastrophic annihilation. Sporadic leakage of matter and antimatter through
this barrier is possible in principle (even without bringing in
quantum-mechanical notions about motion), because of incompletely mutually
coordinating (without this leakage) self-cooling of external and internal parts
of not absolutely cold hollow body. This self-cooling disturbs the common
equilibrium and thus leads to radial migration of singular surface relatively
to matter and antimatter. Due to matter and antimatter annihilation, which is
the cause of this leakage, unlimited in time maintaining of radiant emmitance
of hollow body with as cold as desired boundary surfaces is possible. In
nonrigid and quasirigid intrinsic FRs of
self-cooling hollow bodies the value of luminosity radius of median singular
surface is continuously decreasing. All events that coincide in matter
intrinsic FR can be brought into accord with every concrete value of this
radius (as well as with the value of radius of observer horizon [18, 48]).
Because of gradual displacement of median singular surface of self-cooling
hollow body in its intrinsic space, the value of velocity of light on this
surface (as well as on the singular surfaces of pseudohorizons of past and
future [48]) can be as small as desired but nonzero in rigid and quasirigid
FRs. This guarantees the possibility of unimpeded one-way overcoming of barrier
between matter and antimatter, viz – the possibility of continuous penetration
of antimatter to matter (to the external part of hollow body). Thus, continuous course
of the process of gradual annihilation of matter and antimatter in hot hollow
bodies is guarantied. And, therefore, annihilation of matter and antimatter is
the main source of energy of hollow bodies.

It should be
noted, that before the moment of discontinuity of mainly hydrogenous continuum
of Universe into single gas aggregates there was no antimatter in
Universe. Initial
self-organization of antimatter could take place only because
of the origination of ultrahigh eigenvalues of matter density, pressure and
temperature, and, consequently, because of the origination of critical density
of energy of thermal electromagnetic bremsstrahlung and origination of space
region with unstable spherocylindrical metrics in the center of gigantic gas aggregates.
Therefore, formation of initial (“seed”) antimatter, which have caused the
transformation of unstable uniform spherocylindric metrics at first into
topologicaly inhomogeneous metrics and then into extraordinary metrics of its
intrinsic space, may took place because of the birth of pairs of particles and
antiparticles, which have correspondingly ordinary and extraordinary metrics of
intrinsic microsubspaces and, therefore, don’t have time
for mutual annihilation, in photon gas. Unification
of microsubspaces that have extraordinary metrics into space-time continuum
have led to localization of singular state of matter only on spherical singular
surface, which began to “inflate” (increase its radius) in absolute space. Transformation of originated, as well as
of already existed, elementary particles into antiparticles realized as
singular surface inflated due to reversal of the wave front of their spiral
waves.

Separate gas aggregates have catastrophically self-contracted
in intrinsic space, because of origination and rash increase of spherically
symmetrical physical macroinhomogeneity of space, which led to nonconservation
of linear momentum in space. Self-contraction of gas aggregates have been realized because of the
growing of both momentum increment of inward (centripetal) and momentum decrement of outward (centrifugal) virtual photons in the process of Van der Waals
electromagnetic interaction between gas molecules. Physical macroinhomogeneity of space (originated only
in the process of this and identifiable with gravitational field), of course,
have led to polarization of physical microinhomogeneities of space, which are
formed by atoms. Therefore, virtual π-mesons
and photons, which realized intra-atomic interactions between protons and
correspondingly neutrons and electrons [18], also took part in pushing of atoms
to the center of gas aggregate. They take part now in production of body free
fall and in setting body in motion by any nongravitational forces. And also
they are indirectly accounted for atoms inertia because of finiteness of
frequency of these interactions.

All this has caused the origination of gigantic gas aggregates
with hollow topological form in the Universe. Quasars have been originated from
the nuclei of the most stable gas aggregates. Because of the large accidental,
as well as autowave, fluctuations of thermodynamical characteristics of matter
and antimatter inside quasars, rather substantial radial migration of their
median singular surface took place. This, together with unequality to zero of
the value of velocity of light on this singular surface, was the cause of
intensive course of the process of matter and antimatter annihilation, and,
therefore, the cause of extraordinarily high luminosity of quasars. The process
of formation of supernovas from hollow stars is also accompanied by
annihilation of matter and antimatter. Short-term extraordinarily high
luminosity of supernovas is caused exactly by this.

Absolute matter stability is caused by the presence of
the phenomenon of scattering of distant objects from
observer (Universe expansion). On the contrary, absolute antimatter stability
is caused by the presence of the phenomenon of crowding of distant objects on
the observer. Therefore, Universe expansion in principle never can turn into
its contraction. This expansion is an infinitely long evolutionary
process. This process is caused, the same as continuous existence of matter in
Universe, by continuous gauge-evolutionary change of physical vacuum properties
(physical vacuum ageing).

Full version of the article PDF ( 295 kb), DOC ( 211 kb).

[1].
Einstein, A., The Meaning of Relativity, Princeton: University Press, 1953

[2].
Ivanenko, D. D., Actuality of Einstein theory of gravitation, in: Einstein
Centenarium, ed. H.-J. Treder, Berlin: Akademie Verlag, 1979

[3].
Möller, C, Progress and limitation of Einsteinian theory of relativity and
gravitation, in: Astrofisica e Cosmologia Gravitazione Quanti e Relativita,
Firenze: Giunti Barbera, 1982

[4].
Möller, C., Are the singularities inevitable in the theory of gravitation?,
in: Einstein Centenarium, ed. H.-J. Treder Berlin: Akademie Verlag, 1982

[5]. Hawking, S. W., Path integrals, in: General Relativity, An
Einstein Centenary Survey, ed. S. W. Hawking and W. Israel, Cambridge:
Cambridge University Press, 1979

[6]. Hawking,
S. W., Penrose, R., Proc. Roy. Soc., 1970, v. A314, p. 529

[7]. Hawking, S.W., Ellis,
G. F., The large scale structure of spacetime, Cambridge: Cambridge University
Press, 1973

[8]. Weyl,
H., Phys. Z., 1923, b. 24, s. 230

[9]. Weyl, H.,
Philos. Mag., 1930, v. 9, p. 936

[10].
Möller, C., The Theory of Relativity, Oxford: Clarendon Press Oxford, 1972

[11]. Utiyama R. What had physics come for? (From the theory of relativity to the theory of gauge fields), Moscow: Znaniye, 1986 (in Russian)

[12]. Dirac, P.
A. M., Directions in Physics, New York: J. Willey and Sons, 1978

[13]. Gorelik, G. E., The history of relativistic
cosmology and coincidence of large numbers, in: Einsteinian collection,
1982-1983, ed. Kobzarev I.Yu., Moscow: Nauka, 1986, p.302 (in Russian); Hermann Weyl and Large Numbers in Relativistic Cosmology, in: Einstein Studies in Russia. [Einstein Studies, Vol. 10.]
Eds. Yu. Balashov, V. Vizgin. Boston: Birkhaeuser, 2002. p. 91-106.

[14]. Lemaitre,
G. J., Math. and Phys., 1925, v. 4, p. 188

[15].
Robertson, H. P., Philos. Mag., 1928, v. 5, p. 839

[16]. Danylchenko, P., Pseudoinertial contracting
frames of reference, in: The Gauge-evolutionary theory of the Creation (space,
time, gravitation and the Universe expansion), Ukraine, Vinnytsia, 1994, v.1,
p. 22 (in Russian)

[17]. Danylchenko, P., Foundations of the
Gauge-evolutionary theory of the Creation (space, time, gravitation and the
Universe expansion), Ukraine, Vinnytsia, 1994 (in Russian); web-edition, 2005

(http://pavlo-danylchenko.narod.ru/docs/Osnovy_Eng.html)

[18]. Danylchenko, P., The nature of relativistic
length shrinkage, in: Gauge-Evolutionary Interpretation of Special and General
Relativities, Vinnitsa, O. Vlasuk, 2004, p. 3

(http://pavlo-danylchenko.narod.ru/docs/Nature_Eng.html)

[19].
Danylchenko, P., The gauge foundations of special relativity, in: Gauge-Evolutionary Interpretation of
Special and General Relativities, Vinnitsa, O. Vlasuk, 2004, p. 15

(http://pavlo-danylchenko.narod.ru/docs/Foundations_Eng.html)

[20]. Penrose, R., Conformal
interpretation of infinity, in: Relativity, Groups and Topology, ed. De Witt
C., De Witt B., New York – London, 1964, p.565

[21].
Bondi, H., Cosmology, Cambridge, 2nd Ed., 1960, p. 38, 45

[22]. Linde, A. D., Particle Physics and
Inflationary Cosmology, Switzerland, Chur: Harwood Academic Publishers, 1990

[23]. Weyl H. Raum-Zeit-Materie, 3rd edn. 1920; 5th edn. – Berlin 1923; Space,
Time and Matter. – Methuen, London, 1922

[24]. Poincaré H. La Science et l’hypothése, Paris,
1902; London: Walter Scott
Publishing, 1905

[25]. Sawyer W.W. Poincare Universe in: Prelude to
Mathematics, Penguin Books, 1955

[26]. Mostepanenko A. Space and time in macro-, mega- and
microworld. Moscow: Politizdat, 1974 (in Russian)

[27]. Riess A. et al*. *Type Ia
Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy
Evolution, Astrophysical Journal, 2004,
v. 607. – P. 665-687. (astro-ph/0402512)

[28]. Fuller, R. W., Wheeler, J. A., Phis. Rev., 1962, v. 128, p. 919

[29].
Wheeler, J. A., Gravitation as geometry (II), in: Gravitation and Relativity, ed. H.-J. Chiu and W. F.
Hoffmann, New York – Amsterdam: W.A. Benjamin. Inc., 1964

[30]. Mikhailov, A. S., Foundations of Synergetics
I. Distributed Active Systems, 2nd revised edition; Berlin: Springer 1994

[31]. Winfree, A.T., Strogatz, S.H., Physica, 1983, v. 9D, p. 35

[32]. Winfree, A.T., Strogatz, S.H., Physica, 1983, v. 9D, p. 65

[33]. Winfree, A.T., Strogatz, S.H., Physica, 1983,
v. 9D, p. 333

[34]. Winfree, A.T., Strogatz, S.H., Physica, 1983,
v. 13D, p. 221

[35]. Wheeler, J. A., Mach
principle as boundary condition for Einstein equations, in: Gravitation and
Relativity, ed. H.-J. Chiu and W. F. Hoffmann, New York – Amsterdam: W.A.
Benjamin. Inc., 1964

[36]. Salam, A., Gauge interactions,
elementarity and superunification., Preprint IC/81/9, Intern. Theor.
Phys.,Trieste, 1981

[37]. Clifford, W.K., Lectures and Essays, eds.
Stephen, L., Pollock, F., London: Macmillan, 1879, p. 244, 322

[38]. Clifford, W.K., Mathematical Papers, ed. Tucker, R., London: Macmillan, 1882, p.
21

[39]. Misner, C. W., Thorne, K. S., Wheeler, J. A.,
Gravitation, ed. Freeman, W.H. and company, San Francisco, 1973

[40]. Wheeler, J.A., Geometrodynamics, New York:
Academic Press, 1962

[41].
Bohr, N., Atomi stability and conservation laws, in: Att del Convegno di fisica
nucleare della Fondatione A. Volta, 1931, Roma, 1932, p.75

[42].
Gorelik, G. E., The fate of N. Bohr hypothesis about energy nonconservation,
in: Nils Bohr and science of XX century, Kiev: Naukova dumka, 1988, p. 83 (in
Russian)

[43].
Einstein,
A., Podolski B., Rosen N., Philos. Rev., 1935, v. 47, p.
7

[44]. Vigier J.-P., Paper on
Einstein-Podolski-Rosen paradox, in Einstein Centenarium, ed. H.-J. Treder,
Berlin: Akademie Verlag, 1982

[45]. Heisenberg W., Physics and
philosophy, New York: Harper Torchbooks, 1958

[46]. Zelmanov, A.L.,
Diversity of the material world and the problem of infinity of the Universe,
in: Infinity and Universe, Moscow: Mysl’, 1969, p. 274 - 324 (in Russian)

[47]. Menger K., The Theory of Relativity and
Geometry, in: Albert Einstein: Philosopher-Scientist, p. 474

[48]. Danylchenko, P., Nonrigid frames of references
of coordinates and time, which self-contract in Minkowski space-time, in: The
Gauge-evolutionary theory of the Creation (space, time, gravitation and the
Universe expansion), Ukraine, Vinnytsia, 1994, v. 1, p. 52 (in Russian)

[49]. Shirokov Yu. M. Reports of the USSR Academy of Sciences, 1956, III, p. 1123 (in Russian)

Хостинг от uCoz