**Pavlo ****DANYLCHENKO**

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**Synopsis**

Let Δ*L _{j}* and Δ

The rate of the process of evolutionary self-contraction of
matter in the space-time continuum (STC) of PV is characterized by a relative
change of the value of an unobservable (hidden) parameter *N*. That’s why in every point of physically inhomogeneous
fundamental space this rate must be proportional (as well as rates of any
observable physical processes) to standard normalized value in it of
interaction frequency:

|(∂*N*/∂*T*)* _{R}*|/

where the *H*(*r*) function, independent on cosmological
(absolute) time *T*, depends on spatial
distribution in the matter of the eigenvalue of its enthalpy density. In space
free from matter this function (as it will be seen from the following) is
gauge-unchangeable eigenvalue of Hubble constant *H _{e}*.

It is necessary to renormalize continuously the distances in
fundamental space accordingly to continuous recalibration of rigid metrical
scale of fundamental space by a certain evolutionary decreasing in PVFR
material scale. Using of a metrically homogeneous scale of absolute time (MHSAT)
[2], based on proportional synchronization of course rate of this time with
course rates of proper quantum time of every point of
all the gauge-self-contracting bodies (that is why it is a metrically
homogeneous scale of cosmological time), allows avoiding continuous
renormalization of absolute (cosmological) time. And, consequently, this allows
considering not relative *d**T*, but absolute value of time increment *dT*=[1–*H _{e}*(

Analogously (3), the “speed” of radial change of standard values of
interaction frequency must be proportional in every point of fundamental space
to the values of spatial frequencies *N* in them.
And, besides this, it must be – inversely proportional to the square of
eigenvalue (i.e. value, renormalized according to eigenvalue of material length
standard) of radial distance, identically equal to luminosity radial distance
in intrinsic FR of a physical body. This is caused by decrease in
three-dimensional homogeneous space by this dependence of density of a flux of
the source of any physical effect, which is not weakened by anything.
Therefore, analogously to Poisson equation [6] (∂*f**
*/∂*R*)* _{T}*=

The stability of values of relativistic exceedings of shrinkages of
radial dimensions above the shrinkage of matter meridian dimensions is the
necessary condition of energy conservation by gauge-self-contracting matter [2]
as well as the condition of homogeneity of cosmological time, considered here.
These exceedings of shrinkage of radial dimensions take place only in
fundamental space (as well as metrical inhomogeneity of matter) and they are
unobservable in principle in matter intrinsic space. The stability of the
values of these exceedings is guaranteed only in the case of stability of the
ratio *V _{j}*

*V _{j}*=

where gauge-invariant magnitudes *V _{j}*

Considering the stationarity of relativistic exceeding of shrinkage in fundamental
space of radial dimensions above the shrinkage of meridian dimensions of the
matter (gauge-evolutionarily self-contracting in fundamental space) improper
value of the velocity of interaction of propagation and, consequently, improper
(coordinate) value of the velocity of light are constant not only in proper
quantum time of points, where they propagate. They are also permanent while
taking time readings by a clock of any other points of this space and, consequently, they are
permanent in astronomic
(coordinate) time *t*, common for the whole
physical body. Exactly this determines physical as well as metrical (due to principle
metrical homogeneity of the matter intrinsic space) homogeneity of
coordinate-like intrinsic time of a body, gauge-self-contracting in the
fundamental space. And conseqently, this also allows using of normalized improper value of the velocity
of light *v _{cj}*

This means that the equality to unity of product of *a*(*r*)=(∂*r _{metr}*/∂

At the direction of parameter *r _{ge}* to zero (that responds to decreasing to a zero value of power of the
source of gravitational induction of the spatial inhomogeneity PV properties)
the average statistical interaction frequency of elementary particles,
connected to this in the absolute free space lacking gravitational field, must
remain finite by value. Besides, identical objects (frequency standards) must
have identical frequencies in all space (

But in intrinsic conventionally free space of evolutionary
gauge-self-contracting body, the radial distribution of normalized improper (coordinate)
value of the velocity of light will be the following: *v _{cj}*

In physically homogeneous space, inertial pseudo-force, which only compensates but not equilibrates the force, accelerating the body motion, is proportional to hamiltonian and gradient of logarithm of relativistic shrinkage of the length of moving body. Hamiltonian intensity of inertial pseudoforce is equivalent to the acceleration of the motion of classical physics. During the body free fall in the gravitational field (that is not equilibrium but inertial motion of the body in physically inhomogeneous space) inertial pseudoforce compensates (but not equllibrates) the gravitational pseudoforce [2, 3]. Therefore, at the invariance of eigenvalue of the free falling body mass its Hamiltonian (covariant component of energy-momentum tensor, to which covariant general-relativistic value of mass is equivalent) also stays invariable.

Hamiltonian conservability at the process of inertial motion of the
body in some cases makes the usage of logarithm of improper value of the velocity of light as scalar potential of gravitational field more expedient. This
potential is used instead of the potential, which determines the strength of
gravitational pseudoforces relatively to contravariant general-relativistic
value of mass [6], nonconservating at the body free fall in the gravitational
field (so at inertial motion of the body in physically inhomogeneous space). Total
energy of
body (contravariant component of energy-momentum tensor, to which contravariant
general-relativistic value of mass is equivalent) includes, besides hamiltonian,
also collectivized in gravitational field energy of gravitational binding. This
binding energy (due to the presence of gravithermodynamical negative feedback)
is an additive compensation of multiplicative transformation of energy of body in the
equilibrium process of its quasistatic transfer along the direction of gradient of
gravitational field.

Gravitational forces affecting an object are determined only by its
Hamiltonian or hamiltonian strength of the gravitational field. Therefore, they
do not depend directly on eigenvalue of energy density, and consistently, on
eigenvalue of density of matter mass of the object. This corresponds not only
to the objects situated in the free space, but also to the objects that are
component parts of physical bodies (bodies possessing a gravitational field). Not only strength of
gravitational field in a matter, but also the curvature of intrinsic space of
the matter, which is characterized by the *a*(*r*) function,
does not depend directly on eigenvalue of density of the matter mass. Because
of this we have: (*H**′*/*H*)–(*H**′*/*H*)_{0}=–*κ**c*^{2}*ar*(*μ*–*μ*_{0})/2,
where *κ** *is Einstein
gravitational constant. In general case, the velocity
of propagation of interaction in the matter is to depend on spatial
distribution of eigenvalue of the matter enthalpy density *σ*=*μ**c*^{2}+*p*. At hypothetical isobaric decreasing of eigenvalue of enthalpy
density to zero (which cannot be realized only locally at nonzero value of *b*, as it is shown below) enthalpy is to be determined by standard normalized
value of interaction frequency of elementary particles in the PV, the same as
for practically free space: *f*(*r*)=[1–*r _{g}*(

Improper
value (determined in the astronomic time) of *p _{j}*
pressure, created in the matter by gravitaty, is connected with its eigenvalue

*p _{j}*=

Here: *ε*_{j}*=**μ*_{j}_{ }*·**cv _{cj}* and

The initiation of gravitational macrofields in the Universe, as it
was shown in [3, 4], is caused by evolutionary self-contraction of the matter
in the fundamental space and by the presence of electromagnetic interaction
between elementary particles of neighboring atoms and molecules of the matter.
Van der Waals forces of intermolecular interaction cased the breakage of the
whole gas environment of the Universe into separate aggregates of gas molecules
in the process of recombination of protons and electrons and made these
molecules evolutionarily self-contract in common. If these forces did not
exist, every molecule would continue contract by itself in fundamental space
the way galaxies do. And consequently, physical macroinhomogeneity of this
space, identifiable here with gravitational macrofields, would not take place.
But in the FR of every single molecule (atom) of gas all the rest of molecules
(atoms) would continue to continuously inertialy distancing from it at the
Hubble velocity. Therefore, it is not possible in principle to build a globally
static (without the effect of expansion) model of the Universe with metrically
stable intrinsic space either at semi-uniform distribution of the matter
density in the fundamental space, nor at real uniform distribution of the
density of a gaseous matter, filling uniformly all Universe in its far past.
Considering metrical macrohomogeneity of the fundamental space in the far
cosmological past, the linear element of gauge-evolutionarily self-contracting
gaseous matter fully corresponded to the linear element, found by Lemetre [6,9]
and (independently on him) by Robertson [6,10] for pseudoeuclidean STC of FR,
not comoving with matter. In this STC (practically corresponding to the
absolute space and

Physical model of evolutionary change of collective space-time state of the matter based on the main principles of gauge-evolutionary theory [2-4] and fully corresponding to the mathematical model of STC of GR, allows studying physical processes in matter realizing on the level of its elementary particles and therefore hidden from observation in principle. This model reveals physical entity of equations of GR gravitational field and gives an objective and internally consistent explanation to basic features of this relativistic theory of gravitation. At this, as it was shown in [4], in contrast to other well-known GR interpretations, it is devoid of paradox phenomena as well as of paradox physical objects.

Full version of the article PDF ( 132 kb), DOC ( 102 kb).

[1]. Newton, I.,
Philosophiae Naturalis Principia Mathematica, London, 1686, revised by A. Cajori,
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paperback, 1962

[2].
Danylchenco, P., Pseudoinertial
contracting frame of reference, in: The Gauge-evolutionary theory of the
Creation (space, time, gravitation and the Universe expansion), Ukraine,
Vinnytsia, 1994, **1**, 22

[3]. 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/myarticles.html);

[4]. Danylchenko, P., About
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Special and General Relativities,

[5]. Danylchenko, P., The gauge foundations of special relativity, in: Gauge-Evolutionary
Interpretation of Special and General Relativities,

(http://pavlo-danylchenko.narod.ru/docs/Foundations_Eng.html); Gauge interprenation of SR. Kiev, NiT, 2005 (in Russian) (http://n-t.org/tp/ns/ki.htm

).

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

[7]. Gliner,
E. B., UFN, 2001, 172, 221

[8]. De
Sitter, W., Mon. Not. R. Astron. Soc., 1916, **76**, 699; **77**,
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[9]. Lemaitre,
G. J., Math. and Phys., 1925, **4**, 188

[10]. Robertson,
H. P., Philos. Mag., 1928, **5**, 839

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