Pavlo DANYLCHENKO
Full version of the article PDF ( 132 kb), DOC ( 102 kb).
Synopsis
Let ΔLj and Δlj be standard average
statistical values (universal means) of distance between interacting elementary
particles of standard substance, which is situated in an arbitrary point j of spherically symmetric gravitational field. These standard
values of the distances of interaction are being determined via standard
average statistical frequency of interaction and improper value of the velocity
of propagation of the wave of interaction (between exchange virtual particles
and quasiparticles). Also let Rj and rj be luminosity radiuses of the j point (distances to this point from the center of gravity of
a body, possessing a gravitational field), being determined via the spherical
surface area, correspondingly by a conventionally rigid in it metrical scale,
common for Euclidean fundamental (absolute) space, and by matter intrinsic
metrical scale, evolutionarily self-contracting together with the substance.
Because of this, Δlj, in contrast to ΔLj, is the same at all the
identical standards and, consequently, vary neither in space nor in time. Then in
fundamental space the standard normalized value of spatial frequency Nj (which is set by standard average
statistical value of the interaction distance ΔLj) and the standard
normalized value of the frequency fj of interaction of
reference substance elementary particles can be determined in the following
way: Nj= Δl
/ ΔLj =rj /Rj, and fj=NjVcj/c=Vcj/crj/Rj, where: Vcj/c=Vcj/c
is a
normalized value in the j point of the velocity of
propagation of interaction, which is a dimensionless quantity (as well as standard
normalized values of spatial frequency Nj and frequency of events fj); Vcj is the absolute (not normalized) improper value of the velocity of propagation of
interaction in PVFR; c is the light velocity
constant (the eigenvalue of the velocity of light).
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|/N=|(∂lnr/∂T)R|=H(r)·f,
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 He.
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 dT, but absolute value of time increment dT=[1–He(T–Tk)]
–1
dT.
Here
metrically inhomogeneous (nonuniform) absolute time T =Tk+(1/He)[1–exp{He(Tk–T)}] is read by
an exponential (nonuniform for matter) physically homogeneous scale of absolute
time (PHSAT) [2,3], which guarantees invariability in PVFR of improper value
of the velocity of light Vc in every
point of gauge-self-contracting matter, but requires at this continuous
renormalization of reading time.
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=η(r)N
/r2= η(r)/NR2, where η(r) is a parameter, depending in general on quantity of matter,
confined in a sphere with radius r, as well as on pressure in the
matter. Beyond the bounds of a physical body (in a conventionally free space),
this parameter is a constant value ηe that determines the
power of the source of gravitational induction of the PV properties spatial
inhomogeneity.
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 Vj/c(r) between improper values of velocity of radial motion Vj of points of an evolutionarily self-contracting body (and its intrinsic physical space, rigidly connected with it) and improper values of velocity of light Vcj=cVcj/c in the same points:
Vj=dRj/dT=cVj/c(r)fj
/Nj=–Hj(r)Rj,
where gauge-invariant magnitudes Vj/c(r)=Vj /Vcj and Hj(r)= –cVj/c fj /rj can be functions only of eigenvalues of radial coordinates of body points. Consequently: Rj=Rjk exp[–Hj(T–Tk)]. However, from the condition of continuity of intrinsic space of self-contracting physical body follows that H=const(r) and therefore is a universal constant. And more over, from the condition of permanency of improper value of the velocity of light Vc, determined in PVFR by the PHSAT (5), the value of constant H is equal to the eigenvalue of Hubble constant He. This takes place because of independence on cosmological time of the value of radial coordinate Rjk=rj of point j, determined at the moment of time Tk of calibration of the size of the length standard in the PVFR by its size in the matter FR, as well as of the value ∂Rk/∂r.
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 vcj/c=vcj/c instead of standard normalized value of interaction frequency as average statistical characteristic of physical inhomogeneity of the matter intrinsic space. From the condition of unobservability in a rigid body intrinsic space of its gauge self-deformation in the PVFR the ratio between the increments of luminosity and metrical radial intervals, determining the curvature of physical body intrinsic space in free space will be equal by absolute value to normalized value of the velocity of light in it.
This means that the equality to unity of product of a(r)=(∂rmetr/∂r)2 and b(r)=vc2/c2 functions of linear element [4,6] in Schwarzschild external solution is caused directly by the presence of matter evolutionary self-contraction in the fundamental space and is caused by the realization of this process accordingly to the Hubble relation. Here ∂rметр – increment of metrical radial interval. Because of ∂f/∂r=η(r)He/H(r)fr2, for a conventionally free space we have f=[2ηe(1/rge–1/r)]1/2. The body gravitational radius rge=rmin (critical minimal value of luminosity radial coordinate in a intrinsic conventionally free space of the body [6]) corresponds to a hypothetical absence of interaction between elementary particles of its matter in the case of hypothetical concentration of all the matter on a spherical surface with this radius (Rge radius in the fundamental space [4]).
At the direction of parameter rge 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 (f=1). And it is possible only when ηe=rge/2. Therefore f=(1–rge/r)1/2. For a
conventionally free space we have Rj=Rgerj[1+(1–rge/rj)1/2H/He]2/rge and
correspondingly to this
rj=rge(Rj+Rge)2/4RjRge, where H=–He when R<Rge
and H=He when R>Rge; Rge is the continuously decreasing value of body
gravitational radius in the conventionally free fundamental space. Considering
this, in the conventionally free fundamental space we have fj=(Rj–Rge)/(Rj+Rge). Radial
distribution of value of improper value of the velocity of light in PVFR is set
by the dependence Vcj/c=4RgeRj2(Rj–Rge)/rge(Rj+Rge)3.
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: vcj/c=(1–rge/rj–rj2He2/c2)1/2. This fully corresponds to the distribution of value of the velocity of light in the space of Schwarzschild external solution of the GR gravitational field equations vcj/c=(1–rge/rj–rj2λ/3)1/2=[1–rge/rj–(1–rge/rc)rj2/rc2]1/2, where λ=3He2/c2=3(1–rge/rc)/rc2 is the cosmological constant and rc is the radius of observer horizon of the body intrinsic space. So, two regions of fundamental space (external (R>Rge , H=He) and internal (R<Rge , H=–He)) correspond to a conventionally free space of a body, possessing a linear element (world interval) of Schwarzschild external solution. These regions are separated by Schwarzschild sphere and practically do not differ from one another in the matter FR. Despite of physical impossibility of realization of Schwarzschild sphere, this is not accidental. In hollow astronomical bodies [4] these regions correspond to real physical spaces – external and internal.
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=–κc2ar(μ–μ0)/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=μc2+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–rg(r)/r]1/2. Therefore, we see that hamiltonian strength of gravitational field, as it was supposed to be, does not depend on eigenvalue of matter mass density also in nonvacuous space. At the cosmological constant λ=3He2/c2 we receive expressions, which are identical to the GR gravitational field equations for intrinsic FR of ideal liquid [6]. This shows full correspondence of physical model, considered here, to mathematical model of STC of GR.
Improper value (determined in the astronomic time) of pj pressure, created in the matter by gravitaty, is connected with its eigenvalue pj by the following dependence:
pj=pj εj/εj=pjvcj/c=pj fj (1–Vj/c2)1/2=pjHe/Hj(aj)1/2,
Here: εj=μj ·cvcj and εj=μj ·c2 are matter energy densities, determined in its intrinsic FR correspondingly in astronomical (coordinate) and proper quantum (standard) time of the j point. Taking this into account, at σ=0 we have the following: ∂p/∂rmetr=0 and ∂μ/∂rmetr=0. This confirms the principal impossibility of only local fulfillment of the condition σ=0 at inequality of a to infinity, and correspondingly at inequality of b to zero [4], at which ∂σ/∂rmetr=0 as well as ∂H/∂rmetr=0. The fulfillment of the (∂p/∂rmetr)t=0 and (∂μ/∂rmetr)t=0 conditions is impossible in principle in the matter FR, which uniformly filled whole fundamental space in the far past and at this gauge-evolutionarily self-contracting in this space. It is connected with the lack of simultaneity in the PVFR of events, simultaneous in the FR of matter molecules, and is caused by presence of synchronism in whole absolute space of evolutionary change in cosmological time (read in not the matter FR, but in the PVFR [4]) of pressure in the matter and its mass density eigenvalue. Therefore, the condition σ=0 (p=–μc2), corresponding to so-called vacuum-like state of physical environment [7] and de Sitter universe [6-8] is impracticable in principle in intrinsic FR of any protomatter. And, consequently, it can be considered only as hypothetical.
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).
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