Pavlo
DANYLCHENKO
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Synopsis
Clausius's Hypothesis about opportunity of the heat death of the Universe (1865) and also the misconceptions about non-invariance
of thermodynamics equations to relativistic transformations led to false
conclusion that methods of thermodynamics cannot be applied to the analysis of
evolutional processes in megaworld. It is known now
that the Universe cannot cool down at any as long as possible finite time
period. Self-organization of spatially inhomogeneous thermodynamic states and
gravitational fields that correspond to those states prevent matter from
complete cooling down. The thing that prevents unlimited growth of entropy
in the Universe
is the self-organization of different structural formations, the complexity of
which grows with every new hierarchy level of self-organization of natural
objects that form them. Relativistic generalization of thermodynamics with the invariant absolute
temperature is currently considered as the most acceptable generalization [1;
2].
Thermodynamics was already used in
this or that manner for analysis of the processes of formation of megascopic Universe objects [3 - 7]. The main researches
that should be highlighted: researches on gravitational plasma [7; 8],
researches based on the kinetic theory of rarefied gas [9], and also the theory
of spatio-temporal evolution of nonequilibrium
thermodynamic systems [10]. Recently, being based on the analysis of
self-organization processes in nonequilibrium systems
[11] and on the more wide usage of the methods of statistical physics,
thermodynamics of self-gravitating systems achieved the quite significant
success [12 - 14]. However thermodynamic and gravitational descriptions of the
self-organization processes of Universe astronomical objects are still not
naturally merged. Therefore, phenomenological justification of the united
nature of thermodynamic and gravitational properties of the matter [15] is very
important for the studying of megascopic astronomical
objects and global processes in the Universe.
Thermodynamic states of matter, examined in
General Relativity (GR), are self-inducted by matter spatially inhomogeneous
states of this matter. This fact is caused by the presence of gravitational
field in matter: Gravitational field is the cause of spatial inhomogeneity of
rates of intra-atomic physical processes in matter and, therefore, it inducts
not only the curvature, but also physical inhomogeneity of intrinsic space of
matter [16; 17]. In rigid frames of reference of time and spatial coordinates (FR) this physical inhomogeneity of the space is in the mutual
inequality of values of such hidden thermodynamic property of the matter as coordinate-like
velocity of light in different points of this space [18].
The equations of GR gravitational field should
be considered as just the equations of spatially inhomogeneous thermodynamic
state of utterly cooled down matter. Such matter can be represented only by hypothetical
substances such as ideal gas, ideal liquid and matter of absolutely rigid body.
Real matter is doomed to cool down infinitely long without reaching the state
that is described by the equations of GR gravitational field. This state of
gradual quasi-homogeneous cooling down is described by considered here modified
tensor equations of GR - equations of relativistic gravithermodynamics
(RGTD).
Increasing of coordinate-like
velocity of light during the distancing from compact matter of astronomical body
can be the consequence of gradual change of thermodynamic parameters of the
atmosphere and the
outer space that
surround this body. In this case spatial distributions of coordinate-like
velocity of light, which are set by gravitational field, strictly correspond to
concrete spatially inhomogeneous thermodynamic states of matter. Adding of the third independent parameter - coordinate-like
velocity of light to any of two mutually independent thermodynamic parameters
in GR guarantees only conventional consistency of this theory with objective
reality. Indeed, the solutions of equations of gravitational field for
any cluster of gravitationally-bounded matter are always examined in
conventionally empty Universe. However, the Universe is not empty and, as united
solution of equations of gravitational field and equations of thermodynamics
for ideal liquid shows [19], values of coordinate-like velocity of light are
not vacuum values, but pseudovacuum gravi-baric values. They are determined by the values of
thermodynamic parameters of ideal liquid accurate to gauge coefficient. Only
this coefficient can be considered as pseudovacuum
value of coordinate-like velocity of light. In the case of presence of both
mechanical and thermal equilibriums in ideal liquid this pseudovacuum
value of coordinate-like velocity of light is the same within the whole liquid,
which self-organized its spatially inhomogeneous equilibrium state and
gravitational field that corresponds to this state [19]. This fact allows us to
consider this vacuum value as gauge parameter, that interconnects
spatial and temporal metrics and cannot be observed in hypothetical gravi-quantum
intrinsic FRs (GQ-FRs) of matter and in people’s world FR in
principle.
Conventionally empty space that surrounds such
compact matter of The Universe has really never
been empty and never will be completely empty. Even the highest cosmic vacuum should be
considered as very rarefied gas-dust incoherent matter, which obey the thermodynamic laws
the same as ideal gas of non-interacting molecules. The limitation of the velocity of physical
bodies is indeed exists in such matter. However, this limitation is not related
to the velocity of light in the matter or in hypothetic absolute vacuum. In
airspace, as well as in dense matter, the charged micro objects (protons) can
propagate faster than the velocity of light. That is confirmed by the
origination of the radiation, found by Cherenkov, in this case. On the other
hand, hypothetical velocity of propagation of intranuclear
interaction (pseudovacuum velocity of light of GR)
decreases while approaching the gravity center unlike the real velocity of
propagation of electromagnetic interaction in matter, which increases. This is
in a good correspondence with the fact that thermodynamic and gravievolutional processes have opposite directions and is
related to the fact that velocity of propagation of electromagnetic waves in
matter is greater when the temperature of the matter is greater. Due to the
same reason the physical processes flow faster not on the surface but in hotter
bowels of
the astronomical
objects despite the gravitational slowing down is predicted by GR for those
processes.
Maximal possible velocity of matter
The reason for limitation of velocity of
physical bodies is indeed the nature of matter movement in the space. Physical
vacuum is not carried away by physical body. Matter is only the non-mechanic
excitement of physical vacuum (space-time modulations of its physical
characteristics). Therefore, the perception of high-frequency discrete movement
of the body in the space as the continuous motion is similar to cinematographic
perception of discrete change of image frame. The limitation of body velocity
can be related to the fact that it is impossible to reach infinitely high
frequency of discrete change of Gibbs collective thermodynamic microstate (quantum “hologram”)
of the whole its RGTD-bonded matter and to the fact that it is impossible to
reach the zero value of the length of spatial step shift (quantum micromovement) of the body. This frequency and this micromovement are de facto the de Brogile
frequency νB and wave length λB of the moving body. That is why
instead of denying the possibility of moving body to overcome the velocity of
light we should state the principal impossibility
to reach the extremely big velocity vl=(vvB)1/2=vBmin, that corresponds to the tending of νB to infinity, and tending of λB=vl/νB to zero, when phase velocity of de Brogile wave propagation vB reaches its minimal value, equal to
maximal possible group velocity vmax
of the whole matter of the body (vBmin= vmax≡vl).
Physical essence of gravitational field
There is a thermodynamic quasi-equilibrium
between gravitationally self-contracted compact matter and surrounding it
arbitrary rarefied matter of the outer space. Therefore, pseudovacuum
value of the coordinate velocity of light in this rarefied liquid matter cannot differ from pseudovacuum value of the coordinate velocity of light in the space filled in by
compact matter. And, consequently, this value should be the same in the whole
Universe space, filled by gaseous and liquid matter. Thus, vacuum value of the coordinate velocity of light, which is a gauge
parameter, should be considered as strictly equal to the constant of the velocity
of light c in the whole space, filled
in by any gaseous and liquid matter that is in quasi-equilibrium
thermodynamic (thermal and mechanical) state. And then, due to isotropy of
radial distribution of the pressure in such matter we can reach the following
conclusion. The fact that the rates of hypothetical gravi-quantum
time differ in the points of matter, where values of gravitational potential
are different, is caused only by inequality of thermodynamic parameters of the
gaseous or liquid
matter, which fills the whole space, in those points. And, therefore, such
matter is not only in the state of mechanical and thermal equilibrium, but also
on the same stage of evolutional decreasing of the level of improper value of
its intranuclear energy.
Anisotropy of radial distribution of the
pressure in matter is the characteristic for solid matter. That is why solid
matter and liquid matter, located above the world Ocean level, are on the
certain stage of lagging of evolutional decreasing of the level of improper
value of its intranuclear energy. The water of world
Ocean is also on the certain stage of lagging of this process since it covers
the rigid body. It means that gravitational field is the field of non-equal
(spatially inhomogeneous) lagging of evolutional decreasing of improper value
of matter intranuclear energy.
In correspondence with all this, gravitational
red shift of emission radiation spectrum can take place only for astronomical
objects with a solid photosphere, as well as for liquid and gaseous
astronomical objects, which are in non-equilibrium thermodynamic states. And, of course,
gravitational redshift of radiation spectrum is the
consequence of lagging of evolutional decreasing of intranuclear
energy of radiating matter. Frequencies of emission radiations are determined
only by the differences between energy atomic levels, values of which are not
changed in atoms at quasi-equilibrium thermodynamic processes. Radial changes
of matter RGTD-parameters, when
liquid or gaseous matter is in hypothetical equilibrium thermodynamic state,
lead to the change of only the frequency of quantum interactions in atomic
nuclei. And it is not accompanied by redshift of its
spatially homogeneous emission radiation and by widening of spectral lines of
that emission radiation.
Thermodynamic nature of the majority of gravitational effects
Analysis of solutions of the equations of GR gravitational field [15; 19] specifies the thermodynamic
nature of majority of gravitational effects. All gravitational phenomena,
except the phenomenon of curvature of intrinsic space of matter, are strictly
thermodynamic in fact. For example, the fact that bodies, more dense than
surrounding medium, tend to the gravity center, as well as the fact that
bodies, less dense than surrounding medium, tend from the gravity center, is
caused by the fact that the whole system (which consists from all bodies and
the medium surrounding them) tends to the state of the minimum of the integral value of their thermodynamic enthalpy [19]. In the case of
presence of heat exchange integral value of purely thermodynamic Gibbs free energy also tends to minimum, while
integral value of entropy tends to maximum. From the other hand, the pressure
in ideal gas and in any other incoherent matter is not caused by intermolecular
electromagnetic interaction and, consequently, this pressure itself has purely
gravitational nature. And, therefore, physical phenomena and properties of
matter, which are examined by thermodynamics and theories of gravity in a different
phenomenological way, are based on the same fundamental nature of matter
micro-objects (elementary pseudoparticles) [16; 21].
In classical physics
potential energy of gravitational field was considered as something external
for the matter, while in GR potential energy is contained in matter itself.
Indeed, free fall of the body is an inertial motion. Released potential energy
of intranuclear
bonds and intranuclear interactions in the atoms cores of matter of falling body
together with the energies of nucleons that form these atoms transform into
kinetic energy of body motion. And the excessive level of evolutionary lost intranuclear energy of matter, in fact, decreases. As it
follows from united solutions of equations of gravitational field and thermodynamics
equations [19; 21], all characteristics that determine gravitational properties
of matter and phenomenon of Universe expansion are also contained in matter
itself and cannot be considered as something external for the matter.
Gravithermodynamic FR of people’s world
In classical thermodynamics all intensive
thermodynamic parameters of matter are determined via measuring of extensive
parameters (which depend on those intensive parameters) of matter itself or
matter of measuring instruments that are in thermal equilibrium with this
matter. For example, the main method of temperature measuring is in the
measuring of volume occupied by thermometer liquid. Pressure is determined via
measuring of elastic deformation (caused by this pressure) of any element of
recording instrument. Deformation and volume are both extensive parameters.
This makes closed system of the pairs of mutually complementary intensive and
extensive matter parameters self-consistent and guarantees invariance of
intensive thermodynamic parameters to time transformations. And, thus, there is
not only temporal invariance, but also Lorentz-invariance of used in
thermodynamics proper values of intensive and extensive characteristics of
matter. And it is similar to the principal invariance of the value of velocity
of light by the intrinsic clock in the point of its dislocation and to the
principal invariance of Hubble constant. The majority of measurings of physical characteristics in FR of people’s
world is purely relative. They are strictly bonded not only to intrinsic clock,
but also to other intrinsic instruments of operator who performs measurement.
And, therefore, the influence of the instrument on the measurement result takes
place not only in quantum, but also in classic physics. In contrast to microworld, in the macroworld the
measurement results are only strictly determined.
And,
therefore, invariant values of thermodynamic parameters and characteristics of
motionless matter, which are used in classical thermodynamics, are self-sufficient
and do not need to be a member of any FR. They can be members only of certain
tracking system: system that tracks changes of thermodynamic parameters and
characteristics of matter. And, from the other hand, global FR can be formed
based on this tracking system. The presence of phenomena, for which frequency
of their elementary acts depends only on absolute temperature, is necessary for
this global thermodynamic FR (GT-FR) to be
non-artificial in nature. Then, the scale of absolute temperature can be linearly
calibrated based on this frequency. The clock, using which the rates of hypothetical gravi-quantum
proper times can be compared and dependences of these rates on parameters of
thermodynamic states of these matters can be analyzed, can be realized based on
this phenomenon.
And such phenomenon exists:
dependence (obtained by Wien) of electromagnetic wave frequency, which
corresponds to the maximum of spectral density of equilibrium thermal
radiation, only on absolute temperature and proportionality of this frequency
to absolute temperature. Therefore, united thermodynamic time is used in people
world in fact, instead of gravi-quantum time, rate of
which is not similar for different matters and depends on their thermodynamic
states. Quantum processes in etalon matters can only be used for the counting
of this time due to the stability of their rate in this matter when temperature
T
and pressure p remain unchanged. Thermodynamically invariant atomic characteristics - differences
between energy levels ΔEij in atoms and frequencies of
emission radiation νij=ΔEij/h (here h is the Planck constant) corresponding to them also can be used for this
time counting. Energy levels are defined by radiuses of allowed orbits of
electron shells in the atom and, similar to intensive thermodynamic parameter,
are the characteristic defined by extensive parameter (radius of allowed orbit)
and, therefore, dependent on transformations of spatial coordinates not time.
Therefore, electrons energy and, thus, energy levels in atoms are, similarly to
thermodynamic internal energy of matter U, Lorentz-invariant and does not
depend on the level of inert intranuclear energy of nucleons as well as on the rate of
hypothetic gravi-quantum intrinsic time of matter.
And, therefore, the frequency of the same emission radiation remains the same
within the whole matter that is located in spatially inhomogeneous equilibrium
state in GT-FR, as well as in any other GQ-FR. It means
that widening of spectral lines of emission radiation can be only Dopplerian - can be caused only by the thermal fluctuations
of molecules of the matter. This is confirmed by the absence of gravitational
smearing of spectral lines of excited atoms of cold rarefied galaxy medium even
when values of their main quantum numbers are n≈1000 (λ=20 m) [20].
Absolute temperature is an intensive
parameter that characterizes only the level of thermal internal energy U(T, p) of matter, which includes also
potential energy
of interatomic and intermolecular bonds. Invariance of
all thermodynamic parameters and matter characteristics to time transformation
denotes that all of them should be relativistic invariants. Therefore,
temperatures of phase transitions should remain internal properties of moving
matter. This means that the change of thermodynamic parameters and
characteristics of matter should have indirect influence on the change of
matter thermodynamic (inert) mass. And, therefore, nonchemical internal
potential energy of interatomic and intermolecular
bonds can transform into kinetic energy only of chaotic, but not directed,
motion of matter molecules.
Inert intranuclear energy of matter
Not the total energy of matter UGT=E+U, but only the inert intranuclear energy E=mc2 can be equivalent
to the inert mass m. Thermal internal energy of matter U can be considered
analogically to kinetic energy and to electromagnetic radiation energy only
as the external energy of molecules and atoms.
In
classical thermodynamics the intranuclear energy
considered as one that is not changed in thermodynamic processes. In fact, it
is not true. Part of potential intranuclear energy
of gas, which pressure is adiabatically increasing, transforms into energy of chaotic
state of its nucleons and potential
energy of stressed state of matter of the vessel that contains this gas [15].
The release of intranuclear potential energy, which
is reserved in deformed shell of the vessel that is in stressed state, takes
place during the heating of compressed gas. Solid body freely expands during
the process of its heating and the frequency of interaction of its nucleons
decreases [15; 16].
Thus, dilation of its gravi-quantum time takes place
in a similar way as it happens during body free fall. However, increasing of thermal energy of the body, which is accompanied by the
increasing of his thermal temperature T, is only non-significantly
compensated by the decreasing of its intranuclear
energy due to decreasing of intranuclear entropy SN, which corresponds to one mole of
matter, and due to decreasing of intranuclear
temperature TN. That is why no essential
dependence of molar mass of matter on its thermal internal energy can be
observed. And it takes place despite the presence of mutual correlation between
inert energy E and purely thermodynamic Gibbs free energy G of matter. During the cooling down of the body
non-significant part of its thermodynamic internal energy is spent on
replenishment of inert intranuclear energy. The similar decreasing of
frequency of interaction of nucleons and releasing of intranuclear
energy that corresponds to it takes place during the experiments with rotating
gyroscope.
Generalization of RTGD equation
Inert energy of matter should be taken into account in
generalized differential equations of thermodynamics by
means
of multiplicative parameter of direct
action fN=ηmvlb/c=(1-mcr-2c-4TNcr2SN2)1/2≤ (1+NRE2)1/2<2-1/2, which is
proportional to the extremal value of local group velocity of matter vlb in an comoving
FR in expanding Universe (CFREU) and, therefore,
proportional to almost identical to it pseudovacuum
coordinate-like velocity of light of GR in CFREU (vcbv=vlb) [15; 16]. These equations
should also contain a multiplicative parameter of reverse action that realizes
the negative feedback. Such parameter is obviously the relativistic external
scale factor NRE=NE/ΓE=vl/vlb=(1-pNcr-2pN2)-1/2≥1, that increases while approaching the
gravity center (and, therefore, while deepening into cosmological future) and
is responsible for the curvature of intrinsic space of matter and for the
presence of spatial inhomogeneity of intranuclear
values of pressure pN and pseudo-volume VN. Here: ηm - parameter that corresponds to
certain matter and that defines the dependence between fN and vlb; NE=r/R - external scale
factor; r and R - radial coordinates of matter in GT-FR and CFREU
correspondingly,
ΓE - relativistic shrinkage of the
length of radial segments of the body that happens due to its evolutionary
self-contraction in CFREU, while TNcr and pNcr - not similar
for different matters critical values of intranuclear
temperature and pressure. In
correspondence with this, the rate of quantum processes of intranuclear interaction between nucleons in global
GT-FR can be characterized by relative average statistic value of frequency of
this interaction fG=fNNRE=ηmvl/c<ηm, that is proportional to the extremal value of local group velocity of matter vl, in GT-FR (and, therefore, proportional to
almost identical to it pseudovacuum coordinate-like
velocity of light of GR in GT-FR vcv= vcbvNRE=vl [15; 16]). Precisely fG, similarly to vcv in GR, is responsible for the presence of
gravitational pseudo-force FG, that forces matter for free fall. And this
pseudo-force is proportional not to the mass, but to the Hamiltonian of the
body H=const(r).
According to it, frequency of nucleons intranuclear interaction in GT-FR:
fG=NREfN=m/mcr=(GGT-SNTN+VNpN-GT)/(GGTcr-SNcrTNcr+VNcrpNcr-GTcr)
is equal to the
division of the mass m of one
mole of matter by the value of this mass mcr, which corresponds to “critical”
equilibrium value GGTcr=GTcr+SNcrTNcr-VNcrpNc+mcrc2 of Gibbs
free RGTD-energy:
GGT=GN+GT=(E+SNTN-VNpN)+(U-ST+Vp)=NREfNmcrc2+SNTN-VNpN+GT.
It is obvious that not only mcr, ηm, TNcr and pNcr,
but also GGTcr, GTcr, GNcr are individual parameters that characterize
certain matter and are, possibly, related only to its certain aggregate or
phase state.
Gibbs free RGTD-energy
GGT, the same as Hamiltonian, is saved in the process of matter free fall.
Moreover, GGT, the same as gravitational intranuclear Gibbs free energy GN, tends not to its minimum (in contrast to thermodynamic Gibbs free energy GT), but to its maximum during the process of body free fall and during
the process of matter evolution. It is obvious that the tending of
thermodynamic Gibbs free energy to its minimum is the partial compensation for gradual increasing of intranuclear Gibbs free energy. And since in CFREU: NEb=NEexp[HE(τ-τ0)]=NE/(1+z), ΓE=const(τ), fNb=fNexp[HE(τ-τ0)]=fN(1+z), then: fG=fNbNEb=fNNE=const(τ) and, consequently, in people’s
world FR the evolutional increasing of Gibbs free RGTD-energy cannot be observed in principle. Here:
HE - Hubble constant, that sets the speed of evolutional expansion of the Universe, τ -
cosmological time, counted in CFREU by
metrically homogeneous scale (dτ=dt), z
- Dopplerian redshift of
the wave length of radiation of astronomical object, characteristics of which
are being determined. However in CFREU according
to Hubble law both molar intranuclear Gibbs free energy and inert intranuclear
molar energy are changed and, therefore, the also
equivalent to it molar
mass is changed:
GNb=GNNEb=GNNEexp[HE(τ-τ0)]=GNNE/(1+z),
Eb= mbc2=E/NEb=(E/NE)exp[-HE(τ-τ0)]=(E/NE)(1+z).
Not only the molar mass itself ([1+z]
times), but also its concentration in intrinsic space of the matter ([1+z]3 times) was bigger in that distant time [30]. And
it means that the need in “dark non-barionic matter”
can be fictive.
While in all fast-flowing
physical processes that are not accompanied by the performing of the work
directed at the increasing of matter energy UGT,
the Gibbs free RGTD-energy GGT can only increase (as it is
expected) in case of
isobaric (dp=0, dpN=0) heating of
the body, the increasing of both intranuclear
temperature dTN≥(S/SN)dT and intranuclear
Gibbs free energy dGN=SNdTN-≥SdT takes place. And due to EGN=mcr2c4=const the
following situation will take place. The inert intranuclear
energy and corresponding to it gravitational mass of the matter will decrease
the same number of times as intranuclear Gibbs free
energy is increased. This is in a good correspondence with the results of
experiments since for the many heated metallic bodies the decreasing of their
mass is observed [23]. In the process of cooling down of the body its intanuclear molar volume is increasing to its former value and intranuclear pressure will perform work to restore the former level of its inert energy (dE=pNdVN>0).
Spatially inhomogeneous equilibrium RGTD-state of liquid and gaseous matter takes place in the case of fulfillment of the following: GGTj=(fGi/fGj)GGTi. In the case of isotropy of radial distribution of physical parameters and characteristics of homogeneous matter of astronomical object it can be shown in the following way: fG(r)GGT(r)=const(r). In the case of radial altitudinal multi-layer distribution of inhomogeneous matter this condition is fulfilled layer by layer, with the break on the boundaries of two media: fG(k+1)GGT(k+1)<fGkGGTk, where (k+1) - serial number of
the less dense and, therefore, more distanced from the Galaxy center matter.
In equations of GR gravitational field the thermodynamic enthalpy HT=GT+ST is de facto used instead of Gibbs free RGTD-energy. Equilibrium state of ideal liquid in GR is reached only in case of mutual absence of radial gradients of the following characteristics: Hg=HTvcv/c=const(r), Tg=Tvcv/c=const(r), S=const(r) [19]. This conditions, supplemented by the condition of homogeneity of ideal liquid ηm=fGc/vcv=const(r), fulfill the more general RGTD
condition of equilibrium state of liquids and gases:
GTg=fGGT=(ηmvcv/c)GT=ηmGg=ηm(Hg-STg)=const(r).
Equilibrium RGTD-states of matter,
in which external gravitational pressure of upper layers of matter is
counterbalanced not only by intrinsic pressure inside matter, but also by
radiation (thermal) pressure (Tg≠const(r)), are not considered
at all in GR, in contrast to RGTD. And, therefore, GR not only reflect physical
reality in more simple way, but also is applied to equilibrium states of only extremely cooled down homogeneous matter (Tg=const(r), ηm=fGc/vcv=const(r)). That is why the reflection of physical
reality in GR should be considered only as the special case of its reflection
in RGTD.
Internal energy U of real gases and
liquids depends on many pairs of their intensive (Ai) and extensive (ai)
thermodynamic parameters. However, it can also be shown as a sum of internal
energy of hypothetic ideal gas (liquid) Uid and output of multiplication of resulting intensive (Aρ=TS/RT=T2S/pV) and
extensive (aρ≡RT=pV/T)
thermodynamic parameters:
U=Uid
+∑Aiai=Uid+Aρaρ,
dU=TiddSid+Aρdaρ-pdV=TdS-pdV,
where: Tid=TRT/RT0, Sid=SRT0/RT, Aρaρ=TidSid=TS.
For gases: ai=RT0BiVi+1, Bi
- virial coefficients that depend on both temperature
and individual gas properties [2], while RT and RT0 - individual and universal gas
constants correspondingly.
“Ideal” component Uid of internal energy is de facto
identical to Helmholtz free energy FT, while “ideal” component HTid of enthalpy is
identical to the Gibbs free energy GT.
This, of course, is caused by the
absence of binding energy in ideal gas and ideal liquid due to the absence of electromagnetic
interaction of their molecules and atoms. Self-organization of hierarchically more complicated interactions and
interconnections in matter is in the tendency of Helmholtz and Gibbs free energies to their minimum.
Lower layers of matter, loaded by
its upper layers form the extended system. The energy of such extended system [2] that consists of the whole RGTD-bonded
matter is indeed equivalent to enthalpy. Moreover, as it is shown further, Aρ
parameter takes the same value in the whole space filled by quasi-equilibrium
cooling down homogeneous matter (∂Aρ/∂r=0). And, therefore, Gibbs energy “behaves” as
it is expected and only changes in time. And when Gibbs energy changes in space
it “behaves” like enthalpy (like the energy of extended system).
This is quite logical and reflected
in static equations of GR gravitational field. However in dynamics the
four-momentum should be formed not by enthalpy, but by Gibbs energy (free
energy of extended system). And, of course, it should be not the
Lorentz-invariant thermodynamic Gibbs energy, but relativistic intranuclear Gibbs energy.
So, if equations of GR gravitational
field are designed to get the solutions that correspond only to ideal
(extremely cooled down) matter, then the usage of enthalpy instead of Gibbs
free energy in those equations is justified. But, of course, not the
Lorentz-invariant thermodynamic enthalpy (intrinsic value of enthalpy), but
Lorenz-noninvariant intranuclear
enthalpy (improper value of enthalpy) should be used in those equations.
However, in order to get the solutions that correspond to quasi-equilibrium
cooling down astronomical objects we should include not enthalpy, which
includes free and binding energy of extended system, but intranuclear
Gibbs free energy with transition to functionally related to it thermodynamic
Gibbs free energy (to the intrinsic value of Gibbs energy in FR of people’s
world).
Spontaneous change of RGTD-state of
coherent matter and, consequently, its free fall are possible only when they
are accompanied by continuous decreasing fG
and thereby decreasing of matter
thermodynamic mass at
rest.
Physical space that is rigidly
connected with cooling down body self-contracts not only in CFREU, but also in intrinsic metric space of the
body that has non-rigid intrinsic FR [34]:
R=ρexp[-(HE+HT)(τ-τ0)],
r=ρexp[-HT(t-t0)],
where: ρ - radial coordinate,
which is counted by rigidly connected with body coordinate grid not in metric
space but in physical space of gradually cooling down body, HT - parameter that characterizes the
speed of observed shrinkage of the dimensions of cooling down body.
During matter free fall (dS=0, dV=0, dURGT=0)
gravi-evolutional increasing of intranuclear
entropy that is accompanied (as a compensation to its increasing) by increasing
of molar value of intanuclear volume and, thus, by
the release of intranuclear energy (instead of
thermal energy) with its further transformation into kinetic energy of it
ordered motion takes.
Obviously, in the tensor
of the energy-momentum of GR gravitational fields equations we should use
Lorentz-noninvariant intranuclear
RGTD-characteristics of matter instead of Lorentz-invariant and temporally
invariant thermodynamic characteristics. For gradually quasi-equilibrium
cooling-down matter we should use the density of intranuclear
Gibbs free energy GN/N=mcrc2/Vvcb=mcrc2ηm/VfGb instead of the density of enthalpy.
It should also be mentioned here
that, according to GR and RGTD, the ideal gas (pV=RT0T) cannot have gravitational field in principle. Molar energy of ideal
gas and, consequently, coordinate-like velocity of light in it are the same at all
points of the space filled by this gas. And it means
that the phenomenon of gravitation is related to electromagnetic interaction of
molecules of matter and, therefore, has purely electromagnetic nature.
Generalized equations of thermodynamics
Thermodynamic processes
in matter confront the intranuclear evolutionary and
gravitational processes in it. When intranuclear Gibbs free RGTD-energy of matter is continuously increasing in CFREU, the
thermodynamic Gibbs free energy in naturally
flowing physical processes is tending to its minimum. Therefore, frequency of intranuclear
interaction fG=fNNRE=ηmvl/c≤ηm
corresponds to inversely proportional to it frequency of intermolecular
electromagnetic interaction fI=χm/fG=qMNI=(vcm/c)NI=cχm/ηmvl≥/χm/ηm,, which is changing together with
the change of velocity of light vcm
in matter and with the change of internal scale factor NI=δlcr/δl≥1 of matter [15]. Here: χm=χm0/Γm; Γm - relativistic shrinkage of the length of molecules of cooling down
matter; χm0, ηm and δlcr - the
constant or critical values of the parameters of a certain matter, which are
not equal for different matters and not dependent both on strength of
hypothetic gravitational field and on matter thermodynamic parameters.
In contrast to used in cosmology spatially inhomogeneous external
scaling factor NE, which
is the cause of the curvature of matter intrinsic space, internal scaling
factor NI depends
on thermodynamic state of matter and takes nonsimilar
values for different matters. This factor characterizes the distinction between
average statistic value of interaction distance δl in the atoms of
concrete matter and the value of this distance δlcr that corresponds to
critical equilibrium value of internal energy Ucr, Gibbs free energy GTcr, temperature Tcr, pressure pcr and radiation
refractive index nm on the wavelength of maximum of energy of
thermal radiation. And if qM=vcm/c=1/nm<1 characterizes the difference
of real velocity of electromagnetic interaction propagation in matter from the
constant of velocity of light c, then NI is responsible for compensation of
the influence of decreasing of propagation velocity of electromagnetic wave on
the frequency of electromagnetic interaction fI of
matter microobjects. If for gases and simplest
liquids the dependencies of instantaneous values of their thermodynamic
parameters and potentials on qM and NI allow to separate these variables, then instantaneous value of their Gibbs free energy (that corresponds to their instantaneous
thermodynamic microstates) can be expressed via these two parameters and via
their function RT in the examined in current article
way. Methods of thermodynamics allow us to analyze equilibrium states of matter
even when there is no analytic dependence of thermal energy of matter on its
thermodynamic parameters. With the purpose of revealing of some features let us
examine analytic representation of such
dependency for gases and simple liquids.
The comparison of reflection of
physical reality in RGTD and in GR
For liquid and gaseous astronomical
bodies, not containing solid nucleus, frequencies of interaction fG and fI are strictly determined by the values of
pressure and temperature in matter. For solid or containing solid nucleus
astronomical bodies those frequencies can also depend on the magnitude of
lagging of evolutionary decreasing of their intranuclear
energy. However, in equilibrium RFTD-states of the whole set of different
matters the gradients of logarithms of fI and fG of all
matters are strictly determined by gradients of pressure and temperature in
them and, therefore, are strictly equal to the gradient of extremal
velocity of motion vl of the
whole RGTD-bonded inhomogeneous
matter. Moreover, at the fulfillment of GNvl=const(r) condition the GNfG=GNvlηm/c=const(r), GT/fI=GTfG/χm=GTvlηm/χmc=const(r), GTvl=const(r) and GT/GN=const(r)
conditions are also fulfilled within the borders of the whole RGTD-bonded continuous
homogeneous matter that is in the state of mechanical and thermal equilibrium.
All this allows using in the modernized GR only intranuclear
properties of matter for the formation of metric tensor, but both intranuclear and thermodynamic properties of matter for the
formation of energy-momentum tensor. However, Lorentz-invariance of pressure in
the matter is ignored in the such
modernized GR.
All
the more so, separate contributions to gravitational potential of velocity of
light in matter vcm and
internal scaling factor NI are not important for the determination of
gravitational pseudo-forces. However, the form of radial distribution of
gravitational potential in space-time continuum (STC) of astronomical body that
consists of this matter and the form of generalized relativistic linear element
depend on their contributions [33]. Therefore,
the conversion of these characteristics are not gauge when the named
contributions are redistributed. The presence of internal scaling factor is not
taken into account in GR: function only of coordinate-like velocity of light is
used as gravitational potential. In intrinsic spaces of matter changes of electromagnetic
interaction
distances are unobservable in GR in principle, while spatial inhomogeneity of this distance for uniform matter that
takes place in background Euclidean space (and, consequently, spatial inhomogeneity of the values of its scaling factor) causes
the curvature of matter intrinsic space. The one thing that points on it is the
usage of the function of not the interaction frequency, but of common for all
substances pseudo-vacuum coordinate-like velocity of light in GR as the
gravitational potential.
Size of
quantum length standard of the gas is decreasing in people world at the
adiabatic increasing of this gas. This fact and the fact that change of
distances of interaction of matter micro-objects (which
determine size of its quantum length standard) is unobservable in GR in
principle leads to increasing of corresponding to this gas gravi-quantum
value of metrical volume of the vessel that contains this gas. Therefore, gravi-quantum metrical value of gas molar volume is
decreasing not so fast as thermodynamic metrical value of its molar volume due
to the presence of negative feedback [15; 17]. Such gravitational shrinkage of
the size of quantum standard of length that takes place on the matter micro-objects level is
analogous to relativistic shrinkage of the size of quantum standard of length
along the direction of matter motion. However we cannot introduce the common
space for GQ-FR of all matters because of the presence of the different
intrinsic metrics of the space for each matter [15]. Therefore, not gravi-quantum but
thermodynamic metrical value of matter molar volume is used in the GR and in people’s
world. In analogy to quantum clock, quantum and any other length standards can be used in GT-FR of people world
only due to stability of their length when values of temperature and pressure
remain constant. The
least influenced by temperature and pressure are only the atomic standards of
length that are based on the stability of frequencies of emission radiations.
According to all of this, in RGTD,
the same as in GR, it is rational to use only the common for all matters intrinsic space
of GT-FR. And, that is why fG, fI and vl should be considered as the
parameters that are not identical, but equivalent to pseudo-vacuum
coordinate-like velocity of light vcv
of GR. The usage of
the common for the whole gravitationally-bonded matter thermodynamic time that
is counted by standard atomic clock (instead of conventional gravi-quantum times, which flow rate is different for
different matters and in different points of the space, and which are counted
by their hypothetical quantum clock) is quite rational. It allows avoiding the
necessity of transformation of time within the whole matter that is in the sate
of RGTD-equilibrium. The possibility and necessity of this is due to the
existence of closed system of all self-consistent pairs of additive one to another intensive and extensive parameters of matter when it
is in the state of RGTD equilibrium. Existence of
such closed
system is revealed in the fulfillment of the Le Chatelier-Braun
principle in all RGTD-processes.
In
contrast to gravitational potentials and external scaling factors used in GR, RGTD-values of gravitational
potentials and internal scaling factors are not equal for different contacting
matters. Only spatial gradients of the logarithms of frequency fG
of intranuclear and fI of electromagnetic interaction in all matters (they
are identical to gravitational field strength), as well as spatial gradients of
the logarithms of internal scaling factor NI, are mutually equal in the same
world point. These spatial gradients of logarithms fG (gradlnfG=gradln(vl/c)≡ gradln(vcv/c)) for all matters are identical to the
gravitational field strength in this point. The presence of identical spatial
gradients in the same point of space justifies the usage in GR of the
conventional pseudo-vacuum velocity of light vcv instead of intranuclear
frequency of interaction fG.
Related to it problems appear in GR only in the
process of “stitching”
of the solutions of equations of gravitational field for different matters. And
this is related also to their stitching with fictive solutions for physically
unreal absolutely empty space (spatially inhomogeneous pseudo-vacuum) [15]. So,
differential equations of GR gravitational field are definitely determine only the gradients of potentials and not the gauge
transformed potentials of gravitational field themselves. However, in non-empty
space they principally allow to switch from vcv to fG,
fI
and vcm And,
therefore, these problems are solvable in GR. It is necessary and enough to
determine (from equations of thermodynamics) the values of fI0 and vcm0 only in any single point of matter that is in the equilibrium
RGTD-state. Then the spatial distributions of fI and vcm in any matter can be
determined with the help of the solutions of GR equations. It is necessary to
use correspondent vcm0 and fI0 values of coordinate-like velocity
of light vcv0 and the known dependency of vcm on fI or on
correspondent to fI thermodynamic parameters of
matter.
Decreasing
of the wave length of radiation in quasi-equilibrium compressed gas (proton-electron
plasma) is practically completely compensated by decreasing of velocity
of radiation propagation in it. This is also confirmed by the fact that
emission radiation frequencies practically do not depend on thermodynamic
parameters of matter.
However,
such total compensation is absent at non-equilibrium state of ionized gas of
quasars, situated in strong electromagnetic field (very saturated by
radiation). Due to this and due to the proximity of the photosphere of
shell-like quasars to the singular sphere they have the big gravitational redshift of the wavelength of emission radiation.
In contrast to “cooling down” stars, supernovae are
heating up and, therefore, not contracting but catastrophically
expanding due to annihilation of matter and antimatter [16; 19]. Instead of undercompensation
of gravitational shift of radiation spectrum its thermodynamic overcompensation
takes place - as a result, not red but blue gravithermodynamic
shift of this spectrum takes place. Decreasing of quantum length standard (increasing of NI) that is not
completely compensated by the decreasing of velocity vcm of interaction propagation causes not only
the increasing of the frequency of electromagnetic interactions
fI=NIvcm/c≠const
for the supernovae, but also increasing of the frequencies of
emission radiation ν=ν0NIvcm/NI0c≠const.
Therefore, energy of ionized rarefied gas of the dropped supernovae shells, as well as
non-Doppler values of its emission radiation spectrum, should be increasing
along with increasing of pressure in the outer space at the advancing to cosmological past. Actual
value of red shift of supernovae radiation spectrum
is substantially lower than its theoretical value, determined by Hubble
relation, due to the presence of such negative feedback. So the presence of
dark energy in the Universe is not necessary.
Obviously in GR gravitational
field equations not strictly thermodynamic value
of matter molar volume is mainly used. Therefore, additional coordinates
transformation is required for the transition from used in GR local intrinsic
FRs of matter and from similar to them GQ-FRs to GT-FRs of people’s
world. Only in this case the curvature of intrinsic spaces of matter is
determined only by spatially inhomogeneous relativistic shrinkage of radial
intervals and by radial delay in gauge evolution of matter self-contracting in CFREU (by gravi-evolutionary “deformation” of its micro-objects).
Internal
contradictions in the theory of relativity and the main differences between the
theory of relativity and relativistic gravithermodynamics.
Below
is the list of facts that are internal contradictions in GR and SR:
1. The
necessity in use of proper time (instead of classical absolute time) of moving
matter, rate of which is determined by the rates of quantum processes in
matter, is declared in SR. However, standard atomic or quartz clock is used
instead of quantum clock of this matter. The rate of standard atomic or quartz
clock, in contrast to the rate of quantum clock, is proportional not to the
time standard, but to the used in them length standard. And, therefore, their time count, in contrast to quantum clock, does
not depend or dismissively weakly depend on coordinate-like velocity
of light and, therefore, on correspondent to it thermodynamic parameters of
matter. Thus, the influence of pressure and temperature on relativistic dilation of proper
quantum time of matter is not taken into account in the process of non-comfort
motion of this matter that is accompanied by the appearance of internal
stresses and elastic deformations in it. The
influence of pressure and temperature in matter on conformal-relativistic (non-elastic)
shrinkage of
coordinate intervals in matter is also not taken into account. Exactly this shrinkage is responsible for the origin in observer’s
FR of the gravitationally-kinematic curvature of the part of its intrinsic
space filled by “non-comfort” moving (accelerating or rotating) matter. This leads not only to the unsuitability of SR
transformations of increments of coordinates and time for the transition from
intrinsic FR of rotating matter to observer FR (Ehrenfest
paradox), but also to the separate
problems in GR.
2. The fact that intrinsic STC of
matter is formed directly by matter itself is declared in GR. In spite of this,
values of components of STC metric tensor are considered to be independent from
all properties of matter, located in concrete point of space. Thus, metric tensor
in this point determines equal (not gauge mutually transformable, as it is
expected) values of gravitational potentials for all possible thermodynamic
states of matter Therefore, coordinate-like velocity of light, used in GR, is
not a characteristic of matter, but, in fact, is a characteristic of the form
of matter being - space, and can take any values that do not correspond to
thermodynamic matter parameters and to real velocities of propagation of
electromagnetic waves in it. This leads to the necessity of using in GR the
special differential operators for dependencies of matter energy and momentum
on its physical parameters. It also leads to the need to replace very massive
neutron stars, which have the topology of a hollow body in the background Euclidean
space and mirror-symmetric inner space, fictional "black holes".
3. Influence of gravitation on
matter, as well as influence of nonuniform motion on
matter, causes not only spatial inhomogeneity of the gravi-quantum rates of proper time of matter. This influence also leads to inhomogeneous deformation of matter on the level of correspondent to its nucleons terminal outlets of the turns of the common
spiral-wave formation of the Universe in both background intrinsic space of the
observer and in background Euclidean space of CFREU [31]. The principle of unobservability of such
deformation in all matter intrinsic FRs remains valid in GR. However, there is
some exception in GR for relativistic length shrinkage: it is considered as
observable in all FRs, not comoving with moving
matter. This leads to a false relativistic generalization of
thermodynamics with Lorentz-invariant volume [28].
4.
Changeability of values of interaction distances of matter micro-objects in thermodynamic processes (these
values together with the velocity of propagation of interaction determine the
frequency of interaction) is not taken into account in GR. This causes the fact
that GR gravitational field equations correspond to FRs of STC, but not to
GT-FR of all matters, to which RGTD equations correspond. This makes GR equations useable
only for homogeneous matter.
The
fact that vacuum (coordinate-like pseudo-vacuum) velocity of light is more
privileged than true velocity of light in matter in SR and GR makes these theories
more corresponding to unrealizable in principle - degenerate states of matter
than to real states [15; 19]. The fact that relativistic time dilation, as well
as gravitational potential (and integral equations of gravitational field in
matter), are strictly independent from concrete values of any characteristics, of this matter denotes the excessive simplicity of SR and GR that
causes the primitiveness of representation of objective reality by these
theories. The “beauty” of these theories, related to their simplicity, does not
correspond to, in fact, not very “beautiful” objective reality.
In
spite of this, the most of the original positions and principles of SR and GR
are saved in RGTD. The main
distinguishing characteristics of RGTD
are the following original positions and principles:
1.
Physical vacuum is a continuous (structureless)
substance that is not involved in motion and rests in CFREU. Matter micro-objects (elementary
pseudo-particles) and electromagnetic waves are only
the non-mechanically excited states of this substance [16].
2. RGTD-state of matter is the spatially
inhomogeneous average statistical macrostate of this
matter. This state is determined by statistical distribution of possibilities
of various collective space-time microstates (Gibbs microscopic states) of the
whole gravitationally bonded matter. Discrete changes of collective space-time
microstate of matter take place at de Broglie frequency, which corresponds to
the collection of all jointly moving objects of this matter, and propagate as
the quanta of action with a superluminal phase velocity. This takes place
instantly in FR, comoving with matter, because of the
fact that propagation front of quantum of action (that is responsible for the
change of collective space-time micro-state of matter) is identical to the
propagation front of succeeding time instant of moving matter both
in CFREU and in FR of each of the observers of its motion.
3.
Transfer of phase changes of collective space-time microstate of matter, as
well as of graviinertial field (gravitational field,
removable by coordinates transformation) strength, at
a superluminal velocity do not accompanied by the propagation of changes of
electrical and magnetic field strengths in the matter and, so, not accompanied
by energy transfer [32]. Released intranuclear energy of matter transforms into
kinetic energy of directed motion before matter is filled in with external
energy transferred at velocity of sound. Therefore, despite of the change of its motion velocity, matter moves only inertially during this period of time. In
fact, free fall of matter in graviinertial field
takes place.
4. Any
arbitrarily rarefied
matter of cosmic vacuum should be considered as incoherent matter, which abides
to the thermodynamic
laws, in analogy to ideal gas of non-interacting molecules [15]. Because of this, and also
because of principal unattainability of the zero
value of pressure in gas-dust matter of cosmosphere,
it is inadmissible not to take into account gradual decreasing of pressure in
cosmic vacuum at the distancing from compact matter. And, therefore, vacuum
solutions of gravitational field equations are senseless.
6.
Relativistic transformations of spatial coordinates and time of SR are the
vacuum degeneration of generalized relativistic transformations [33].
Relativistic shrinkage of coordinate increments (“coordinate intervals”) is
conform-Lorentz in general case. And it depends
not only on velocity of matter motion, but also on the pressure inside the
matter. The fact that graviinertial field is
originated in nonuniformly rectilinearly moving
matter, as well as in rotating matter, causes the fact that unobservable in
principle relativistic deformation of matter is gravitationally-kinematic, in
fact. Relativistic time dilation in moving matter is also
gravitationally-kinematic. Graviinertial field in GR can be considered as removable only
conventionally. Spatial inhomogeneities of
thermodynamic state and of observable (non-relativistic) deformation of moving
matter that correspond to coordinates transformation are not removed at this
transformation. Differentiated tracking of the influence of removable and unremovable gravitational fields on spatial inhomogeneity of thermodynamic state of matter is
impossible in GR in general case. Therefore, in GR, in contrast to RGTD, in
general case gravitationally-relativistic dilation of physical processes in
matter cannot be decomposed on multiplicative components that separately
correspond to unremovable (external) and eliminable
gravitational fields and to purely kinematic impact.
7.
Intrinsic spaces of matter are metrically homogeneous (isometric) in principle.
Gravitational, as well as relativistic, shrinkages of dimensions (length
standards) and molar volumes are unobservable in these spaces. Gravitational
curvature and comoving with moving object kinematic “curvature”
of intrinsic space of motion observer are observable in these spaces, instead
of these shrinkages. Therefore, relativistic transformations of SR are the
transformations of the increments only of coordinates, but not of metrical
intervals [28].
8.
Covariance of equations of matter motion and state (and, in fact, covariance of
the majority of physical laws) to the coordinates transformations takes
place only for spaces of the GT-FRs of matter, namely,
only for the
spaces, in which matter deformations caused by relativistic and gravi-evolutional “deformations” of its micro-objects
(correspondent to them spiral-wave formations) are
unobservable in principle. Such deformations are “observable” in background Euclidean space [31]
of CFREU (only in this space Universe can be
homogeneous). A completely different formulation of the majority of nature
laws, as well as other transformation of intensive and extensive parameters and
characteristics of matter that correspond to this formulation and possibly
different form of equations that determine interrelations between them are
needed for intrinsic GQ-FRs of matter, in which not only evolutionary but also RGTD-“deformations” of its micro-objects (changes of their interaction
distances) are unobservable in principle.
9. All thermodynamic parameters and
characteristics of matter are invariant under both transpositional
gravitational (spatio-temporal) and relativistic transformations
of coordinates and time in principle. And, consequently, temperatures of phase
transitions are the internal properties of matter of not only resting, but also
moving bodies. The permanence (Lorentz-invariance) of observed thermodynamic
state of moving matter when switch from its observation from any of IFR to the
observation from any other IFR is provided
by
the
calibration
effect of classic inertial (hypothetic uniform) motion
on the matter. It is guaranteed by the save of initial proportionality of
observed rates of all physical processes to the rate of intrinsic time of
moving matter. Ant the cause of all this is the self-consistency of all pairs
of intensive and extensive thermodynamic parameters of matter that are
complementary to each other. They form the self-enclosed RGTD-system.
10. Spatial inhomogeneity
of RGTD-state of the whole
gravitationally bonded matter (including extremely strongly rarefied incoherent matter of the outer space) is the cause of the presence of
gravity. This inhomogeneity is reflected in
homogeneous matter as certain spatial distribution of Gibbs free energy and of corresponding to this energy the nominal
intensive parameter - relative average statistical value of the frequency of
intra-atomic interactions (alternative to pseudo-vacuum coordinate-like
velocity of light of GR). This field was originated due to the delay in the
evolutionary process of decrease of intranuclear
energy and the corresponding to it increasing of the Gibbs free RGTD-energy of matter. And
it is the consequence of self-organization of collective macrostate of
jointly moving matter that corresponds to the minimum of total (integral) value
of the purely thermodynamic Gibbs free energy of this matter.
12. Bodies free fall in gravitational
field - is an original realization of tendency of the whole gravitationally
bonded matter to the minimum of the integral value not
only of intranuclear energy, but also of thermodynamic
Gibbs free energy.
Bodies that fall independently accelerate in physically inhomogeneous space. In
such way bodies transform their continuously released intranuclear energy into kinetic energy.
13.
Removable gravitational (graviinertial) field, which
is inducted by quasi-hyperbolic motion of matter during the process of its free
fall, totally compensates external gravitational field. And, therefore, more
dense particles cannot overtake less dense particles of incoherent matter in
principle. Pressure in this matter, as well as relative frequency of intranuclear interactions, is spatially homogeneous (and
this is reflected in the zero-gravity state). Matter free fall can be strictly
inertial motion of matter only in hypothetic absolute vacuum. Therefore, matter
free fall in atmosphere, as well as in the outer space, is only a quasi-inertial motion.
14.
Not the total energy of matter, but only its inert intranuclear
energy, which is equal to the sum of energies of nucleons and energies of intranuclear bonds and interactions, is equivalent to inert
mass. Therefore, gravitational force that does not execute work is equal to the
product of the Hamiltonian of only inert energy of the matter and the gradient
of logarithm of relative frequency of intra-atomic interactions. By analogy, d’Alembert inertial pseudo-force is equal to the product of
the Hamiltonian of matter intranuclear energy and the
derivative of logarithm of relativistic time dilation along traversed path.
And, consequently, there is no need in the proving of mutual equality of
gravitational and inert masses of matter.
15.
When the thermodynamic state of liquid or gaseous matter is equilibrium the
gradients of conventional average value of intranuclear
interactions are determined only by the gradients of its thermodynamic
parameters. The frequency of the wave of one and the same emissive radiation
remains the same in the whole (and even extremely rarefied) gas that is located
at the long distance from the gravity center. And, therefore, declared in GR
gravitational shift of the spectrum of emissive radiation of purely
liquid-gaseous matter (which is strictly in thermodynamic equilibrium) of the
astronomical object that does not have solid nucleus is impossible in
principle. The shift of the maximum of heat radiation of this astronomical
object is strictly determined only by the temperature of matter in its
photosphere. Gravitational redshift of the spectrum
of emission radiation can take place only for non-rigid (liquid or gaseous)
matters that are in non-equilibrium thermodynamic state or for any solid
(rigid) astronomical objects (the process of evolutionary decreasing of intranuclear energy of matter of which is
always lagging). And,
therefore, gravitational redshift of the spectrum of
emission radiation is very negligible for the majority of astronomical objects.
Mainly the Dopplerian widening of spectral lines
takes place for them. The very significant gravitational redshift
can be found only for the radiation of electron-proton plasma of quasar
photosphere, where the lagging of the process of evolutionary decreasing of
energy of protons is very big.
Conclusion
Gravitational field is
the field of spatial inhomogeneity of thermodynamic
state of matter and is not an independent substance
(form of
matter). Gravitational
field cannot exist without matter, in principle, and, consequently, cannot have
its own energy and own linear momentum that differs from energy and linear
momentum of matter, which formed that field. Therefore, conservation of the
sums of values of energy-momentum and moment of momentum together for matter
and for gravitational field [35] is not necessary both
in GR
and in the RGTD.
All bonds and interactions between matter structural elements have the same
electromagnetic nature [16; 21], despite they all considerably differ one from
another. And, therefore, gravitational field cannot be completely similar by
its properties to electromagnetic field. Nature abhors uniformity. Nature “uses”
new forms of bonds and interactions between matter structural elements on each
new hierarchical level of self-organization of matter objects. However, for
sure, all these forms are rather similar, because they are based on the same
laws and principles of appropriateness. Statistical laws, which guarantee the
correspondence of equations of RGTD-state
of matter to the variational principles and,
consequently, Le Chatelier-Braun principle, are the
basis of gravitational and other RGTD
properties of matter. Gravity forces are gravi-evolutionary pseudo-forces that force all matter
objects to tend to spatially inhomogeneous collective equilibrium states with
the maximum of the integral Gibbs free RGTD-energy and
with the minimum of the integral thermodynamic Gibbs free energy of the whole gravitationally bonded matter. Because of this, GR
gravitational field equations are, in fact, relativistic equations of spatially
inhomogeneous RGTD-state of
gauge-evolving matter (equations of RGTD)
[15]. And, therefore, gravity is only the
peculiar (sui generis) manifestation of electromagnetic nature of the matter on
the appropriate hierarchical level of self-organization of matter objects. And,
of course, there are no such objects as gravitons and gravitational waves that
transfer energy (if, of course, moving matter itself is not considered as these
waves).
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