Theoretical misconceptions and imaginary entities in astronomy, cosmology and physics
The majority of theoretical misconceptions and the most significant misunderstandings in modern astronomy, cosmology and physics are caused by a purely mathematical approach and ignoring philosophical comprehension of physical reality and, as a result, by not deep enough understanding of the essence of certain physical phenomena and objects. Foremost, it's all about phenomena and objects that are under consideration by Special and General Relativity. Author have analyzed historical roots of discussed here misconceptions and misunderstandings and have shown the possible ways to overcome them. Such constructive approach gives us the hope for getting rid of the majority of revealed here misconceptions and misunderstandings. Unfortunately, this is the problem of not only the astronomy and cosmology, but also of physics in general. Our perception and reflection of physical reality is still very primitive and, foremost, mainly mechanistic, macrocentric and anthropolimited. The unreality of black holes, Big Bang, nonbaryonic dark matter, dark energy, photons and neutrinos is justified in details. The current usage of exponential scale instead of metrically homogeneous scale of cosmological time in cosmology is shown. Therefore, the ignorance of the fact that only the infinitely far cosmological past on the event horizon and infinitely far cosmological future on Schwarzschild sphere are simultaneous with any event in people’s world is shown. The ignorance of the fact that this pseudohorizon covers the past of all infinite Universe is also shown. The possibility of existence of antimatter inside the neutron stars and quasars that have the hollow body topology and mirror symmetry of their intrinsic space is justified. The big redshift and long lasting high luminosity of quasars are explained.
The spatiotemporal noninvariance of the gravitational constant and the fictiveness of Etherington's identity are proved. The absence of gravitational fields in the Universe up to the moment of discontinuity of its uniform gas continuum is shown. The origination of the gravity phenomenon is related to the formation of spatially inhomogeneous thermodynamic states by the matter and to the tendency of the whole gravithermodynamically bonded matter to reach the maximum of the integral value of its intranuclear Gibbs energy as well as to reach the minimum of the integral value of its thermodynamic Gibbs energy. The fact that spatial distribution of gravitational field strength, defined by logarithmic gravitational potential, perfectly corresponds to astronomical observations is shown. The fact that Hubble’s redshift is linearly dependent on comoving distance instead of luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. It is concluded that such concepts as corpuscle and elementary particle are purely macroscopic. The inadmissibility of the presence of “thinginitself” in physics is shown. The possibility of spiralwave nature of the matter microobjects – the terminal local drains of turns of the spiral waves of high frequency spacetime modulations of the dielectric and magnetic permeabilities of the physical vacuum (singularities of the field according to Einstein hypothesis) – as a whole is shown.
Key words: black hole, quasar, Big Bang, nonbaryonic dark matter, dark energy, redshift, luminosity distance, gravitational potential, Etherington's identity, Hubble's law.
Einstein had believed that the particles were singularities of the field in space In quantum field theory we have learned in the meantime that the particles are singularities – namely poles – in momentum space, not in ordinary space. For Einstein the field was real; it was in fact the ultimate reality and determined both the geometry of the world and the structure of the material bodies. In quantum theory, the field distinguishes, as in classical physics, between something and nothing; but its essential function is to change the state of the world, which is characterized by a probability amplitude, by a statement concerning potentialities.
Werner Heisenberg (Single Field Theory)
Introduction
Tensor equation of gravitational field of the General Relativity (GR) can be represented using either curvature of Riman’s spacetime continuum (STC) or metric inhomogeneity and metric instability of Euclidean space [Danylchenko, 2004a: 33; 2004a: 62; 2008: 45]. The solution of this equation in metrically homogeneous Riman’s STC corresponds to the solution in the background Euclidean space [Zeldovich & Grischuk, 1988]. This background Euclidean space is metrically inhomogeneous. Either metrically homogeneous time scales or exponential time scales can be used in such space [Danylchenko, 2004a: 33; 2004a: 62]. Such metrically inhomogeneous scales allow performing conformal transformations of time. Either infinitely far past or infinitely far future can become finite due to such time transformations.
General covariance of formulation of physical laws regarding the transformations of spatial coordinates and time in GR takes place during the transition from any stable and metrically homogeneous frame of reference of spatial coordinates and time (FR) to another stable and metrically homogeneous FR. In metrically instable and inhomogeneous spaces the dimensions of length standard are different at different moments of time in the same point and also at one moment of time in different points. Therefore, not only metrical and physical characteristics of distant in time or space objects and events, but also fundamental physical constants should be renormalized in FR of such spaces [Danylchenko, 2008a: 106]. Such renormalization should be done even when there was no transition to another point of observation in space.
The concept of Universe homogeneity may be applied only to comoving FR in the expanding Universe (CFREU). In CFREU (Weyl's FR) the radial distancing of galaxies from the observer is absent. Mutually proportional evolutional shrinkage of length standard and of all macro and micro objects of matter takes place in CFREU instead. All infinite fundamental space of CFREU is covered by the event horizon (pseudohorizon of the past) in the gravithermodynamic FR (GTFR) of evolutionally selfcontracting matter. Relativistic failure to comply with simultaneity of simultaneous in CFREU events takes place in GTFR. As a result, only infinitely far cosmological past is simultaneous with any event in people’s world (in GTFR) on this pseudohorizon [Danylchenko, 2004a: 33; 2004a: 62]. Metrical distance to the event horizon, thereby, tends to infinity while approaching event horizon. Thus, concentration of astronomical objects in GTFR inevitably increases while approaching this pseudohorizon of the past and, consequently, while deepening into cosmological past. Therefore, the Universe can not be homogeneous in GTFR’s intrinsic space in principle.
1. Imaginary Black Holes
For the reasons mentioned above, only the infinitely far cosmological future is always present on Schwarzschild’s singular sphere [Danylchenko, 2004a: 33; 2004a: 62; 2005a: 95]. Finite value of its radius r_{s} in GTFR corresponds to zero value of its radius R_{s}=0 in the background Euclidean space of CFREU. This fact corresponds to hypothetic selfcontraction (into “point”) of any object (in CFREU) in infinitely far cosmological future. That is the reflection of conformity of both infinity and zero [Penrose, Roger, 1968: 161]. That’s why the very suggestion about possible collapse of the matter from outside to the inside of the fictive Schwarzschild sphere and into infinitely far cosmological future is frankly absurd. The same conclusions can be made based on the solutions of GR equations for spatially inhomogeneous thermodynamic state of matter. Tending of coordinate velocity of light to zero while approaching real singular surface always corresponds only to the tending of temperature and pressure of matter to infinity [Danylchenko, 2004a: 33; 2008a: 4; 2008a: 19; 2009: 47; 2009a: 75; 2010: 38].
Therefore, real singular sphere can be only median sphere [Danylchenko, 2004a: 33; 2004a: 62; 2005]. It can separate external matter from internal antimatter in hollow astronomical bodies. Thus, catastrophic annihilation of matter and antimatter is prevented. Therefore, extraordinary neutron stars can be considered by mistake as compact or supermassive “black holes”. Those extraordinary neutron stars have the hollow body topology in the background Euclidean space and mirror symmetry of intrinsic Riman’s space (see Fig. 1). The space inside the singular sphere is turned inside out [Danylchenko, 2004a: 33; 2004a: 62; 2005]. Due to strong gravitational field in intrinsic space the eigenvalues of the area of covering spheres is not more but less than eigenvalues of the area of covered by them spheres.
Fig.1. Curved intrinsic space of the hollow astronomical body and this body in Euclidean fundamental space of CFREU
The possibility of existence of such unusual bilayered topology of astronomical bodies is confirmed by the solutions of equations of GR gravitational field. This is confirmed not only in GTFR, but also in CFREU. Internal surface of hollow astronomical body is convex in its STC. At the same time the phenomenon of contraction of “internal Universe” takes place in internal intrinsic “empty” space covered by that internal surface. Only such phenomenon is acceptable for the longlived existence of antimatter (diverging spiral wave formations) [Danylchenko, 2004a: 33; 2004a: 62; 2008: 45; 2009; 2009a: 75; 2010: 38; 2014: 21; 2020: 5]. Universe expansion phenomenon is acceptable only for the longlived existence of matter (converging spiral wave formations).
2. Quasars
Bilayered shelllike quasars also have mentioned above topology. The thickness of both external layer of matter and internal layer of antimatter of such quasars are much less that the radius r_{s} of median singular sphere. Therefore, the photosphere of bilayered shelllike quasars is very close to the singular sphere. As a result, such quasars have very big gravitational shift to the red area of spectrum of radiation frequency ν. The observed gravitationallyDoplerlike redshifts of wavelength λ=c/ν of the quasars radiation spectra are much bigger than mostly the Dopler redshifts z=Δλ_{D}/λ_{0} of the radiation spectra of the stars from galaxies that surround that quasars. Continuous gradual annihilation of matter and antimatter, apparently, guarantees extra longlived ultrahigh luminosity of quasars [Danylchenko, 2004a: 33; 2004a: 62; 2005].
The mass of bilayered shelllike quasar and the radius of its median singular sphere can be determined based on excess of redshift of quasar radiation spectrum (compared to the Doppler redshift of surrounding stars in the galaxy) and imaginary deficit of baryonic matter.
3. Imaginary Big Bang
Only two known solutions of equations of GR gravitational field can be juxtaposed to expanding Universe. Those are: Schwarzschild solution [Schwarzschild, 1916: 189] when the value of cosmological constant is Λ=3H^{2}/c^{2} [Danylchenko, 2004: 62], which corresponds to the local representation of the process of Universe expansion, and Friedman solution when Λ=0 [Friedman, 1922: 377] (Λ≠0 in ΛCDM model [Semiz and Çamlibel, 2015]), which corresponds to the global representation of the process of Universe expansion.
According to Schwarzschild solution and Einstein hypothesis distant galaxies are falling free on the “event horizon” constantly moving along the geodesic lines of spacetime continuum (STC) of their observer. They fundamentally cannot reach that pseudohorizon of the past because it belongs (at any moment of observer’s time) to infinitely far cosmological past (in coordinate cosmological time) as well as to infinitely distant objects of the Universe in its background Euclidean space [Zel’dovich&Grishchuk, 1988]. And this is, of course, related to the conformity (Penrose, 1968) of these two infinities that are mutually compensated in the gravithermodynamic FR (GTFR) of Schwarzschild solution [Danylchenko, 2020: 5]. Exactly in this the background Euclidean space of the Universe, where physical vacuum rests [Danylchenko, 2004: 33; 2004: 62], according to Weyl hypothesis [Weyl, 1923; 1930] galaxies perform only small peculiar moves. And standards of length are evolutionally decreasing together with all objects of matter in this space.
Friedman solution due to negligibly small values of average density of mass in the Universe (comparing to 3H^{2}/4πG) and pressure in the outer space (comparing to 3H^{2}c^{2}/4πG) is the special case of the Schwarzschild solution in the background Euclidean space of the Universe: namely in the FR of physical vacuum [Danylchenko, 2004: 33; 2004: 62] of identical comoving FR in the expanding Universe (CFREU) when the value of gravitational radius of astronomical object, from which the observation of Universe expansion is performed, is negligibly small. In contrast to Schwarzschild solution that includes pseudohorizon of events in the equations of Friedman solutions (as well as in the equations of Schwarzschild solution in background Euclidean space) event horizon (on which the speed of light is equal to zero) is absent. This denotes the absence of the Hubble radial motion of galaxies and, thus, the absence of relativistic effects in the space of Friedman solution. Galaxies in this space perform only small peculiar moves while distances between them are increasing in this space due to mutually proportional decreasing of the dimensions of both length standards and all material objects in this space. This, of course, requires the constant renormalization of nonnormalized spatial parameters to align them with the new values of length standard.
Thus, there fundamentally cannot be any radial motion of objects in Friedman solution because of the absence of singular surface of event horizon in this solution. Therefore, Doppler Effect and other relativistic effects related to motion are not applicable for this solution.
Gravitational dilation of time, counted by quantum clock, takes place in GTFR. Therefore, it makes sense to call this dilated time as graviquantum time, and to call all correspondent to that time values of physical characteristics as graviquantum values. The graviquantum time of any certain observer can be proportionally synchronized with the unified astronomical coordinate time (gravithermodynamic time [Danylchenko, 2009; 2020: 5]) t_{E} owing to the possibility of proportional synchronization of all graviquantum clocks in GTFR of Earth. Thus, that graviquantum time will also be proportionally synchronized with the cosmological time τ, counted in the point of observer’s disposition according to metrically homogeneous scale of cosmological time (CTMHS).
Comparison of the solutions of equations of GR gravitational field with cosmological Λpart in GTFR and in CFREU shows that precisely Λpart is responsible for Hubble's expansion of the Universe [Danylchenko, 2004: 33; 2004: 62]. The value of Hubble constant is also determined by this Λpart: H=c(Λ/3)^{1/2}. Λpart also limits the maximal value of Schwarzschild radius r_{c}≈c/H=(3/Λ)^{1/2} in the space of GTFR. However it does not form the horizon of past events in GTFR [Danylchenko, 2004: 33; 2004: 62]. World points of the pseudohorizon, formed by Λpart in GTFR, correspond to infinity in space and time in CFREU. Mentioned above fact guarantees the possibility of existence of infinitely far cosmological past in CFREU when use CTMHS [Danylchenko, 2005b; 2008: 95; 2009: 47].
According to the Friedman’s solution of equations of GR gravitational field for the flat space, the Universe expands strictly exponentially. Therefore, its size should asymptotically tend to zero while deepening into infinitely far past. However, the time that corresponds to any event of the past is finite in principle. That’s why finite coordinate cosmological time is set in the Universe based on the imaginary primacy of any specific event. Of course, that time is based on assumed finiteness of the far past in the Universe. Big Bang of the Universe has been proclaimed as such fictive primary event.
Therefore, finite cosmological proper time and infinite cosmological coordinate time should be distinguished. The former defines only the nominal age of the Universe from the moment of spontaneous transformation of its protomatter into continuous hydrogen medium. The latter is based on the infinitely long evolution of the Universe both in the future and in the past.
The one more thing is that we should not exclude is the possibility that GR can be inapplicable to the description of the universe evolution in far cosmological past – before the breaking (disruption) of its uniform gas continuum. Gravitational fields originate in Universe only after that discontinuity.
4. On the inapplicability of GR for describing the evolution of matter and the Universe as a whole up to the moment of its gas continuum breaking
Firstly, on the very early stages of matter evolution many notions used in GR were inapplicable to that matter. Even nowadays, macroscopic metrics is not very applicable to the description of the microworld. That is because of physical inhomogeneity and instability of intrinsic spaces of matter microobjects.
Secondly, even after primary hydrogen was formed there were no forces of gravitational attraction between its atoms. In contrast, positively charged nuclei of hydrogen repelled one another [Danylchenko, 2004a: 62].
Thirdly, the gravitational gradients of coordinate velocity of light were absent in Universe gas continuum before its breaking. Therefore, no gravitational field yet existed [Danylchenko, 2004a: 62].
That’s why it should be admitted that gravity is the purely macroscopic thermodynamic phenomenon [Danylchenko, 2008a: 19; 2009: 47; 2009a: 75; 2010: 38; 2020: 5]. It is based on the presence of gradients of coordinate velocity of light in the space and on tending of the whole gravithermodynamically bonded matter to the collective state with the minimums of integral values of its inert free energy [Danylchenko, 2021] and thermodynamic Gibbs free energy. Such state could selforganize only after the discontinuity of entire gas substance of the Universe. Spatial gradients of coordinate velocity of light spontaneously originated as a result of that discontinuity. This finally caused the nonconservation of the momentum of matter microobjects. And, thus, this caused the gradual mutual attraction of those microobjects in the process of electromagnetic and other interactions.
Therefore, tensor equations of GR gravitational field is, in fact, the equation of selforganized spatially inhomogeneous gravithermodynamic state of matter [Danylchenko, 2008a: 19; 2009a: 75; 2010: 38; 2020: 5]. Such state of matter corresponds to the minimums of integral values of its inert free energy and thermodynamic Gibbs free energy. This equation connects the energymomentum tensor with the tensor of curvature of spacetime via only the gravitational constant. Therefore it is based on the laws of classic thermodynamics as well as on the ability of matter to selfdeformate in the background Euclidean space on the level of its microobjects. Thus, the curvature and physical macroinhomogeneity of the space of gravithermodynamically bonded matter and the gravitational field that corresponds to that macroinhomogeneity are formed. And only the cosmic rays can be considered as the gravitational radiation (gravitational waves). Other types of gravitational waves that transfer the energy cannot exist.
Therefore, usage of GR tensor equation to describe the Universe evolution before the breaking of its uniform gas continuum is, for sure, the nonsense. There was no spatial inhomogeneity of thermodynamic state of matter and, therefore, no gravitational fields and gravitational waves at that time.
Evolutional selfcontraction of terminal spiral wave formations in CFREU that correspond to hydrogen nuclei (protons), for sure, took place not only after but also before the breaking of Universe gas continuum [Danylchenko, 2004a: 33; 2004a: 62; 2008: 45; 2009a: 75; 2010: 38; 2014: 21; 2020: 5]. However it did not have any relation to the gravity (gradients of coordinate velocity of light) that originated later. That selfcontraction should be determined by equations and dependences of the synergetics and not the GR.
5. Spatiotemporal noninvariance of the gravitational constant
There are two types of time in GR: intrinsic graviquantum metrical time and unified astronomical coordinate time. The dilemma of the usage of one of those times (metrical or coordinate) in the formulation of certain physical laws is quite up to date.
Coordinate pseudovacuum velocity of light v_{cj}(r) is determined for certain point j in unified (for all gravithermodynamically bonded matter of the Earth) coordinate astronomical time t_{E}. It is identical to the critical velocity of baryonic matter in the relativistic gravithermodynamics (RGTD) [Danylchenko, 2009a: 75, 2020: 5] and its value depends on Schwarzschild radial coordinate r of that point. It decreases in GTFR while approaching the pseudohorizon or the gravity center. Graviquantum value of coordinate velocity of light:
is also dependent on coordinate velocity of light v_{ci} in the point i of observer disposition. Metric eigenvalue of velocity of light is the spatiotemporal invariant (gaugeinvariant and Lorentzinvariant constant) by intrinsic clock. This eigenvalue (proper value in Special Relativity) is equal to the constant of velocity of light in any point of space:
In contrast to velocity of light, gravitational constant G is not spatiotemporaly invariant constant. Its graviquantum value on Earth:
depends on Schwarzschild radial coordinate of the point i of observer disposition. And, consequently, gravitational constant is noninvariant in relation to the transformation of time rate when switch to the time count by another quantum clock. Therefore, graviquantum value of gravitational constant ^{i}G_{E} cannot be equal to solar gravitational constant G_{S}. This gravitational constant G_{S} is determined in the coordinate astronomical time t_{S} unified for the whole gravitationallybonded matter of Solar system. All the more so, ^{i}G_{E} is not equal to Universe gravitational constant G_{u}, that is determined in coordinate cosmological time τ. Solar value G_{S} that is used nowadays in astronomy slightly exceeds both Universal value G_{u}, and Galactic value G_{g}. Moreover, Galactic value:
could significantly exceed its current value in far cosmological past. Gravitational influence of galaxies one on another during their mutual distancing constantly decreases. Therefore, not only the coordinate velocity of light in the outer space ^{u}v_{cos}, but also its Galactic value ^{u}v_{cg} steadily tend to the value of the constant of velocity of light.
Thus, gradual decreasing of galactic value of gravitational constant takes place contrary to the Dirac hypothesis not directly in time but indirectly due to gradual increasing of coordinate velocity of light in the outer space (external gravitational potential that is formed by all other galaxies of the Universe) and, therefore, due to evolutional decreasing of the average density of matter in the Universe.
Masses of the Sun and the planets of Solar system are determined based on Earth gravitational constant G_{E}. Possibly, value of gravitational constants of the planets and the Moon can differ from the values predicted for them based on G_{E}. Therefore, it would be advisable to perform space experiments for determination of the values of gravitational constant at least on the nearest planets and the Moon.
6. Logarithmic gravitational potential
Physical laws are based only on increments of metrical distances and not on increments of coordinates. Therefore, gravitational field strength k is determined via its gravitational potential φ in the following way:
where: a is square of the ratio between increment of metrical segment and increment of radial coordinate r, and r_{g }is gravitational radius of astronomical body, from where observation takes place.
Nowadays, the following gravitational potential is used in GR and in practical calculations:
When Λ=0 that potential forms the same spatial distribution of gravitational field strength as in classical physics:
.
However, it does not correspond to Einstein’s opinion that free fall of bodies in gravitational field is inertial motion. According to this potential the kinetic energy of falling body is less that the difference between rest energies of the body in the starting point of the falling and in the point of its instantaneous disposition. Wrong opinion that gravitational field has own energy corresponds to that gravitational potential [Logunov and Mestvirishvili, 1989].
In contrast to this potential, the potential that is in a form of logarithm of the rest energy E_{0} of matter corresponds to inertial motion of freely falling body with the conservation of its total energy (Hamiltonian) [Danylchenko, 2004a: 33; 2004a: 62]:
(1)
Such representation of potential is based on the possibility of proportional synchronization of all quantum clocks and on proportionality of pseudoforces of inertia and gravitation to the Hamiltonian of matter. This is in good correspondence with the principle of mass and energy equivalence. Such representation also makes the proof of equivalence of inert and gravitational masses redundant. Logarithmic gravitational potential forms the following spatial distribution of gravitational field strength:
Effective value of gravitational constant:
(2)
tends to infinity while approaching the Schwarzschild sphere and is continuously decreasing while distancing from the gravity center. And, of course, this should successfully prevent the false conclusions about the deficit of baryonic matter in the centers of the galaxies.
Usage of logarithmic gravitational potential does not require the adjustment of the values of mass of the Sun and the planets. If gravitational radius of Sun is 2.95 km then its mass should be decreased on just two millionth parts of it. It is 35 times less than the determination error of Sun mass. On the Mercury orbit the strength of Sun gravitational field should be decreased on just 20 billionth parts of it. The Earth itself has very small gravitational radius 0,887 cm. Due to this fact Earth mass should be decreased on just one billionth part of it. At the same time, Earth mass determination error is 100000 bigger.
Unlike for the Solar System, the usage of logarithmic gravitational potential can be very essential for the far galaxies.
7. Imaginary Etherington's Paradigm
Luminosity of fast moving galaxies is isotropic only in their intrinsic FRs. However, this luminosity is also considered as isotropic in the GTFR of any far observer during the astronomical photometric calculations. Therefore, relativistic transformations of angular coordinates are ignored in those calculations [Danylchenko, 2008a: 106; Weisskopf, 1972]. Thereby, distances to galaxies are not determined by those calculations in the GTFRs of observer. They are, in fact, determined in CFREU. Only in CFREU the luminosity of all galaxies is isotropic and the Universe itself is uniform. However, the imaginary Etherington’s identity [Etherington, 1933: 761] for uncorrected luminosity distance D_{L} and for imaginary value of angular diameter distance ^{i}D_{A}, that corresponds to it, in the calculations is also taken into account:
Etherington’s identity is based on the imaginary relativistic dilation of intrinsic time of the galaxy by (1+z) times [Hogg, 2000]. That time dilation (inherent to GTFR) is actually absent in CFREU when using the CTMHS. The primary frequency of radiation of the galaxy is the same as the frequency of identic to it radiation in nearby vicinity of observer in CFREU by CTMHS. That frequency is only progressively decreasing in “ontogenesis” (in the process of propagation of that radiation) together with decreasing of velocity of light in CFREU in accordance with CTMHS [Danylchenko, 2004a: 33; 2004a: 62].
Such imaginary time dilation by (1+z) times takes place in CFREU by physically homogeneous scale of cosmological time (CTFHS). The velocity of light does not change during its propagation when using the CTFHS, in contrast to CTMHS. The frequency of radiation that is lesser by (1+z) times corresponds to “phylogenesis” (to the process of the emission of that radiation). The infinitely far future becomes finite when using the exponential CTFHS. As we go deeper into the cosmological future, the rate of physical processes increases according to CTMHS. That is, for sure, similar to the imaginary increasing of the rate of physical processes while deepening into cosmological past, caused by the use of the exponential scale of the cosmological time (CTES). This CTES is currently used in cosmology. Infinitely far cosmological past imaginarily becomes finite by that CTES.
Thus, we are dealing with the Etherington’s paralogism. This paralogism is caused by the mixing of observations in two different FRs – in CFREU and in GTFR. The Universe is observed in CFREU as uniform (monotonous), with the single for all its objects cosmological time and without the presence of global relativistic effects. Consequently, the relativistic time dilation on the astronomical objects moving away from each other in the expanding Universe, which is observed in the GTFR of each of the objects, is imaginary (fictive) for CFREU (and, therefore, for the global perception). The Universe is nonuniform (not monotonous) in GTFR. And not only relativistic time dilation on far astronomical objects, but also relativistic anisotropy of their luminosity is observed in the GTFR. That relativistic anisotropy of luminosity was ignored by Etherington in contrast to relativistic time dilation. Of course, Etherington could consider these relativistic effects (inherent to Schwarzschild solution only) as applicable for Friedman solution without understanding that the Hubble radial motion of objects of matter is absent in this solution.
Moreover in any observer’s FR the coordinate sizes of these objects (in the moment when they emit the radiation) are conformally reduced in their crosssection more than it is required for the absence of dilatation of their intrinsic time. According to GR their transverse scale factor formally exceeds its limit value, beyond which there should be not a deceleration but acceleration of the rate of intrinsic time of moving body [Danylchenko, 2008: 106]:
,
where: ; is the velocity of radial motion of distant galaxy; is the transverse comoving distance to the galaxy in CFREU.
According to the increment of the interval:
,
when: , and the , , , will take place, and:
.
And, consequently, the dilatation of intrinsic time of astronomical objects of far galaxies that are distancing from observer is absent in conformally transformed time t of the observer FR and all the more so by its real clock that counts universal astronomical time . So, according to GR formalism not the dilatation but vice versa the fastening of the rate of intrinsic time of distant galaxies takes place by the observer’s clock: . However, if just the gravitational dilatation of the rate of time of distant galaxies is completely compensated by the free fall of distant galaxies on the pseudohorizon of events, then indeed there fundamentally cannot be any contraction or dilatation of the unified gravithermodynamic (not coordinate) time of matter of these galaxies. And this can take place in the case of the conformal gravitationallyLorentz transformations of increments of space coordinates and time, which guarantee the relativistic invariance of Hamiltonian of inertially moving body as well as of all thermodynamic potentials and parameters of its matter.
The similar imaginary effect of mutually observed time dilation in two inertial FRs (IFRs) takes place in the clocks paradox in Special Relativity (SR). This is due to the fact that events at different points are not simultaneous events in the observer's IFR, although they are simultaneous events in the IFR of the observed moving body. And such resultant time dilation becomes true only for the observer that transits from one IFR to another IFR that moves in opposite direction in order to make remeeting possible. In the case of mutual observation of time dilation for two distant galaxies that are mutually distancing only in GTFR and resting in CFREU such difference between these galaxies is absent. That is why time dilation is fictive (seeming) for both distant galaxies.
It is worth to mention, that Lorentz transformations in SR are only the transformations of increments of the coordinates and not of the increments of metrical intervals (segments) [Danylchenko, 2009a: 75; 2010: 38; 2020: 5]. That is, apparently, why relativistic dilation of only coordinate time, and not metric time, takes place in distancing galaxies when observations are performed in GTFR of that galaxies. According to conformLorentz transformations of increments of spatial coordinates and time (that guarantees the invariance of thermodynamic potentials and parameters of matter to them) the relativistic dilatation of intrinsic time is absent at all for inertially moving bodies [Danylchenko, 2020a]. The distancing from observer far galaxies are namely inertially fall onto the pseudohorizon of events and, therefore, there, of course, should not be any relativistic dilatation of intrinsic time for them.
Intrinsic time dilation in distancing galaxies, which is defined based on the redshift of radiation spectrum, is just the imaginary phenomenon. That time dilation is the similar to such imaginary phenomenon as the movement of the Sun across the earthly sky. And, of course, it is the similar to the phenomenon of Universe expansion in people’s world “from nothing” and “into nowhere”. That is why relativistic decreasing of the quantity of radiation quanta, which are registered by observer, is determined in its GTFR by the (z+1) factor, and not by (z+1)^{2} factor, which is declared by unreliable Etherington’s identity.
So, nowadays Etherington’s identity is only the imaginary Paradigm. The real astronomic identity should, of course, be taken instead of it:
.
This identity, in fact, connects the luminosity distance D_{L} with corrected photometric distance в GTFR r=D_{A}. This photometric distance is used in Schwarzschild solution of GR gravitational field equations.
8. The inconsistency of the motion of galaxies with Kepler's laws
Laws of motion of single astronomical objects, found by Kepler, are based on gravitational influence of mainly central massive body. According to that laws, the velocity of rotation of galactic objects should decrease in inverse ratio to the square root of the distance to galaxy center. However, observations reveal the different picture: this velocity remains quasi constant on quite far distance from galaxy center for many galaxies, including ours [Pogge, 2006; Bennett et al., 2012]:
a)
b)
Fig.2. Dependencies of velocity of rotation of astronomical objects on the distance to gravity center: (a) our Milky Way galaxy [Bennett et al., 2012; Rieke, 2016], (b) comparing to prognosed Keplerian velocities [Pogge, 2006; Thompson, 2011]).
When single objects and their aggregates form big collection (cluster) their total mass can essentially exceed the mass of central astronomical body (supermassive neutron star or quasar). The attraction of astronomical objects of the internal spherical layers of the galaxy can be much stronger than the attraction to the central body of the galaxy. Then, their collective gravitational influence can essentially distort the correspondence of the motion of peripheral astronomical objects to Kepler's laws. And, therefore, according to astronomical observations the velocities of rotation of galaxy’s peripheral astronomical objects required for prevention of joint collapse of all matter of the galaxy are much higher than the velocities of rotation of the separate peripheral astronomical objects required for prevention of the independent fall of those objects onto the central astronomical body.
The quite close dependency to the observed one is the following dependence of galactic velocity of rotation v_{g} of astronomical objects on the distance to the galaxy center. It is determined by the common galactic clock when the radial distribution of the average relativistic density of corrected relativistic mass of matter in the galaxy is the following:
, (3)
where: ,
, ,
v_{z}– zonal velocity of rotation (motion intensity) of astronomical objects by the clock of the outer space that surrounds them and is not dragged by the motion of astronomical objects themselves, μ_{0}, r_{e}, r_{m}_{,}σ – constants.
In this case on the large distances to the central astronomical body with the radius r_{e}_{}(r>>r_{e}) the parameter η is only weakly sinusoidally modulated. And, also, the square of velocity of orbital rotation of astronomical objects of the galaxy, that can be found from the condition of equality of centrifugal pseudo force of inertion F_{i}=Hv_{g}^{2}/c^{2}ba^{1/2}r and pseudo force of gravity F_{g}=(H/c^{2}a^{1/2})d(ln^{u}v_{cg}/c)/dr:
(4)
very slightly depends on r>>r_{e} due to the smallness of exp(r/r_{e}), pressure p in the outer space of galaxy and cosmological constant Λ. And its value can only slightly increase together with increasing of r due to the gradual increasing of the parameter η.
Here “galactic” value of coordinate velocity of light^{ u}v_{cg}=сb^{1/2}, Hamiltonian H=m_{0}c^{2}b^{1/2}(1v_{g}^{2}/bc^{2})^{1/2}=mc^{2}(1v_{z}^{2}c^{2})^{1/2} and increment of the metric radial distance dř=a^{1/2}dr are determined by the parameters b and a=1/(1ηΛr^{2}/3) of the equations of GR gravitational field:
,
.
As we can see, exactly the logarithmic potential of gravitational field and the spatial distribution of gravitational strength defined by it in the extremely filled by stellar substance space of the galaxy correspond to these astronomical observations. The quite significant decreasing of the average density of matter when distancing from the center of the galaxy towards the periphery also corresponds to these astronomical observations. Together with the deepening into cosmological past (τ_{p}<τ_{e}) the average density of matter in the GTFR of the galaxy is decreasing on its periphery proportionally to the square of radial coordinate r_{p}. In the picture plane of astronomical observation this radial decreasing of the density of matter is even more significant:
,
since, in contrast to GTFR of the central astronomical object of the observed galaxy, in GTFR of terrestrial observer all other astronomical objects of this galaxy belong to the same moment of cosmological time τ_{p}=τ_{e}_{.}.
And, therefore, the quantity of baryonic matter currently present in galaxies can be quite enough for examined here justification for observed velocities of astronomical objects of galaxies. The one more contributing fact is that having the same quantity of matter (m_{0}_{p}=m_{0}_{e}) its gravitational mass m=m_{0}b^{1/2 }on the galaxy periphery is bigger than in its center since b_{p}>b_{e}.
The GR gravitational field equations de facto correspond to spatially inhomogeneous thermodynamic states of only utterly cooled down matter. The similar to them equations of RGTD correspond to spatially inhomogeneous thermodynamic states of gradually cooling down matter. That is why in the RGTD the fourmomentum is formed not by enthalpy but by the ordinary internal energy of matter (multiplicative component of its total energy). According to this, in the tensor of energymomentum of the RGTD not only intranuclear pressure p_{N} but also intranuclear temperature T_{N} is taken into account:
, (5)
. (6)
The defined by the same spatial distribution (3) average relativistic density of corrected relativistic mass of galaxy matter in RGTD has the following form:
,
where: ,
μ_{0}=m_{0}/V, V is volume of matter, m_{0}=b^{1/2}m is intrinsic value of the mass of matter that corresponds to “critical” equilibrium value of gravithermodynamic Gibbs free energy (b=1), and ^{u}v_{lg}≡^{u}v_{cg} is maximum possible (extreme) value of velocity of matter in the outer space of the galaxy [Danylchenko, 2009; 2020: 5].
According to this we find the square of the rotation velocity of astronomical object relatively to the galaxy center according to the equations of gravitational field of RGTD:
, (7)
where: .
As we can see, at the same radial destribution of the average density of the mass μ_{r} of baryonic matter the circular velocities of rotation of astronomical objects relatively to the galaxy center are much bigger in RGTD than in GR. And this is, of course, related to the fact that:
.
Therefore, we can get rid of the imaginary necessity of dark nonbaryonic matter in galaxies that follows from the equations of GR gravitational field if we analyze the motion of their astronomical objects using the equations of gravitational field of RGTD.
If we do not take into account local peculiarities of distribution of average density of the mass in galaxies and examine only the general tendency of typical dependence of the orbital velocity of their objects on radial distance to the galaxy center, then the following dependence of this velocity on parameter b and, thus on radial distance r, can be matched with the graphs on Fig.2:
. (8)
Where according to (4):
, (9)
,
and: r_{e} – radius of the conventional friable galactic nucleus, on the surface of which the orbital velocity of objects can take its maximum possible value v_{ze}(b_{e})=v_{z}_{max}.
The smaller value b corresponds to the larger value n of the index of density of friable galactic nucleus on the same big radial distances. However, only when values are extremely large n>2^{25} the significantly lesser average density of matter beyond the friable galactic nucleus takes place and that is why the dependence of orbital velocities of galactic objects on radial distances can be close to Keplerian. When the parameter values are n<2^{15} the orbital velocities of extranuclear objects are, according to (8), quite close to their maximum values v_{z}_{max}<225 km/s (Fig. 2 b)) on quite big radial distances r/r_{e}<20:
.
This, of course, is related to the fact that big gradients of gravitational field on the periphery of such galaxies are formed not by their nuclei but by all large set of their objects.
Then, taking into account the negligible smallness of cosmological constant and of the pressure in the outer space of the galaxy, the following typical radial distribution of average density of mass of matter in the galaxy will take place in GR:
,
where G=κc^{4}/8π – Newton’s gravitational constant, and according to (4):
. (10)
Thus, according to GR, the bigger the index n and the lesser the value of parameter b_{e}, the lesser is maximum possible value of average density of mass of the matter on the edge of the galaxy. However, when v_{z}_{max}=225 km/s, r_{e}=5 kpc, r_{lim}/r_{e}=20, n=2^{15} (v_{z}_{lim}=224,317294 km/s) and b_{e}=0,99999551225433188 (b_{lim}=0,999999888026921702): [μ_{lim}]_{GR} =6,276 10^{24}kg/m^{3} is only 0,4% smaller than its approximate value. And, therefore, due to v<<c it quite weakly depends on the index n of the density of friable galactic nucleus.
In RGTD (taking into account the negligible smallness of only cosmological constant) the completely different typical radial distribution of the average density of mass of the matter in the galaxy takes place:
, (11)
according to which in the case of fulfillment of condition (10) it becomes infinitely small. The tendency to 1 of not only parameter a, but also parameter b, prevents the limitless decrease to zero of average density of mass of matter on the edge of the galaxy. That is why in RGTD, in contrast to GR, there cannot be in principle any shortage of baryonic mass not only in the center, but also on the edge of the galaxy.
Taking into account that in the outer space on the periphery of the galaxy a_{lim}1≈1b_{lim} and, thus, a_{lim}=1,00000111973203677 (when 2v_{z}_{lim}^{2}с^{2}=1,11973203777 10^{6}), having the same initial data we can find the acceptable value of the average density of mass of matter on the edge of the galaxy: [μ_{lim}]_{RGTD} =5 10^{26}kg/m^{3}. However, of course, when we have value b_{e}, that guarantees δ_{lim}<10^{15}, the significantly smaller average density of mass of the matter on the edge of the galaxy can take place in RGTD. When n=1 (v_{z}_{lim}=224,99999999936 km/s) and the same value δ_{lim}=10^{15 }(b_{e}=0,99999606363264543, b_{lim}=0,999999436721227408) [μ_{lim}]_{RGTD} =1,4 10^{27}kg/m^{3}.
As we can see in RGTD, in contrast to GR, index n=2^{15} quite significantly (almost 36 times) increases the acceptable average value of density of mass of matter on the edge of the galaxy. However, due to mutual dependence of variable parameters n, b_{e} and a_{e}_{,} that is defined by the principles of expedience and by corresponding to them negative feedbacks, the increasing of [μ_{lim}]_{RGTD}_{}will be indeed significantly smaller. The increasing of [μ_{lim}]_{RGTD} on the galaxy periphery due to n=2^{15} can be partially compensated by its decreasing due to decreasing of the value δ_{lim.}
As a result of evolutional decreasing of average density of matter in the Universe and gradual cooling down of the galaxy nuclei their parameters n, b_{e} (b_{lim}) и a_{e} (a_{lim}) are gradually changing. It is manifested in a gradual distancing of astronomical objects from the galaxy center. The speeds of gradual change of these parameters are not equal for different galaxies that may result in the nonequality of galactic values of Hubble constant. However, the difference of galactic values from the global value of Hubble constant, which corresponds only to evolutional expansion of the Universe, is negligibly small in modern time. But in far cosmological past it could be more significant due to the big values of average density of matter in the Universe and, thus, due to the smaller values of parameter b (and, consequently, of defined by them values of coordinate velocity of light) in the outer space of the Universe. Nowadays it is more significant only in nonrigid FRs [Danylchenko, 1994: 52] of coolingdown astronomical bodies.
Radial distribution of parameter a can be found via the solution of differential equation:
and, taking into account that dr=(rc^{2}/2v_{z}^{2}b)db, and v_{z}_{max}<<c, – of another equation:
. (12)
9. Imaginary nonbaryonic dark matter
According to fictive Etherington’s identity (paralogism) only imaginary (wrong) value of transverse comoving distance to the galaxy is determined nowadays in astronomical photometric calculations:
It is (1+z)^{1/2} times smaller than the right (real) value of transverse comoving distance to the galaxy:
And, therefore, it is (1+z)^{1/2} times smaller than the radial coordinate R=^{ r}D_{M} of the galaxy in Euclidean space of CFREU in the moment of registration of its radiation [Danylchenko, 2004a: 33; 2004a: 62]. And it is also (1+z)^{1/2} times bigger that the Schwarzschild radius of the galaxy in GTFR:
This radius is equal to radial coordinate R_{0} of the galaxy in CFREU in the moment of radiation emission. And, therefore, it is identical to corrected photometric distance to the galaxy in GTFR and is equal to the right (real) value of angular diameter distance ^{r}D_{A}. That is because of:
However, usage of the wrong value of the angular diameter distance to the galaxy:
allows only to reduce the imaginary necessity in phantom nonbaryonic “dark matter” in the Universe. According to many astronomical observations the usage of ^{i}D_{A} does not allow to completely get rid of that fictive need.
It is obvious that not very massive bilayered shelllike quasars that have strong gravitational field only in their close neighbourhood are located in the centers of many galaxies. That is possible because the effective value of gravitational constant (2) tends to infinity while approaching to median singular sphere of the quasar when logarithmic gravitational potential is used. G_{eff} depends on angular diameter α of circular orbit in the following way:
when the orbital plane of astronomical body is perpendicular to the radiusvector of the galaxy center.
It is possible that imaginary deficit of baryonic matter in friable nucleus of the galaxy is indeed compensated by quite big effective value of gravitational constant for all its astronomical objects. And exactly that deficit of baryonic matter allows us to consider logarithmic gravitational potential (1) as the most effective alternative to phantom nonbaryonic dark matter.
Of course, the radiation spectrum of far galaxies for sure cannot depend on the imaginary time dilation, “observed” in GTFR in the points of instantaneous disposition of these galaxies, because the relativistic dilation of the GTFR's intrinsic graviquantum time occurs only within the extended empty space of the Earth. This expanded empty space is only formally (imaginary) evolutionarily selfcontracting in CFREU along with the Earth. Therefore, the time dilation is also only formally “observed” in the GTFR. That’s why, according to line element of GTFR [Danylchenko, 2004a: 33; 2004a: 62] velocities of astronomical objects in the picture plane in intrinsic graviquantum time of the observer do not depend at all on the dilation of intrinsic graviquantum time of GTFR in the points of instantaneous disposition of those objects.
Of course, the counting of intrinsic graviquantum time of the observer could be replaced by the counting of dilated graviquantum time in those points of GTFR. However, then the graviquantum value of gravitational constant (calibrated accordingly) should be used:
Results of such imaginary “observation” of the motion in the picture plane of distant astronomical object in dilated graviquantum time of point j of its disposition, of course, will be changed. However, those results will correspond to the same regularities as the results of observation in standard astronomical time of observer’s GTFR.
It is worth mentioning that analysis of the motion of astronomical objects can be done in accordance to CTMHS in CFREU using the real metrical distance ^{r}D_{M}=R to them instead of ^{i}D_{M}. Such analysis would require taking into account that length standard in CFREU (at the moment of observation) is (1+z) times smaller than its size during the emission radiation. Therefore, it would be also required to use in CFREU (1+z) times bigger values of accelerations and velocities of those objects, as well as, values of the velocity of light in the points of dispositions of those objects. Furthermore, it would be required to use (1+z)^{3} times bigger value of gravitational constant in the points of disposition of observed objects. However it is much simpler to use in CFREU not the ^{r}D_{M}, but the normalized by (1+z) its value. That is because it is identical to the angular diameter distance:
If we follow mentioned above simpler approach, we would not need to perform all mentioned here transformations of all other characteristics and of gravitational constant. The total mutual correspondence of the motion of distant astronomical objects in picture plane in GTFR and in CFREU denotes the possibility of mentioned above. That correspondence takes place due to invariance of angular characteristics in the case of radial transformations. Members of line elements of GTFR and CFREU that correspond to that motion exactly match each other when performed normalization of distance ^{r}D_{M}=R (usage of the distance ^{r}D_{A}=R_{0}=r instead of it) is taken into account [Danylchenko, 2004a: 33; 2004a: 62].
It is obvious, that one of the possible reasons of fictive necessity of imaginary nonbaryonic dark matter in the Universe is the significantly smaller density of stellar substance in CFREU and, therefore, in corresponding to it picture plane of distant observer, than in GTFR of observed galaxy.
It is obvious, that according to results of galaxies observations in more wide spectral diapason there would be no deficit of ordinary matter [McGaugh et al., 2016: 201101] (of course when using the real value of the angular diameter distance ^{r}D_{A}=R_{0} in CFREU or the Schwarzschild coordinate r=R_{0} in GTFR). However we can totally get rid of fictive necessity of nonbaryonic dark matter only when using the logarithmic gravitational potential as well as tensor of energymomentum of RGTD. It means that, all motions of astronomical objects, observed in picture plane, can be explained without involving of phantom nonbaryonic dark matter [Danylchenko, 2006; McGaugh et al., 2016: 201101]. For any arbitrary low value of density of the mass of matter on the edge of the galaxy μ_{lim} the corresponding to it values of variable parameters a_{e }and n can be found according to (12) [Danylchenko, 2020: 85].
If imaginary deficit of mass occurs during some astronomical observations and when using logarithmic gravitational potential and tensor of energymomentum of RGTD in calculations, then it can be caused by the ignoring of the possibility of selforganization of astronomical objects into cluster with extraordinary topology. That could be, for example, spiral and toroidallike elliptical galaxies or shelllike globular clusters and spherical elliptical galaxies. These clusters and galaxies have multitude of gravity centres in the form of median line or median surface accordingly. In this case even the presence of central massive astronomical object is not required [McGaugh et al., 2016: 201101].
10. On the possible correlation between the imaginary relativistic and real gravitational time dilation on distant astronomical objects
Earth and Solar system are under the gravitational influence of not only our Milky Way galaxy and neighboring galaxies that are the part of “Local group”, but also of more distant astronomical objects. That is due to the fact that gravitational potentials of all of them are summed up in the points of Earth disposition:
.
Nowadays that total gravitational potential is quite close to zero. However, in far cosmological past it could be much bigger. The distances between our galaxy and clusters of other distant galaxies were much smaller in far cosmological past in GTFR. Coordinate gravitational value of the velocity of light ^{u}v_{cos} in the outer space that surrounds astronomical objects was much smaller than the constant of the velocity of light с.
Isn’t it possible that the value of gravitational time dilation on distant astronomical objects correlates with the value of imaginary relativistic time dilation on them in GTFR? And, therefore, astronomers are probably right that they decrease the distance to objects during their photometric calculations due to mentioned above facts. And that deceasing is performed via the multiplication of measured radiation flow (1+z)^{2} times instead of (1+z) times (as it is required using the CTMHS). Then, the real metrical value of commoving distance ^{r}D_{M} could be considered as equal to its imaginary calculated value ^{i}D_{M}_{.}
However, it would mean that only half of registered redshift could be related to gravitational redshift as well as to Doplerian redshift:
Therefore, the problem of mutual inconsistencies of distances that are determined via photometric calculations and based on the redshift could become more significant. Thus, bigger quantity of dark energy could be required to be present in the Universe. That’s why we should deny the possibility of such correlation.
It is obvious, that we can admit the correlation of gravitational time dilation in that far past only in outer space to essentially smaller time dilation in appropriate distant point of intrinsic space of GTFR:
11. Imaginary Dark energy
Equations of GR gravitational field, in fact, describe the isolated from outer world states of matter and of its STC. Spatial distribution of the mass of matter in those equations specifies how the STC should be curved, while the STC specifies in what spatially inhomogeneous thermodynamic state matter should be.
Consequently, the external gravitational influence on that isolated matter and on its STC is not taken into account in those equations. That external influence can be reflected in the tensor of energymomentum due to the normalization (calibration) of gravitational constant that is the part of the expression for the Einstein’s constant:
.
It can be reflected in the tensor of spacetime curvature only using the normalization of cosmological Λpart. That is because in contrast to coordinate velocities of light that are defined by the tensor of energymomentum:
the constant of the velocity of light c (which is used in the spacetime curvature tensor) cannot be normalized. It is the spatiallytemporal invariant.
It is obvious, that the increment of logarithm of Hubble’s parameter defined by the Λpart may be connected by certain proportionality coefficient m with the increment of gravitational potential of outer space: .
And, probably, this increment can be also connected by proportionality coefficient n with the increment at the distant point j of GTFR of gravitational Hubble’s potential:
,
Then, evolutional change of Hubble’s parameter can be defined by the following empirical dependency:
The dependency of the increment of metrical value of comoving distance ^{r}D_{M} to distant galaxy in CFREU on the increment of redshift z of radiation spectrum will be the following:
Dependencies of luminosity distance D_{L} to supernovas of type Ia on the redshift z of their radiation spectrum have been modeled [Riess, Adam G. et al, 1998: 1009; Semiz and Çamlibel, 2015; Dempsey, 2016; Soloviev, 2016] based on the results of astronomical observations of supernovas of type Ia [Perlmutter, et al, 1999: 565; Riess, Adam G. et al, 1998: 1009]. According to graphs of that dependencies (q.v. Fig. 3) evolutionary change of Hubble’s parameter is almost not observed (k=0).
Fig. 3. Dependencies of distances to astronomical objects on the redshift of radiation of astronomical objects z:
a) luminosity distance D_{L} (solid line) to those objects [Soloviev, 2016] and metrical transverse comoving distance ^{r}D_{M} (dotted line) to astronomical objects in CFREU, as it is justified here;
b) graphical MD (straight) and ΛCDM (curve) models, and the onesigma confidencelevels. The inset shows the right end, magnified [Semiz and Çamlibel, 2015].
That is because in case we use the most suitable values of Hubble constant the values of luminosity distance ^{g}D_{L} shown on graphs (see Table) are very slightly different from their calculated values:
.
Table
H, km/ sMpc 
D, Gpc 
Z 

0,2 
0,4 
0,6 
0,8 
1,0 
1,2 
1,4 

62,164 
^{r}D_{M} 
0,96 
1,93 
2,89 
3,86 
4,82 
5,79 
6,75 
^{r}D_{A} 
0,80 
1,38 
1,81 
2,14 
2,41 
2,63 
2,81 

D_{L} 
1,06 
2,28 
3,66 
5,18 
6,82 
8,58 
10,46 

62,295 
^{r}D_{M} 
0,96 
1,92 
2,89 
3,85 
4,81 
5,77 
6,74 
^{r}D_{A} 
0,80 
1,37 
1,80 
2,14 
2,41 
2,62 
2,81 

D_{L} 
1,05 
2,28 
3,65 
5,17 
6,81 
8,57 
10,44 

a) ^{g}D_{L} 
1,03 
2,25 
3,65 
5,2 
6,9 
8,65 
10,5 

65 
^{r}D_{M} 
0,93 
1,85 
2,77 
3,69 
4,62 
5,54 
6,46 
^{r}D_{A} 
0,77 
1,33 
1,73 
2,05 
2,31 
2,52 
2,69 

D_{L} 
1,01 
2,18 
3,50 
4,95 
6,52 
8,21 
10,01 

b) ^{g}D_{L} 
1,00 
2,16 
3,50 
4,955,0 
6,46,8 
8,28,8 
9,911,0 
Thus, teams of astronomers leaded by Perlmutter and Riess indeed confirmed (with high precision) the linearity of the dependence of redshift of radiation wavelength of distant galaxies on transverse commoving distance to them. And this their achievement is not at all less than attributed to them “discovery” (in reality – false one) of accelerated expansion of the Universe.
It is taken into account that the Hubble constant, like the length standards and the constant of the velocity of light, is a fundamentally unchangeable quantity in the rigid FRs. And this follows from the condition of continuity of spatial continuum in rigid FRs [Danylchenko, 1994: 22]. The most corresponding to astronomical observations value of Hubble constant is the value determined by the following empiric dependencies of it on the well known physical constants and characteristics:
,
where: Λ is the cosmological constant, N_{Dn}=1,5(t_{p}ν_{B}_{n})^{2}= 3πchm_{n}^{2}/G= 0,999885•10^{40} is the neutron large Dirac number, α=e^{2}/cħ is the fine structure constant, ν_{Bn}=m_{n}c^{2}/2πħ is the de Broglie wave frequency of the neutron, t_{p}=(c^{5}ħG)^{1/2} is the Planck time, ħ=h/2π is the DiracPlanck constant, G is the Newton’s gravitational constant, e is the electric charge of the proton and electron, m_{n} is the mass of neutron.
However, the value of Hubble constant H=(π^{4}α/8N_{DH})ν_{BH}=62,16420 [km/sMpc] (Λ=1,35457·10^{52} [m^{2}]), that corresponds to the de Broglie wave frequency of hydrogen atom ν_{BH}=m_{H}c^{2}/2πħ=2,270262·10^{23} [s^{1}] (m_{H}=1,67375·10^{27} [kg], N_{DH}=1,5(t_{p}ν_{BH})^{2}=1,001292·10^{40}), only for small distances guarantees slightly worse correspondence to the data of graphical extrapolation of the results of astronomical observations. It is possible that Hubble constant took “hydrogen” value only after spontaneous transformation of quark or neutron medium of the Universe into hydrogen medium. However, of course, it was impossible before that to metrically characterize its continuous protomatter and, therefore, it is senseless to characterize it by “neutron” Hubble constant. Therefore, the final choice of one of these two close values of Hubble constant can be done based on the more precise results of astronomical observations.
It is obvious that supposed need in the presence of dark energy in The Universe is based not only on the taking into account the imaginary (fictive) dilation of the time on distant astronomical objects (postulated by Etherington’s identity), but also on the wish to have the linear dependence of redshift of radiation spectrum z on luminosity distance D_{L} to those objects. In fact, according to GR [Danylchenko, 2004a: 33; 2004a: 62; 2008: 45; 2008a: 106] the redshift is linearly dependent only on the transverse comoving distance D_{M}:
and on the angular diameter distance:
Moreover, the supposed dark energy could not be a certain physical entity at all. It could be just the effect of ubiquitous negative feedback. The deceleration of evolutionary selfcontraction of matter in CFREU could take place in the distant past due to the presence of this negative feedback. Thus, evolutionary decrease of the velocity of light in CFREU using CTMHS in the distant past would also be decelerated. This deceleration, of the outer space course, could have been the greater the smaller the coordinate velocity of light ^{u}v_{cos} in the outer space in GTFR had been in distant past.
However, it is quite probable that Hubble’s parameter is indeed unchangeable in time, as we had to make sure of it here. It even can be a spatiallytemporal invariant alike the proper value of the velocity of light. The value of Hubble’s constant can be precised after the more accurate processing of results of astronomical observations.
Conclusion
Isn’t it the right time to proceed from the generation of new physical entities to the essential reduce of the number of previously invented mythical thingsinthemselves?
Worship of the unknown is peculiar to human. And science society itself as a whole is subject not only to longterm theoretical misconceptions (science delusions [Sheldrake, 2012; Asprem, 2013; Rutskiy, 2015]). He constantly needs new "idols", which are sometimes endowed with even fantastic properties. Physics did not avoid such fate. Microworld has been flooded by various exotic particles that are the “thingsinthemselves”. Our fantasy is not timid. That is why such imaginary particles as neutrino have even acquired the ability to spread faster than the velocity of light. But after all, the neutrino was actually introduced only in order to have the possibility to ignore the physical microinhomogeneity of the intranuclear space [Danylchenko, 2004a: 33].
Noether has explained the conservation of energy and momentum by the uniformity, respectively, of time and space [Noether, 1918: 235]. That is why the free fall of the bodies in physically inhomogeneous space, in which the gradient of coordinate velocity of light (related to gravitational field) is present, is accompanied by a continuous change of their momentum. What kind of the momentum balance can we talk about in the process of nuclear decay? After all, the restructuring of the intranuclear STC occurs during nuclear decay. Moreover, total energy of central nucleons is less that total energy of peripheral nucleons in physically microinhomogeneous space of nucleus. Only the eigenvalue of energy is the same for those nucleons. That is why the energy excess (not taken away by the decay products) is only redistributed within the remaining nucleons. And, consequently, that energy excess is not contained in an phantom neutrino (it never appears as a constituent of matter [Weisskopf, 1965: 290]). Indeed this energy excess is “consumed” on the decreasing of absolute value of total negative energy of the bond of all protons and neutrons of nucleus. Moreover, neutrino, in fact, is not recorded during the process of nuclear βdecay. The changes of collective spacetime microstate of the whole gravithermodynamically bonded matter are indeed recorded. Only those changes can spread de facto instantly (with the superluminal velocity attributed by neutrino). That is because of the fact that every moment of intrinsic time of the matter corresponds precisely to the certain collective spacetime (gravithermodynamical) microstate of that matter (and, consequently, to its specific Gibbs thermodynamic microstate).
Photon is also just a quant of energy of electromagnetic field [Weisskopf, 1964: 290], and not a particle [Danylchenko, 2004a: 33; 2014: 21]. After all, radiation and absorption of electromagnetic energy only in the form of its quanta (proportional to the frequency of an electromagnetic wave) is a property of microobjects of matter, and not at all of the electromagnetic wave itself. And it is natural that electromagnetic wave cannot contain photons in principle. That is the same as there can be no raindrops in the rainwater tank. The appearance of two mutually correlated photons in the process of annihilation of any microobject of matter and its corresponding microobject of antimatter (that allows not to obey the Heisenberg Uncertainty Principle according to EinsteinPodolskyRosen paradox) also points on this. If we measure the coordinates of one of those photons with arbitrary high accuracy, then we can find the value of its momentum with the same arbitrary high accuracy due to the possibility to measure the momentum of correlated with it second photon with high accuracy.
Weisskopf has repeatedly pointed out that not only the photon, but also the neutrino are not particles [Weisskopf, 1965; 1972]: “We do not count the light quantum among particles, since it is the quantum of the electromagnetic field and obeys Bose statistics. The neutrino is not included since it never appears as constituent of matter."
Moreover, it is quite possible that so called corpuscularwave dualism is just the dualism of our primitive description of physical reality and not the dualism of physical reality. And the particle (corpuscle), obviously, is only a macroscopic concept. And, consequently, our physical representations are still mainly mechanistic, macrocentric and anthropolimited. And we are simply unable to understand that in the microworld there is no, and in principle there can be no elementary particles. Terminal local drains of turns of the single global spiralwave formation in the Universe are indeed taken for “elementary particles”. Certain topological restrictions are imposed on the terminal spiralwave formations [Danylchenko, 2004a: 33; 2014: 21; Winfree & Strogatz, 1983]. Those restrictions are similar to the restrictions imposed by quantum physics on quarks and the baryons and mesons consisting of them. And the possible number of types of terminal spiralwave formations is, thus, also limited, as is the possible number of socalled elementary particles. And this points to the inadmissibility of the presence of physical microobjects that do not have the spiralwave nature – phantom “things in themselves”.
Therefore, both intranuclear and external electromagnetic waves are just the imposed oscillations of the electrical and magnetic field strength. They are imposed on higherfrequency spacetime modulations of the dielectric and magnetic permeabilities of the physical vacuum. They are those very modulations that actually transfer the changes of the collective spacetime microstate of the entire gravithermodynamically bonded matter. They propagate in GTFR at superluminal velocity and with de Broglie frequency. And it all fits in well with synergetics since, according to synergetics, the protomatter in the evolving (“ageing”) physical vacuum should have been selforganized exactly in a form of spiralwave formation [Danylchenko, 2004a: 33; 2008: 45; 2010: 38; 2014: 21; 2020: 5].
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