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About possibilities of physical unrealizability of cosmological and gravitational singularities in General relativity // Kiev: Library of Ukraine (ELIBRARY.COM.UA). Updated: 22.03.2019 . URL: https://elibrary.com.ua/m/articles/download/11203/3411 (date of access: 19.07.2024 )

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

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

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

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

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

** **

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

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

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

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

*V*=*dR*/*dT*=–*H _{e}R_{k}*exp[–

* *

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

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

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

* *

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

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

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

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

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

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

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

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

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

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

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

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

** **

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

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

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

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

** **

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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