Pavlo Danylchenko
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My Articles

Here you can read and download my books and articles on cosmology, special and general theories of relativity.



Introduction to Gravithermodynamics. (in Russian)
(Collection of articles, Vinnitsa, Nova Knyga, 2008)

The united nature of thermodynamic and gravitational properties of matter is revealed. It is proved that equations of GR gravitational field are the equations of spatialy inhomogeneous thermodynamic state of matter. Relativistic generalization of thermodynamics with strictly extensive molar volume is examined. Falseness of notions about the presence of "black holes", "nonbarionic dark matter" and "dark energy" in the Universe is revealed. The cause of extension of the Universe in people's world is shown. Universe eternity both in future and in the past is substantiated.



Gauge-evolutional interpretation of special and general relativities. (in Russian)
(Collection of articles, second edition - corrected and supplemented, Vinnitsa, Nova Knyga, 2008)

Gauge-evolutional interpretation of special and general relativities. (in English)
(Collection of articles - Vinnitsa: O. Vlasuk, 2004)

It is shown that special and general relativities reflect the gauge effect of motion and gravity on matter. This doesn't allow to observe any changes, originated due to this effect, in proper space and time of matter. The solution of gravitational field equations that correspond to alternative to black holes astronomical bodies is found. Universe eternity both in future and in the past is substantiated.



Gauge-evolutional interpretation of special and general relativities.
(Internet Second Edition - Vinnitsa, 2005; Supplemented version of the book: "Foundations of the gauge-evolutional theory of the creation: space, time, gravity and the Universe expansion (in Russian)", Vinnitsa, 1994.)

The theory, stated here, develops main ideas of special (SR) and general (GR) relativities and allows us to newly comprehend and physically interpret some of their postulates and consequences. It is shown that frames of reference of physical coordinates and time (FR), being used in SR and GR, are the FR of gauge-self-deformated or gauge-self-deforming bodies. This makes them similar to unique fundamental FR - FR of the undeformable (rigid) and undragable physical vacuum (ether of classical physics, undragable by moving bodies) and, consequently, doesn't deny the existence of the latter. In addition, the phenomena of gravity and Universe expansion are caused by the presence of spatial inhomogeneity and evolutional variability of the properties of physical vacuum (PV) correspondingly, and consequently, by the presence of physical inhomogeneity of space and cosmological time correspondingly. In accordance with that, the fact that matter tend to enthalpy minimum causes gravitational, as well as evolutional, self-contraction of micro- and macroobjects of matter in absolute space of PV. It becomes apparent as gravity and Universe expansion correspondingly. Unobservable in FR of evolutionary self-contracting matter relativistic shrinkage of radial dimensions and nonuniform self-contraction (due to spatial inhomogeneity of PV properties) of microobjects of the matter of body cause the curvature of its intrinsic space, which contains all infinite absolute space within the limits of its observer horizon. The absence of such things as so called Big Bang and eternal existence of the Universe in the past, as well as in future, is shown. The principal impossibility of the existence of "black holes" is substantiated. This paper is for the people, who are interested in the physics of space, time and gravity, and cosmology.



The Gauge-evolutional Theory of The Creation (space, time, gravity and the Universe expansion) (in Russian)
(Collection of articles, Vol. 1 - Vinnitsa, 1994)

Phenomenological justification of the Lorentz contraction the length and gauge justification of the special theory of relativity (SR) are set out. We prove the mutual consistency of the SR and the existence of ether. The physical essence of the twins paradox shows. FR Schwarzschild solution is based on assumptions about the evolutionary isoenergetic contraction of matter at the level of elementary particles. This contraction causes expansion Universe in Schwarzschild FR. The phenomenon of gravity is a consequence of physical inhomogeneity of space. It is caused by the tendency of matter to minimize its energy at rest. Investigated various non-rigid frame reference of spatial coordinates and time (FR). Unobservable Lorentz excess of reducing the radial dimensions and metrically nonuniform compression of microscopic matter (as a result of the gravitational polarization of the ether in the FR evolutionarily contracting matter) are the cause of the curvature of its own space of matter. The latter contains all the absolute unlimited space inside observer horizon.




Foundations of Relativistic Gravithermodynamics
(The full version of abridged text of article from Journal "Naukovyi Visnyk VNU", 2009 and from the collection "Proceedings of all Ukrainian seminar from theoretical and mathematical physics TMP'2009" - Lutsk: Volyn'University Press "Vezha", 2009, p. 75; Reports at all Ukrainian seminar from theoretical and mathematical physics, Lutsk, 27.02-1.03.2009 and at the IV Gamov international conference, Odessa, 17-23.08. 2009)

Gravitational field is the field of spatial inhomogeneity of thermodynamic state of dense matter of compact astronomical objects, as well as of however much rarefied gas-dust matter of space vacuum, which is directed by thermodynamic laws the same as ideal gas of noninteracting molecules. This field cannot exist without matter in principle and that is why it is not an independent form of matter. Gravitational coupling, the same as various chemical bonds, is the kind of electromagnetic coupling and corresponds to higher hierarchical level of self-organization of the objects of matter. Statistical laws, which guarantee that equations of gravithermodynamic state of matter satisfy the variational principle and, therefore, Le Chatelier-Broun principle, are the basis of gravitational and of all other thermodynamic properties of matter. All gravitational phenomena, except the phenomenon of curvature of intrinsic space of matter, are thermodynamic in fact. For example, gravitational red shift of radiation spectrum strictly corresponds to the shift, caused by the change of thermodynamic parameters of radiating matter that leads to the change of the velocity of propagation of intra-atomic interaction in this matter. Free fall of bodies in gravitational field - is an original realization of tendency of the whole gravitationally bound inhomogeneous matter to the minimums of the integral values of enthalpy and Gibbs energy. Body that falls is independently accelerated in spatially inhomogeneous cosmosphere or atmosphere. Such bodies transform their continuously released intra-atomic energy into kinetic energy. Nonconservation of the linear momentum of this body is caused by spatial inhomogeneity of thermodynamic state of surrounding matter and therefore by physical inhomogeneity of the space, filled by this matter.




Generalized relativistic transformations (in Russian)
(Paper from the collection "Proceedings of all Ukrainian seminar from theoretical and mathematical physics TMP'2009" - Lutsk: Volyn'University Press "Vezha", 2009, p. 79)

Generalized relativistic transformations of increments of coordinates and rime are examined. These transformations take into account possible influence of thermodynamic state of moving matter on its relativistic deformation and on the dilation of its proper time. It is shown that these transformations cause only inhomogeneous angular distribution of relativistic values of gravibaric velocity of light, which is an alternative to coordinate-like velocity of light in General Relativity. Also these transformations cause the presence of scaling factor in time-like interval. The possibility of experimental verification of the influence of pressure in moving matter on relativistic dilation of its proper time is examined.




United nature of gravitational and thermodynamic properties of matter - the Foundations of Creation (Introduction to Gravithermodynamics). (in Russian)
(Supplemented version of the article from collection of articles "Introduction to relativistic Gravithermodynamics", Vinnitsa, Nova Knyga, 2008 and reports at the XIII Russian gravitational conference, Moscow, 23-28 june 2008 and at third international scientific conference "Philosophy of Cosmism and Modern Aviation", Kyiv, 12-13 april 2007)

Equations of thermal state of matter, which satisfy Tolman condition for thermal equilibrium in spatially inhomogeneous equilibrium states of matter and guarantee the possibility of adiabatic cooling-down of this matter in the early Universe uniformly filled by it, are examined. It is shown that all thermodynamic parameters and characteristics of such matter are determined or interconnected by the relations, which includes gravitational constant, as well as cosmological constant l (or Hubble constant that is determined by it). This denotes the thermodynamic nature of both gravitational field inside of matter and the phenomenon of Universe expansion. All results are obtained here being based on initial statements of General Relativity and, therefore, they do not fully correspond to gravithermodynamics, which conceptually differs from General Relativity, in fact.


(GAUGE-EVOLUTIONAL INTERPRETATION OF SR AND GR)

Global gravitational-optical gradient lens in expanding Universe
(Report at the IV Gamov international conference, Odessa, 17-23.08. 2009)

Gravitational-optical gradient lens, comoving with radiation, is formed in observer's frame of reference of time and spatial coordinates (FR) due to evolutional decrease of average density of matter in the Universe as well as due to evolutional decrease of refraction index of interstellar medium. This diverging lens and Hubble gravitational lens together form virtual image of all infinitely far points of Euclidean background space of FR, comoving with expanding Universe, on its focal surface, which is the imaginary observer horizon. Events that take place in different points but simultaneous in observer's FR are nonsimultaneous in cosmological time of FR, commoving with Universe, due to Universe expansion. Therefore world point of imaginary Big Bang is present in observer's intrinsic space at every moment of his proper time. This point and observer's dislocation point are the opposite poles of four-dimensional hypersurface of observer's space. When gradient lens is not taken into account one may come to a conclusion that Hubble lens forms the horizon of cosmological past (imaginary observer horizon) in vacuum external solutions of equations of gravitational field when cosmological constant is nonzero. This also leads to spatial homogeneity of the negative power of global gravitational lens and, consequently, this leads to a linear dependence of red shift of radiation spectrum of astronomical objects on the distance to those objects. However, when gradient lens is taken into account this dependence becomes nonlinear and corresponds to accelerated expansion of the Universe, while imaginary observer horizon of cosmological past degenerates into point of imaginary Big Bang of the Universe. This is similar to degeneration of the imaginary horizon of cosmological future (Schwarzschild sphere) in internal solution of equations of gravitational field.



Relativistic Values of radial coordinates of distant astronomical objects of expanding Universe. (in Russian)
(Supplemented version of the article from collection of articles "Introduction to relativistic Gravithermodynamics", Vinnitsa, Nova Knyga, 2008 and report at the XIII Russian gravitational conference, Moscow, 23-28 june 2008. Short version of this article is submitted to "General Relativity and Gravitation", Springer, Netherlands in 2007)

Anisotropy of the luminous intensity of distant astronomical objects of expanding Universe in intrinsic space of the observer is shown. The relativistic distance-luminosity relation, by which radial coordinate of astronomical object is being determined taking into account anisotropy of its luminous intensity, is received. As it follows from this relation, values of radial coordinates of distant astronomical objects in intrinsic space of the observer are much smaller than values of their coordinates, calculated by classical distance-luminosity relation. This makes the presence of such hypothetical components of the Universe as dark matter and dark energy unnecessary in principle.



Relativistic generalization of thermodynamics with strictly extensive molar volume. (in Russian)
(Supplemented version of the article from collection of articles "Introduction to relativistic Gravithermodynamics", Vinnitsa, Nova Knyga, 2008)

Main differential equations of relativistic thermodynamics in contravariant and covariant representations are examined. The simplified form of equations of relativistic thermodynamics is proposed. This form guarantees taking into account gravity influence on matter without use of any complex mathematical apparatus of general relativity. The physical essence of Planck and Ott conjugated relativistic temperatures and of mutually complemented contravariant and covariant relativistic values and other thermodynamic parameters and characteristics of matter is revealed. Noninvariance of relativistic values of pressure is substantiated. Mathematical expressions for contravariant and covariant values of linear momentum are received. According to these expressions, these values of linear momentum form four-momentum not with enthalpy but with lagrangian and hamiltonian correspondingly.



About evolutionarity of the process of Universe expansion. (in Russian)
(Report at the XII Russian gravitational conference, Kazan, 20-26 june 2005)

The possibility of evolutionarity of the process of Universe expansion, and thereby - the possibility to guarantee Universe eternity not only in future, but also in the past, is shown. The reality of Universe eternity is confirmed by the results of observations of distant supernovas and is based on the counting of cosmological time in the frame of reference not co-moving with matter, in which by the Weyl hypothesis galaxies of expanding Universe are quasimotionless.



United solution of GR gravitational field equations and thermodynamics equations for ideal liquid in the state of its thermal equilibrium. (in Russian)
(Supplemented version of the article from collection of articles "Introduction to relativistic Gravithermodynamics", Vinnitsa, Nova Knyga, 2008 and report at the XII Russian gravitational conference, Kazan, 20-26 june 2005)

The solution of equations of GR and thermodynamics for ideal liquid, which has topology of hollow body, is examined. Spatial distributions of all main thermodynamical and gravithermodynamical parameters and characteristics of ideal liquid are obtained. The value of photometrical radius of median singular surface, which separate antimatter from matter, is derived.



Phenomenological justification of linear element of Schwarzschild solution of GR gravitational field equations
(Supplemented version of the article from collection of articles "Gauge-evolutional interpretation of special and general relativities", Vinnitsa, O.Vlasuyuk 2004. More new version of this article (published in Vinnitsa in 2008)is available only in Russian)

The possibility of getting a linear element (interval) of Schwarzschild frame of reference of spatial coordinates and time (FR) is shown, founded on the existence of fundamental (Newton absolute) space, which is formally independent on matter and is only a container for it [1]. In addition to it, the presence of evolutionary changeability and spatial inhomogeneity of properties of the physical vacuum (PV), filling all this absolutely rigid (nonexpanding) Euclidean (noncurved) infinite space, is assumed.



Physical essence of twins paradox
(Supplemented version of the article from collection of articles "Gauge-evolutional interpretation of special and general relativities", Vinnitsa, O.Vlasuyuk 2004. More new version of this article (published in Vinnitsa in 2008)is available only in Russian)
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The initial cause of unambiguously younger age of the second twin than age of the first twin at the moment of their meeting is pointed. This initial cause is not the accelerated motion of the second twin, but the fact of changing of its direction or just the velocity of its motion in space itself and, consequently, the fact of its transition from one inertial reference system of spatial coordinates and time (IFR) to another. This is concerned to changing in new IFR of spatial as well as of time coordinates of events, which have realized before, including events, information about which have not come to the twin by the moment of its transition to new IFR. It is shown that imaginary twin paradox (clock paralogism) takes place in general relativity (GR) only because of the impossibility of mutual distinguishing of standard time (path-like proper time of moving object) and coordinate-like internal time of the IFR (or any other FR) and because of neglect of the necessity of re-calculation of events time coordinates as a result.



The gauge foundations of special relativity
(Supplemented version of the article from collection of articles "Gauge-evolutional interpretation of special and general relativities", Vinnitsa, O.Vlasuyuk 2004. More new version of this article (published in Vinnitsa in 2008)is available only in Russian)
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It is shown here that Lorentz transformations are caused by gauge effect of motion on matter (principle nonobservability of effect of motion on matter). This gauge effect of motion is caused by interdependence and mutual determination of propagation velocity of interaction between matter elementary particles and of rate of course of matter proper (standard) time. The Lorentz transformations are derived without any linearity assumptions and being based only on the presence of relativistic shrinkage of the length of moving body and on clock desynchronization at its slowest transfer along this body.



The nature of relativistic length shrinkage

(Article from Spacetime&Substance Journal No.3(28)-2005 (http://www.spacetime.narod.ru/28.html).
More new version of this article (published in Vinnitsa in 2008) is available only in Russian.
Extended version of the article The nature of relativistic length shrinkage from the collection of the articles "Gauge-evolutional interpretation of special and general relativities" - Vinnytsya, O.Vlasuk,2004)

It is shown here, that relativistic shrinkage of the length of moving body appears itself (without the influence of external forces). This shrinkage is caused by isobaric self-contraction of body matter and by propagation of the strength of inertia forces field together with the front of body intrinsic time. A mechanism of kinetic energy filling (accumulation) of a body is considered and propagation of the phase waves of perturbation of gravitational field at supraluminal velocity is substantiated here.



About possibilities of physical unrealizability of cosmological and gravitational singularities in General relativity
(Supplemented version of the article from collection of articles "Gauge-evolutional interpretation of special and general relativities", Vinnitsa, O.Vlasuyuk 2004. More new version of this article (published in Vinnitsa in 2008)is available only in Russian)

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not co-moving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in Weyl FR, when it has hollow topological form in the space of Weyl FR and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this internal part of the space. Inevitability of self-organization in physical vacuum of spiral-wave structural elements, which correspond to elementary particles, and universal electromagnetic nature of all nonfictive particles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter.



The problem of the existence of dark matter and dark energy in the Universe according to the world view of Einstein, Weyl and other physicists. (in Russian)

The possibility that the evolutional process of Universe expansion is inertial (isoenergetic) also at nonzero value of cosmological constant of equations of GR gravitational field is examined according to Einstein physical notions about free (inertial) motion of the body along geodesic world lines of space-time continuum. This makes the presence of "dark energy' in the Universe unnecessary. It is shown that classical photometric method doesn't take into account the curvature of finite intrinsic space of observer (which corresponds to antigravitational field) as well as the relativistic deformation of angular apertures of distant galaxies. Because of this, instead of photometric distances to these galaxies in observer space, continuously renormalized distances (much bigger than photometric distances) to the galaxies in infinite euclidean fundamental space are being determined. This fundamental space together with cosmological time form fundamental frame of references of coordinates and time. Exactly in this, not comoving with matter, frame of reference galaxies of expanding Universe take part only in peculiar motions by the Weyl hypothesis. And this is the cause of the fictive need of the existence of "dark matter" in the Universe.



Relativistic thermodynamics with lorentz-invariant extensive volume

Main differential equations of relativistic thermodynamics in contravariant and covariant representations are examined. The physical essence of Planck and Ott relativistic temperatures and of mutually complemented contravariant and covariant relativistic values and other thermodynamic parameters and characteristics of matter is revealed. Noninvariance of relativistic values of pressure is substantiated.



About significance of taking into account topological configuration of space-time in GPS-measurements. (in Russian)

Topological configurations of intrinsic space-time of both rotating bodies and very massive astronomical bodies are analyzed. Mathematical expressions for components of linear element of rotating body, using which for analysis of high-precision GPS-measurements we can achieve the lower level of mistakes in measurements of spatial coordinates, are examined.



Verification of physical unrealizability of gravitational singularities. (in Russian)

The united solution of equations of GR and thermodynamics for ideal liquid, which has topology of hollow body, is examined. Spatial distributions of all main thermodynamical and gravithermodynamical parameters and characteristics of ideal liquid are obtained. It is shown that these parameters and characteristics take on principally unreachable for them values on the singular surface. This denotes physical unrealizability of gravitational singularities. The value of photometrical radius of median singular surface, which separate antimatter from matter, is derived.



Phylosophical aspects of mutual complementarity of gravithermodynamic parameters. (in Russian)

The interconnection between gravithermodynamic and thermodynamic parameters and characteristic functions, which complete each other, is examined for ideal liquid as an example. The possibility to remove some ambiguities and contradictions at the turn of relativity and thermodynamics is examined.



Extraordinary topology of very massive neutron stars and quasars. (in Russian)
(Report at the XXII conference "The modern problems of extragalactic astronomy", Puschchino, 16-18 july 2005)
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It is shown that in the case of very big value of mass of astronomical body minimum of integral value of body enthalpy is being reached. This minimum corresponds to reflection symmetric configuration of intrinsic space of the body, which was found by Fuller and Wheeler. In euclidean fundamental space of not comoving with matter frame of reference, in which by the Weyl hypothesis galaxies of expanding Universe are quasimotionless, such body, according to the solution of GR equations, is hollow. The presence of phenomenon of contraction of "internal Universe" in internal empty half-space of hollow body corresponds to stability of antimatter in this space. Therefore median singular spherical surface, which is the locus of "centers" of gravity of such body, prevent annihilation of matter and antimatter in hollow neutron stars (which are considered as black holes by mistake) and guarantee possibility of their only non-catastrophical annihilation in quasars. And so, very high luminosity of quasars and initially hpllow supernovas is caused by annihilation of matter and antimetter.



Is Universe eternal? (in Russian)
(Report on the II international scientific conference "Philosophy of Cosmism and Modern Aviation", Kyiv, 7-8 april 2005)

The possibility to avoid the singularity of Big Bang of the Universe in general theory of relativity, and thereby - the possibility to guarantee Universe eternity not only in future, but also in the past, is shown. The reality of Universe eternity is confirmed by the results of observations of distant supernovas and is based on the counting of cosmological time in the frame of reference not co-moving with matter, in which by the Weyl hypothesis galaxies of expanding Universe are quasimotionless.



Physical essence of singularities in Schwarzschild solution of GR gravitational field equations. (in Russian)
(Article from the collection "Sententiae" special edition #1 philosophy and cosmology, Universum-Vinnytsya, 2005, p. 95-104)

It is shown that observer horizon (which is determined by lambda-term in gravitational field equations) of intrinsic space is the pseudohorizon of infinitely far cosmological past, and Schwarzschild sphere is the pseudohorizon of infinitely far cosmological future of the Universe. This is connected with nonsimultaneity (in intrinsic frame of reference of matter that is evolutionally self-contracting in Newton-Weyl absolute space) of events that have the same cosmological age, but realized on different distances from observer. Evolutionary process of Universe expansion is caused by unobservable in principle in matter FR (in FR of people's world) process of gauge self-contraction of matter in absolute space.



Spiral wave nature of elementary particles (in Russian)
(Report at the inyernational scientific conference "D. Ivanenko - outstanding physicist-theorist, pedagogue", Poltava, 23-24 september 2004; Article from the collection of reports - Materials of international scientific conference "D. Ivanenko - outstanding physicist-theorist, pedagogue" - Poltava, 2004. - P. 44-55.)

Unified electromagnetic nature of all fundamental interactions and non-fictious elementary particles of matter is shown.
The possibility of establishing of mutual correspondence between non-fictious elementary particles of matter and spiral autowave self-sustaining structural elements in physical vacuum, taking into account mirror symmetry of intrinsic spaces of some elementary particles, is examined.



Gnoseological approach to the forming of frames of references in General relativity (in Russian)
(Report at the 1-st international interdisciplinary scientific seminar "Problems of verification in electoral process", Kerch, Ukraine, 22 october 2004; Article from the collection of materials of scientific seminar "Problems of verification in electoral process", Kerch, 2004, p. 56-61)

The possibility to avoid realizability of singularity of Big Bang of the Universe in general theory of relativity is examined. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not co-moving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless.
The absence of any limitations of the value of mass of astronomical body, when it has hollow topological form in Newton-Weyl absolute space and mirror symmetry of its intrinsic space, is shown.
Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this part of the space.
Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter.



Space-time: physical essence and mistakes (in Russian)
(Report at the international seminar "The Universe: structure, Milestones of becoming and development", Pereyaslav-Khmelnitsky, 5-7 october 2004; Article from the collection "Sententiae" special edition #3 philosophy and cosmology, Universum-Vinnytsya, 2004, p. 47-55)

Physical essence of the concept of space-time is shown. Various fallacies, connected with imperfect understanding of this essence (twins paradox, Big Bang of the Universe, black holes, time machine, space-time of living and sentient substance) are examined.



Alternatives to Big Bang and black holes
(Article is prepeared for publication in popular scientific journal)

The conception of Universe expansion, which is based on the counting of cosmological time in frame of reference of spatial coordinates and time (FR) that is not co-moving with matter - fundamental FR of physical vacuum, is proposed.
It is shown that under the influence of very strong gravitational field the collapse of matter into hollow astronomical body, which is alternative to the "black hole" and contains antimatter in internal half-space, takes place. Ultrahigh luminosity of quasars and some types of supernovas is caused by the annihilation of matter and antimatter.



Spiralwave model of the Universe (in Russian)
(Article from the collection "Materials of all-Ukrainian seminar on theroretical and mathematical physics: in honour of 85th annivesary of Anatoli Swidzynski", Lutsk Feb 27 - Mar 1, 2014; Report on the all-Ukrrainian seminar on theoretical and mathematical physics)

According to corpuscular-wave dualism all elementary particles of matter have both corpuscular and wave properties. The combination of those properties in one physical object is paradoxical according to classical physics. Corpuscle are local. On the contrary waves are not local. However this contradiction is easily solved if we consider that all non-fictive elementary particles are local outlets or sources of the turns of spiral waves.




e-mail:pavlo@vingeo.com

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