arXiv subjects

Yuri A. Rylov

Publications and source records attributed to Yuri A. Rylov.

At least 37 records · Page 2Linked to original sources

arXiv2008

Why does the Standard Model fail to explain the elementary particles structure?

It is shown, that our contemporary knowledge of geometry is insufficient, because we know only axiomatizable geometries. With such a knowledge of geometry one cannot investigate properly physics of microcosm and structure of elementary particles. One can obtain only a phenomenological systematics of elementary particles, whose construction does not need a discrimination mechanism. The discrimination mechanism, responsible for discrete characteristics of elementary particles, can be created only on the basis of a granular (discrete and continuous simultaneously) space-time geometry.

physics.gen-ph↗

arXiv2008

Multivariance as a crucial property of microcosm

The conventional method of a generalized geometry construction, based on deduction of all propositions of the geometry from axioms, appears to be imperfect in the sense, that multivariant geometries cannot be constructed by means of this method. Multivariant geometry is such a geometry, where at the point P there are many vectors PP', PP'',... which are equivalent to the vector QQ' at the point Q, but they are not equivalent between themselves. In the conventional (Euclidean) method the equivalence relation is transitive, whereas in a multivariant geometry the equivalence relation is intransitive, in general. It is a reason, why the multivariant geometries cannot be deduced from a system of axioms. The space-time geometry in microcosm is multivariant. Multivariant geometry is a grainy geometry, i.e. the geometry, which is partly continuous and partly discrete. Multivariance is a mathematical method of the graininess description. The graininess (and multivariance) of the space-time geometry generates a multivariant (quantum) motion of particles in microcosm. Besides, the grainy space-time generates some discrimination mechanism, responsible for discrete parameters (mass, charge, spin) of elementary particles. Dynamics of particles appears to be determined completely by properties of the grainy space-time geometry. The quantum principles appear to be needless.

physics.gen-ph↗

arXiv2008

Geometrical dynamics: spin as a result of rotation with superluminal speed

Dynamics is considered as a corollary of the space-time geometry. Evolution of a particle in the space-time is described as a chain of connected equivalent geometrical objects. Space-time geometry is determined uniquely by the world function $σ$. Proper modification of the Minkowskian world function for large space-time interval leads to wobbling of the chain, consisted of timelike straight segments. Statistical description of the stochastic world chain coincides with the quantum description by means of the Schrödinger equation. Proper modification of the Minkowskian world function for small space-time interval may lead to appearance of a world chain, having a shape of a helix with timelike axis. Links of the chain are spacelike straight segments. Such a world chain describes a spatial evolution of a particle. In other words, the helical world chain describes the particle rotation with superluminal velocity. The helical world chain associated with the classical Dirac particle, whose world line is a helix. Length of world chain link cannot be arbitrary. It is determined by the space-time geometry and, in particular, by the elementary length. There exists some discrimination mechanism, which can discriminate some world chains.

physics.gen-ph↗

arXiv2007

Discrimination of particle masses in multivariant space-time geometry

Multivariance of geometry means that at the point $P_{0}$ there exist many vectors $P_{0}P_{1}$, $¶_{0}P_{2}$,... which are equivalent (equal) to the vector $\Q_{0}Q_{1}$ at the point $Q_{0}$, but they are not equivalent between themselves. The discrimination capacity (zero-variance) of geometry appears, when at the point $P_{0}$ there are no vectors, which are equivalent to the vector $Q_{0}Q_{1}$ at the point $Q_{0}$. It is shown, that in some multivariant space-time geometries some particles of small mass may be discriminated (i.e. either they do not exist, or their evolution is impossible). The possibility of some particle discrimination may appear to be important for explanation of the discrete character of mass spectrum of elementary particles.

physics.gen-ph↗

arXiv2007

Godel's theorem as a corollary of impossibility of complete axiomatization of geometry

Not any geometry can be axiomatized. The paradoxical Godel's theorem starts from the supposition that any geometry can be axiomatized and goes to the result, that not any geometry can be axiomatized. One considers example of two close geometries (Riemannian geometry and $σ$-Riemannian one), which are constructed by different methods and distinguish in some details. The Riemannian geometry reminds such a geometry, which is only a part of the full geometry. Such a possibility is covered by the Godel's theorem.

math.GM↗

arXiv2007

Deformation principle and further geometrization of physics

The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via the Euclidean world function σ_E and declared to be concepts and objects of any physical geometry, provided the Euclidean world function σ_E is replaced by the world function σof the physical geometry in question. The set of physical geometries is more powerful, than the set of Riemannian geometries, and one needs to choose a true space-time geometry. In general, the physical geometry is multivariant (there are many vectors which are equivalent to a given vector, but are not equivalent between themselves). The multivariance admits one to describe quantum effects as geometric effects and to consider existence of elementary particles as a geometrical problem, when the possibility of the physical existence of an elementary geometric object in the form of a physical body is determined by the space-time geometry. Multivariance admits one to describe discrete and continuous geometries, using the same technique. A use of physical geometry admits one to realize the geometrical approach to the quantum theory and to the theory of elementary particles.

physics.gen-ph↗

arXiv2007

Non-Euclidean method of the generalized geometry construction and its application to space-time geometry

Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for construction of space-time geometries. Uniform isotropic space-time geometry other, than that of Minkowski, is considered as an example. The problem of the geometrical objects existence and their temporal evolution may be considered in the constructed space-time geometry. Such a statement of the problem is impossible in the framework of the Riemannian space-time geometry. Existence and dynamics of microparticles is considered to be conditioned by existence of corresponding geometrical objects and their temporal evolution in the space-time. Geometrization of the particle mass and its momentum is produced.

math.GM↗

arXiv2006

Non-Riemannian geometry as a reason of the third modification of the space-time geometry

The third modification of the space-time geometry is considered. (The first modification is the spacial relativity, the second one is the general relativity.) After the third modification of the space-time geometry the motion of free particles become to be primordially stochastic (multivariant). This circumstance forces one to construct a multivariant dynamics. The multivariant dynamics is the classical dynamics in the non-Riemannian space-time geometry. The multivariant dynamics explains quantum effects without a reference to the quantum principles. Elimination of quantum principles admits one to solve the main problem of relativistic quantum theory: unification of the principles of relativity with the nonrelativistic quantum principles.

physics.gen-ph↗

arXiv2006

Crisis in the geometry development and its social consequences

The reasons of the crisis in the contemporary (Riemannian) geometry are discussed. The conventional method of the generalized geometries construction, based on a use of the topology, leads to a overdetermination of the Riemannian geometry. In other words, at the Riemannian geometry construction one uses the needless information (topology), which disagrees with other original axioms. The crisis manifests in the fact, that the mathematical community cannot see and does not want to see the overdetermination of the Riemannian geometry. The most geometers-topologists deny the alternative method of the generalized geometry construction, which does not uses the topology, because it does not contain theorems. Most geometers see the geometry presentation as a set of definitions and theorems. They cannot imagine the geometry presentation without customary theorems. As a result the most clever topologists, which have acknowledged the negligible role of the topology in the geometry construction and inconsistency of the conventional method of the generalized geometry construction, appear in the difficult situation (conflict with the mathematical community).

math.GM↗

arXiv2006

Dynamical methods of investigation in application to the Dirac particle

The Dirac particle S_D is investigated by means of dynamic methods, i.e. without a use of the principles of quantum mechanics. It is shown that the Pauli particle S_P and the nonrelativistic approximation S_{nD} of the Dirac particle S_D are different dynamic systems. S_{nD} contains the high frequency degrees of freedom, which are absent in the dynamic system S_P. It means that the nonrelativistic Dirac particle S_{nD} is composite (i.e. it has internal degrees of freedom), whereas the Pauli particle S_P is a pointlike particle with the spin. In the absence of the electromagnetic field the world line of the classical Pauli particle S_{Pcl} is a timelike straight, whereas that of the classical nonrelativistic Dirac particle S_{nDcl} is a helix. The characteristic frequency $Ω=2mc^{2}/\hbar $ of this helix is the threshold frequency of the pair production. Using dynamic methods, one shows freely that the Copenhagen interpretation, when the wave function is a specific quantum object describing the state of individual particle, is incompatible with the quantum mechanics formalism. Besides, it is shown that the momentum distribution in quantum mechanics is in reality the mean momentum distribution. Effectiveness of different investigation strategies is discussed and compared.

physics.gen-ph↗

arXiv2006

On strategy of relativistic quantum theory construction

Two different strategies of the relativistic quantum theory construction are considered and evaluated. The first strategy is the conventional strategy, based on application of the quantum mechanics technique to relativistic systems. This approach cannot solve the problem of pair production. The apparent success of QFT at solution of this problem is conditioned by the inconsistency of QFT, when the commutation relations are incompatible with the dynamic equations. (The inconsistent theory "can solve" practically any problem, including the problem of pair production). The second strategy is based on application of fundamental principles of classical dynamics and those of statistical description to relativistic dynamic systems. It seems to be more reliable, because this strategy does not use quantum principles, and the main problem of QFT (join of nonrelativistic quantum principles with the principles of relativity) appears to be eliminated.

physics.gen-ph↗

arXiv2005

Contemporary development of Einstein's ideas on space-time and Brownian motion

Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian) motion of free particles. One considers the space-time modification, based on a new conception of geometry. In the framework of this conception any geometry is obtained as a result of the proper Euclidean geometry deformation. In the framework of this conception it is possible such a space-time geometry, where the free particle motion appears to be stochastic, although the geometry in itself remains to be deterministic. The stochasticity intensity depends on the particle mass. It is small for particle of a large mass, and it is essential for the particle of a small mass. The space-time geometry may be chosen in such a way, that the statistical description of random world lines of particles be equivalent to the quantum description (the Schrödinger equation). At such a description the quantum principles are not used. They can be obtained as a corollaries of the statistical description of nonrelativistic stochastic particles. The nonrelativistic quantum principles may not be used for description of relativistic phenomena.

physics.gen-ph↗

arXiv2005

Euclidean geometry as algorithm for construction of generalized geometries

It is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any proposition S of the proper Euclidean geometry E may be described in terms of the Euclidean world function sigma_E in the form S(sigma_E). Replacing the Euclidean world function sigma_E by the world function sigma of the geometry G, one obtains the corresponding proposition S(sigma) of the generalized geometry G. Such a construction of the generalized geometries (known as T-geometries) uses well known algorithms of the proper Euclidean geometry and nothing besides. This method of the geometry construction is very simple and effective. Using T-geometry as the space-time geometry, one can construct the deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles).

math.GM↗

arXiv2005

Tubular geometry construction as a reason for new revision of the space-time conception

The tubular geometry (T-geometry) is a generalization of the proper Euclidean geometry, founded on the property of sigma-immanence. The proper Euclidean geometry can be described completely in terms of the world function $σ=ρ^{2}/2$, where $ρ$ is the distance. This property is called the sigma-immanence. Supposing that any physical geometry is sigma-immanent, one obtains the T-geometry $\mathcal{G}$, replacing the Euclidean world function $σ_{E}$ by means of $σ$ in the sigma-immanent presentation of the Euclidean geometry. One obtains the T-geometry $\mathcal{G}$, described by the world function $σ$. This method of the geometry construction is very simple and effective. T-geometry has a new geometric property: nondegeneracy of geometry. The class of homogeneous isotropic T-geometries is described by a form of a function of one parameter. Using T-geometry as the space-time geometry one can construct the deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles). Geometrization of the particle mass appears to be connected with the restricted divisibility of the straight line segments. The statement, that the problem of the elementary particle mass spectrum is rather a problem of geometry, than that of dynamics, is a corollary of the particle mass geometrization.

physics.gen-ph↗

arXiv2005

Dynamical methods of investigations in application to the Schroedinger particle

Quantum systems are dynamic systems restricted by the principles of quantum mechanics (linearity of dynamic equations, linear transformation of the wave function etc.). One suggests to investigate the quantum systems simply as dynamic systems, ignoring the quantum principles and constraints imposed by them. Such dynamic methods of investigation appear to be more adequate and effective, than the conventional quantum methods of investigation. Using these methods, which ignore the quantum principles, one can overcome the principal problem of quantum field theory: join of nonrelativistic quantum principles with the relativity principles. Investigation of dynamic system, described by the Schroedinger equation, admits one to prove that the Copenhagen interpretation is incompatible with quantum mechanics formalism. Besides, it is shown that sometimes the application of quantum principles leads to incorrect results.

physics.gen-ph↗

arXiv2005

Formalized procedure of transition to classical limit in application to the Dirac equation

Classical model S{Dcl} of the Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. For investigation of S_D and construction of S_{Dcl} one uses a new dynamic method: dynamic disquantization. This relativistic purely dynamic procedure does not use principles of quantum mechanics. The obtained classical analog S_{Dcl} is described by a system of ordinary differential equations, containing the quantum constant as a parameter. Dynamic equations for S_{Dcl} are determined by the Dirac equation uniquely. The dynamic system S_{Dcl} has ten degrees of freedom and cannot be a pointlike particle, because it has an internal structure. Internal degrees of freedom appears to be described nonrelativistically. One discusses interplay between the conventional axiomatic methods and the dynamical methods of the quantum systems investigation. In particular, one discusses the reasons, why the internal degrees of freedom of the Dirac particle and their nonrelativistic character were not discovered during eighty years.

physics.gen-ph↗

arXiv2005

New crisis in geometry?

The first crisis in the geometry arose in the beginning of XIXth century, when the mathematicians rejected the non-Euclidean geometry as a possible geometry of the real world. Now we observe unreasonable rejection of the non-Riemannian geometry by the official representatives of the contemporary geometry. Class of the Riemannian geometries appears to be too narrow for physical applications. The microcosm physics needs expansion of the class of possible geometries appropriate for the role of space-time geometry. In the framework of the non-Riemannian geometry one can construct the space-time geometry, where the motion of free particles is primordially stochastic, and this stochasticity depends on the particle mass. At the same time the geometry in itself is not stochastic in the sense that the space-time intervals are deterministic. Principles of quantum mechanics can be deduced from such a space-time geometry. The crisis situation in geometry appears to be connected with some preconceptions concerning the foundation of the geometry. The preconceptions as well as the crisis generated by them are not purely scientific phenomena. The human factor (social aspect) is rather strong in the crisis phenomena. The preconceptions and the human factor appear to be so strong, that usual logical arguments are not perceived, and the usual formal mathematical language appears to be inappropriate for perception of an analysis of the crisis origin and of a possibility of its overcoming. In the paper the history and motives of the non-Riemannian geometry construction are presented. There is a hope that such a less formal way of presentation helps to understand and to overcome the existing preconceptions.

math.GM↗

arXiv2004

Is the Dirac particle completely relativistic?

The Dirac particle, i.e. the dynamic system S_D, described by the free Dirac equation is investigated. Although the Dirac equation is written usually in the relativistically covariant form, the dynamic system S_D is not completely relativistic, because its description contains such absolute objects as $γ$-matrices $γ^{k}$, forming a matrix vector. By means of the proper change of variables the $γ$-matrices are eliminated, but instead of them the constant timlike vector $f^{k}$ appears. The vector $f^{k}$ describes an absolute splitting of the space-time into space and time, which is characteristic for the nonrelativistic description. To investigate a degree of the violation of the S_D relativistic description, we consider the classical Dirac particle S_{Dcl}, obtained from S_D by means of the relativistic dynamic disquantization. The classical dynamic system S_{Dcl} appears to be composite, because it has ten degrees of freedom. Six translational degrees of freedom are described relativistically (without a reference to $f^{k}$), whereas four internal degrees of freedom are described nonrelativistically, because their description refers to $f^{k}$. Coupling the absolute vector $f^{k}$ with the energy-momentum vector of S_{Dcl}, the classical Dirac particle S_{Dcl} is modified minimally. The vector $f^{k}$ ceases to be absolute, and the modified classical Dirac particle S_{mDcl} becomes to be completely relativistic. The dynamic equations for S_{mDcl} are solved. Solutions for S_{Dcl} and S_{mDcl} are compared.

physics.gen-ph↗