arXiv subjects

Yuri A. Rylov

Publications and source records attributed to Yuri A. Rylov.

At least 55 records · Page 3Linked to original sources

arXiv2004

Deformation principle as foundation of physical geometry and its application to space-time geometry

Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function σ=d^{2}/2. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function σ_E. Any physical geometry G is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function σ_E by the world function σof G. This method is very simple and effective. It introduces a new geometric property: nondegeneracy of geometry. Using this method, one can construct 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).

physics.gen-ph↗

arXiv2004

What object does the wave function describe?

It is shown that the wave function describes the state of the statistical ensemble E[S] of individual particles, or the statistical average particle . This result follows from the fact that in the classical limit h=0 the Schroedinger equation turns to the dynamic equations for the statistical ensemble of classical particles. The statement that the wave function describes the state of an individual particle is incompatible with the quantum mechanics formalism. It is shown that the statistical interpretation of quantum mechanics is a corollary of the fact, that the QM formalism is the technique of the statistical ensemble description, restricted by constraints of the dynamic equation linearity.

physics.gen-ph↗

arXiv2004

Is the Dirac particle composite?

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 $\hbar$ 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. There are two ways of interpretation of the dynamic system S_{Dcl}: (1) dynamical interpretation and (2) geometrical interpretation. In the dynamical interpretation the classical Dirac particle S_{Dcl} is a two-particle structure (special case of a relativistic rotator). It explains freely such properties of S_D as spin and magnetic moment, which are strange for pointlike structure. In the geometrical interpretation the world tube of S_{Dcl} is a ''two-dimensional broken band'', consisting of similar segments. These segments are parallelograms (or triangles), but not the straight line segments as in the case of a structureless particle. Geometrical interpretation of the classical Dirac particle S_{Dcl} generates a new approach to the elementary particle theory.

physics.gen-ph↗

arXiv2004

Hydrodynamical interpretation of quantum mechanics: the momentum distribution

The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual stochastic system $\mathcal{S}_{st}$. It is a common practice to think that such a construction of quantum mechanics contains hidden variables, and it is incompatible with the von Neumann's theorem on hidden variables. It is shown that the original conditions of the von Neumann's theorem are not satisfied. In particular, the quantum mechanics cannot describe the particle momentum distribution. The distribution $w(\mathbf{p}) =| ψ_{p%}| ^{2}$ is not a particle momentum distribution at the state $ψ$, because it cannot be attributed to a wave function. It is closer to the mean momentum distribution, although the two distributions do not coincide exactly.

physics.gen-ph↗

arXiv2004

Repeated dynamic quantization

In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special concepts, and this procedure cannot be repeated. In the model conception of quantum phenomena (MCQP) the quantum particle is a partial case of a stochastic particle, and the quantum dynamics is a special case of the stochastic particle dynamics. In MCQP the quantization is a dynamical procedure, where a special quantum term is added to the Lagrangian of the statistical ensemble of (classical) particles. This procedure can be repeated many times, because it is not accompanied by introduction of new concepts. It is very convenient from the formal viewpoint, because the set of dynamic quantizations forms a one-parameter group, which allows one to separate the dynamical and statistical (stochastic) properties.

physics.gen-ph↗

arXiv2004

Deformation principle as a foundation of physical geometry

Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $σ=d^{2}/2$. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function $σ_{\mathrm{E}}$. Any physical geometry $\mathcal{G}$ is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function $σ_{\mathrm{E}}$ by the world function $σ$ of $\mathcal{G}$. This method is very simple and effective. It introduces a new geometric property: nondegeneracy of geometry. Using this method, one can construct 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↗

arXiv2004

Classical description of pair production

It is shown that the classical description of pair production effect is possible, i.e. one can describe pair production without a reference to quantum principles. Pair production appears at statistical description of stochastic relativistic particles. There is a special force field which is responsible for pair production. This field is a reasonable consequence of quantum stochasticity. Consideration of quantum systems as stochastic systems and statistical description of them generates hydrodynamic interpretation of quantum phenomena. In the collision problem the hydrodynamic interpretation appears to be alternative to the conventional interpretation, based on quantum principles and on consideration of the wave function as a principal object of dynamics. Hydrodynamic interpretation leads to such a statement of the collision problem, which is alternative to the conventional S-matrix theory.

physics.gen-ph↗

arXiv2004

Statement of problem on vortical inviscid flow of barotropic and incompressible fluids

The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the fluid flow is concentrated in dynamic equations in the form of indefinite functions, whereas the initial and boundary conditions contain information on the fluid particle labeling. It is shown that for determination of the stationary flow of the incompressible fluid the vorticity on any stream line must be given. Giving the velocity on the boundary, one does not determine the vorticity, in general. If there are closed stream lines, the vorticity cannot be given on them via boundary conditions. This circumstance explains existence of different stationary vortical flows under the same boundary conditions.

physics.gen-ph↗

arXiv2004

Model conception of quantum phenomena: logical structure and investigation methods

One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to thermodynamics. Such a possibility is based on a new conception of geometry, which admits one to construct such a deterministic space-time geometry, where motion of free particles is primordially stochastic. The space-time geometry can be chosen in such a way that statistical description of random particle motion coincides with the quantum description. Transition from ACQP to MCQP is a result of correction of some mistakes in the foundation of ACQP. Methods of MCQP in investigation of quantum phenomena appear to be more subtle and effective than, that of ACQP. For instance, investigation of the free Dirac equation in framework of MCQP shows that the Dirac particle is in reality a rotator, i.e. two particles rotating around their common center of inertia. In the framework of MCQP one can discover the force field, responsible for pair production, that is impossible in the framework of ACQP.

physics.gen-ph↗

arXiv2003

Hydrodynamic equations for incompressible inviscid fluid in terms of generalized stream function

Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation contains arbitrary function which is determined by inflow conditions given on the boundary. To determine unique solution, velocity and vorticity (but not only velocity itself) must be given on the boundary. This unexpected circumstance may be interpreted in the sense that the fluid has more degrees of freedom, than it was believed. Besides, the vorticity is less observable quantity as compared with the velocity. It is shown that the Clebsch potentials are used essentially at the description of vortical flow.

physics.gen-ph↗

arXiv2003

Investigation methods in model conception of quantum phenomena

One can construct the model conception of quantum phenomena (MCQP) which relates to the axiomatic conception of quantum phenomena (ACQP), (i.e. to the conventional quantum mechanics) in the same way, as the statistical physics relates to thermodynamics. Such a possibility is based on a new conception of geometry, which admits one to construct such a deterministic space-time geometry, where motion of free particles is primordially stochastic. The space-time geometry can be chosen in such a way that statistical description of random particle motion coincides with the quantum description. Methods of MCQP in investigation of quantum phenomena appear to be more subtle and effective than, that of ACQP. For instance, investigation of the free Dirac equation in framework of MCQP shows that the Dirac particle is in reality a rotator, i.e. two particles rotating around their common center of inertia. In the framework of MCQP one can discover the force field, responsible for pair production, that is impossible in the framework of ACQP.

physics.gen-ph↗

arXiv2003

Deformation principle and problem of parallelism in geometry and physics

The deformation principle admits one to obtain a very broad class of nonuniform geometries as a result of deformation of the proper Euclidean geometry. The Riemannian geometry is also obtained by means of a deformation of the Euclidean geometry. Application of the deformation principle appears to be not consecutive, and the Riemannian geometry appears to be not completely consistent. Two different definitions of two vectors parallelism are investigated and compared. The first definitions is based on the deformation principle. The second definition is the conventional definition of parallelism, which is used in the Riemannian geometry. It is shown, that the second definition is inconsistent. It leads to absence of absolute parallelism in Riemannian geometry and to discrimination of outcome outside the framework of the Riemannian geometry at description of the space-time geometry.

math.GM↗

arXiv2003

Dynamics of stochastic systems and peculiarities of measurements in them

One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with vanishing stochastic component of evolution. Mathematical technique for description of regular evolution component of physical systems (stochastic and deterministic) is constructed. The regular component of the system S evolution is described explicitly by the statistical average system , which is a continuous dynamic system. The action for is reduced to the form of the action for a set of interacting identical deterministic systems S_d. The form of interaction of S_d describes implicitly the character of the stochastic component of S evolution. Interplay between the physical system S and the statistical average system in the measurement process is discussed. There are at least two different kind of measurement: single measurements (S-measurements) connected with measurements in S and mass measurements (M-measurements) connected with measurements in . Conventional identification of S-measurement and M-measurement is a source of many misunderstandings and paradoxes.

physics.gen-ph↗

arXiv2002

Restricted linear properties of scalar product in T-geometry

It is shown that scalar product of two vectors can be introduced in any geometry (metric space) independently of possibility of the linear space introduction. In general, linear properties of scalar product are restricted. Domain of linearity increases in homogeneous geometry.

math.GM↗

arXiv2002

The Euclidean geometry deformations and capacities of their application to microcosm space-time geometry

Usually a Riemannian geometry is considered to be the most general geometry, which could be used as a space-time geometry. In fact, any Riemannian geometry is a result of some deformation of the Euclidean geometry. Class of these Riemannian deformations is restricted by a series of unfounded constraints. Eliminating these constraints, one obtains a more wide class of possible space-time geometries (T-geometries). Any T-geometry is described by the world function completely. T-geometry is a powerful tool for the microcosm investigations due to three its characteristic features: (1) Any geometric object is defined in all T-geometries at once, because its definition does not depend on the form of world function. (2) Language of T-geometry does not use external means of description such as coordinates and curves; it uses only primordially geometrical concepts: subspaces and world function. (3) There is no necessity to construct the complete axiomatics of T-geometry, because it uses deformed Euclidean axiomatics, and one can investigate only interesting geometric relations. Capacities of T-geometries for the microcosm description are discussed in the paper. When the world function is symmetric and T-geometry is nondegenerate, the particle mass is geometrized, and nonrelativistic quantum effects are described as geometric ones, i.e. without a reference to principles of quantum theory. When world function is asymmetric, the future is not geometrically equivalent to the past, and capacities of T-geometry increase multiply. Antisymmetric component of the world function generates some metric fields, whose influence on geometry properties is especially strong in the microcosm.

physics.gen-ph↗

arXiv2002

Associative delusions and problem of their overcoming

Influence of associative delusions (AD) onto development of physics and mathematics is investigated. The associative delusion (AD) means a mistake, appearing from incorrect associations, when a property of one object is attributed to another one. Examples of most ancient delusions are: (1) connection of the gravitation field direction with a preferred direction in space (instead of the direction towards the Earth centre), that had lead to the antipode paradox, (2) statement that the Earth (not the Sun) is the centre of the planetary system, that had lead to the Ptolemaic doctrine. Now these ADs have been overcame. In the paper one considers four modern and not yet got over ADs, whose corollaries are false space-time geometry in the micro world and most of problems and difficulties of the quantum field theory (QFT). One shows that ADs have a series of interesting properties: (1) ADs appear to be long-living delusions, because they are compensated partly by means of introduction of compensating (Ptolemaic) conceptions, (2) ADs influence on scientific investigations, generating a special pragmatic style (P-style) of investigations resembling experimental trial and error method, (3) acting on investigations directly and via P-style, ADs direct the science development into a blind alley. One considers concrete properties of modern ADs and the methods of their overcoming. From viewpoint of application the paper is an analysis of mistakes, made in the quantum theory development. One analyses reasons of these mistakes and suggests methods of their correction.

physics.gen-ph↗

arXiv2001

Anderson's absolute objects and constant timelike vector hidden in Dirac matrices

Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute objects of the Dirac equation. There are two ways of the Dirac matrices transformation: (1) Dirac matrices form a 4-vector and wave function is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor. In the first case the Dirac equation is nonrelativistic, in the second one it is relativistic. Transforming Dirac equation to another scalar-vector variables, one shows that the first way of transformation is valid, and the Dirac equation is not relativistic

quant-ph↗

arXiv2001

Specification of statistical description in quantum mechanics

It is shown that the statistical conception of quantum mechanics is dynamical but not probabilistic, i.e. the statistical description in quantum mechanics is founded on dynamics. A use of the probability theory, when it takes place, is auxiliary. Attention is drawn to the fact that in the quantum mechanics there are two different objects: an individual object to be statistically described and a statistical average object, which is a result of the statistical description. Identification of the two different objects (a use of the same term for both) is an origin of many known quantum mechanics paradoxes.

quant-ph↗