Abstract
It is shown that motion of quantum particles and classical particles can be described in the framework of the same formalism. Stochasticity of particle motion depends on the form of the space-time geometry, which is to be described as a physical geometry, i.e. a geometry obtained as a result of deformation of the proper Euclidean geometry. The new method of the particle motion description does not use quantum principles. It admits one to use the structural approach to theory of elementary particles. The structural approach admits one to consider structure and arrangement of elementary particles, that cannot been obtained at conventional approach, using quantum principles.
Similar content being viewed by others
References
Grigor’yan, A.T.: Mechanics from antiquity till our days. M/ Nauka. (in Russian) (1971)
Madelung, E.: Quanten theorie in hydrodynamischer. Form Z. Phys. 40, 322–326 (1926)
Rylov, Yu.A.: Spin and wave function as attributes of ideal fluid. J. Math. Phys. 40, 256–278 (1999)
Rylov, Yu.A.: Gas dynamics as a tool for description of nondeterministic particles. Int. J. Theor. Phys. 55(5), 2621–2632 (2016). doi:10.1007/s10773-015-2897-3
Rylov, Yu.A: Logical reloading. What is it and what is a profit from it? Int. J. Theor. Phys. 53(7), 2404–2433 (2014). doi:10.1007/s10773.014.2039.3
Rylov, Yu.A.: Dynamic equations for motion of free particle in a discrete space-time geometry. Int. J. Theor. Phys. 55(11), 4852–4865 (2016). doi:10.1007/s10773-016-3109-5
Rylov, Yu.A.: Nature of some conceptual problems in geometry and in the particle dynamics. GJSFR-A Volume 16 Issue 6 Version 1.0 (2017)
Rylov, Yu.A.: Structural approach to the elementary particle theory. in space-time ggeometry and quantum events ed. Ignazio Licata. pp. 227–315, Nova Science Publishers, Inc. ISBN 978-1-63117-455-1 (2014)
Rylov, Yu.A.: The way to skeleton conception of elementary particles. Global J. Science Frontier Research 14(7), 43–100 (2014). ver. 1
Rylov, Yu.A.: Metrical conception of the space-time geometry. Int. J. Theor. Phys. 54(1), 334–339 (2014). doi:10.1007/s10773-014-2228-0
Rylov, Yu.A.: Different conceptions of euclidean geometry and their application to the space-time geometry. e-print/arXiv:0709.2755v4
Rylov, Yu.A.: Tubular geometry construction as a reason for new revision of the space-time conception. (printed in What is geometry? pp. 201–235, Polimetrica Publisher, Italy). http://www.polimetrica.com/polimetrica/406/
Rylov, Yu.A: Coordinateless description and deformation principle as a foundations of physical geometry. e-print/arXiv:math.GM/0312160
Rylov, Yu.A: Geometry without topology as a new conception of geometry, vol. 30. e-print/ arXiv:math.MG/0103002 (2002)
Rylov, Yu.A.: Geometry without topology. e-print/arXiv:math.MG/0002161
Rylov, Yu.A: Discriminating properties of compactification in discrete uniform isotropic space-time. e-print/arXiv:0809.2516v2
Rylov, Yu.A.: Relativity principle in coordinate free presentation. Report at PIRT2015 physical interpretation of relativity theory: Proceedings of international meeting. Bauman Moscow State Technical University, Moscow, 29 june-02 july, 2015. – Moscow : BMSTU, pp. 447-452 (2015)
Rylov, Yu.A.: Dynamic disquantization of Dirac equation. e-print/arXiv:quant-ph/0104060
Rylov, Yu.A: Dynamical methods of investigations in application to the Schroedinger particle. Vestnik RUDN Ser. Mathematics, Informatics, Physics (3-4), 122–129. See also e-print/arXiv:physics/0510243 (2007)
Rylov, Yu.A: Dynamical methods of investigation in application to the Dirac particle. e-print/ arXiv:physics/0507084
Rylov, Yu.A.: Formalized procedure of transition to classical limit in application to the Dirac equation. (report at 6th conference symmetry in nonlinear mathematical physics, Kiev, June 2005). e-print/arXiv:physics/0507183
Rylov, Yu.A: Physics geometrization in microcosm: discrete space-time and relativity theory. (Review) Hypercomplex numbers in physics and geometry 8(2, 16,) 88–117 (2011). (In Russian). English version in e-print:e-print/arXiv:1006.1254v2
Rylov, Yu.A: Dirac equation in terms of hydrodynamic variables. AACA 5, 1–40 (1995). See also e-print/arXiv:1101.5868
Sauter, F.: Zs. Phys. 63, 803 (1930). 64, 295, (1930)
Sommerfeld, A.: Atombau and Spektrallinien. bd.2 Braunschweig (1951)
Rylov, Yu.A: Is the Dirac particle completely relativistic? e-print/arXiv:physics/0412032
Rylov, Yu.A.: Geometrical dynamics: spin as a result of rotation with superluminal speed. e-print/ arXiv:0801.1913. (1913)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rylov, Y.A. Unification of Classical Mechanics and Quantum Mechanics in Unique Conception of Particle Dynamics. Int J Theor Phys 56, 2467–2478 (2017). https://doi.org/10.1007/s10773-017-3398-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-017-3398-3