International Journal of Theoretical Physics

, Volume 53, Issue 7, pp 2404–2433 | Cite as

Logical Reloading. What is it and What is a Profit from it?



Logical reloading is a replacement of basic statements of a conception by equivalent statements of the same conception. The logical reloading does not change the conception, but it changes the mathematical formalism and changes results of this conception generalization. In the paper two examples of the logical reloading are considered. (1) Generalization of the deterministic particle dynamics on the case of the stochastic particle dynamics. As a result the unified formalism for description of particles of all kinds appears. This formalism admits one to explain freely quantum dynamics in terms of the classical particle dynamics. In particular, one discovers κ-field responsible for pair production. (2) Generalization of the proper Euclidean geometry which contains such space-time geometries, where free particles move stochastically. As a result such a conception of elementary particle dynamics arises, where one can investigate the elementary particles arrangement, but not only systematize elementary particles, ascribing quantum numbers to them. Besides, one succeeds to expand the general relativity on the non-Riemannian space-time geometries.


Logical reloading Unified formalism Monistic conception of geometry Structural approach Empirical approach 


  1. 1.
    Rylov, Yu.A.: General Relativity Extended to Non-Riemannian Space-Time Geometry. e-print /0910.3582v7Google Scholar
  2. 2.
    Rylov, Yu.A.: Induced antigravitation in the extended general relativity. Gravit. Cosmol. 18(2), 107–112 (2012). doi: 10.1134/S0202289312020089 ADSCrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Rylov, Yu.A.: Spin and wave function as attributes of ideal fluid. J. Math. Phys. 40(1), 256–278 (1999)ADSCrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Rylov, Yu.A.: Uniform Formalism for Description of Dynamic Quantum and Stochastic Systems. e-print/physics/0603237v6Google Scholar
  5. 5.
    Madelung, E.: Z. Phys 40, 322 (1926)ADSCrossRefMATHGoogle Scholar
  6. 6.
    Rylov, Yu.A.: Quantum mechanics as a dynamic construction. Found Phys. 28(2), 245–271 (1998)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Lin, C.C.: Proceedings of International School of Physics “Enrico Fermi”, Course XXI, Liquid Helium, pp. 93–146. Academic, New York (1963)Google Scholar
  8. 8.
    Clebsch, A.: J. Reine Angew. Math. 54, 293 (1857)CrossRefMATHGoogle Scholar
  9. 9.
    Clebsch, A.: J. Reine Angew. Math. 56, 1 (1859)CrossRefMATHGoogle Scholar
  10. 10.
    Rylov, Yu.A.: Classical Description of Pair Production. e-print /physics/0301020Google Scholar
  11. 11.
    Glimm, J., Jaffe, A.: Phys. Rev. 176, 1945 (1968)ADSCrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Glimm, J., Jaffe, A.: Ann. Math. 91, 362 (1970)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Glimm, J., Jaffe, A.: Acta Math. 125, 203 (1970)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Glimm, J., Jaffe, A.: J. Math. Phys. 13, 1568 (1972)Google Scholar
  15. 15.
    Rylov, Yu.A.: On connection between the energy-momentum vector and canonical momentum in relativistic mechanics. Teoretischeskaya i Matematischeskaya Fizika 2, 333–337 (1970). (in Russian). Theor. and Math. Phys. (USA), 5, 333 (1970), (trnslated from Russian)Google Scholar
  16. 16.
    Rylov, Yu.A.: Int. J. Theor. Phys. 6, 181–204 (1972)CrossRefGoogle Scholar
  17. 17.
    Rylov, Yu.A.: Dirac equation in terms of hydrodynamic variables. Advances Appl. Clifford Algebras. 5(1), 1–40 (1995)MATHMathSciNetGoogle Scholar
  18. 18.
    Rylov, Yu.A.: Statistical ensemble technique in application to description of the electron. Advances Appl. Clifford Algebras 7(S), 216–228 (1997)MathSciNetGoogle Scholar
  19. 19.
    Rylov, Yu.A.: Is the Dirac Particle Composite? e-print /physics/0410045Google Scholar
  20. 20.
    Rylov, Yu.A.: Is the Dirac particle completely relativistic? e-print /physics/0412032Google Scholar
  21. 21.
    Vladimirov, Yu.S.: Geometrodynamics, chpt. 8. Moscow, Binom (2005). (in Russian)Google Scholar
  22. 22.
    Rylov, Yu.A.: Geometry without topology as a new conception of geometry. Int. Jour. Mat. & Mat. Sci. 30(12), 733–760 (2002). see also, e-print/math.MG/0103002CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Rylov, Yu.A.: Deformation Principle and further Geometrization of Physics. e-print/0704.3003Google Scholar
  24. 24.
    Rylov, Yu.A.: Non-Euclidean method of the generalized geometry construction and its application to space-time geometry. In: Dillen, F., Van de Woestyne I. (eds.) Pure and Applied Differential Geometry, pp. 238–246. Shaker Verlag, Aachen (2007). See also e-print Math.GM/0702552Google Scholar
  25. 25.
    Blumenthal, L.M.: Theory and Applications of Distance Geometry. Clarendon Press, Oxford (1953)MATHGoogle Scholar
  26. 26.
    Rylov, Yu.A.: Dynamic equations for tachyon gas. Int. J. Theor. Phys. 52, 133(10), 3683–3695 (2013). doi: 10.1007/s10773-013-1674-4 CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Rylov, Yu.A.: Different Conceptions of Euclidean Geometry and their Application to the Space-Time Geometry. e-print /0709.2755v4Google Scholar
  28. 28.
    Rylov, Yu.A.: Discrimination of Particle Masses in Multivariant Space-Time Geometry. e-print/0712.1335Google Scholar
  29. 29.
    Rylov, Yu.A.: Discrete space-time geometry and skeleton conception of particle dynamics. Int. J. Theor. Phys. 51(6), 1847–1865 (2012). See also e-print/1110.3399v1CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Rylov, Yu.A.: Physics geometrization in microcosm: discrete space-time and relativity theory (Review). Hypercomplex Numbers Phys. Geom. 8, 2 (16), 88–117. In Russian. See also e-print /1006.1254v2 (2011)Google Scholar
  31. 31.
    Bohm, D.: Phys. Rev. 85, 166, 180 (1952)Google Scholar
  32. 32.
    Rylov, Yu.A.: Quantum Mechanics as a theory of relativistic Brownian motion. Ann. Phys. (Leipzig) 27, 1–11 (1971)ADSCrossRefGoogle Scholar
  33. 33.
    Rylov, Yu.A.: Quantum mechanics as relativistic statistics. I: the two-particle case. Int. J. Theor. Phys. 8, 65–83Google Scholar
  34. 34.
    Rylov, Yu.A.: Quantum mechanics as relativistic statistics. II: the case of two interacting particles. Int. J. Theor. Phys. 8, 123–139Google Scholar
  35. 35.
    Menger, K.: Untersuchen über allgemeine Metrik. Mathematische Annalen 100, 75–113 (1928)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia

Personalised recommendations