The possibility of relativistic Finslerian geometry
Foundations of Finslerian geometry that are of interest for solving the problem of geometrization of classical electrodynamics in metric four-dimensionality are investigated. It is shown that parametrization of the interval—the basic aspect of geometry—is carried out non-relativistically. A relativistic way of parametrization is suggested, and the corresponding variant of the geometry is constructed. The equation for the geodesic of this variant of geometry, aside from the Riemannian, has a generalized Lorentz term, the connection contains an additional Lorentz tensorial summand, and the first schouten is different from zero. Some physical consequences of the new geometry are considered: the non-measurability of the generalized electromagnetic potential in the classical case and its measurability on quantum scales (the Aharonov-Bohm effect); it is shown that in the quantum limit the hypothesis of discreteness of space-time is plausible. The linear effect with respect to the field of the “redshift” is also considered and contemporary experimental possibilities of its registration are estimated; it is shown that the experimental results could uniquely determine the choice between the standard Riemannian and relativistic Finslerian models of space-time.
KeywordsGeodesic Equation Natural Parametrization Torsion Tensor Parallel Translation Finslerian Geometry
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- 1.V. G. Alpatov et al., “The current stage of experiments on studying the influence of the temperature and gravity on the 109Ag gamma resonance,” Laser Physics, 10, No. 4, 952 (2000).Google Scholar
- 2.G. A. Asanov, “Electromagnetic field as a Finsler manifold,” Izv. Vyssh. Ucheb. Zaved., Fiz., No. 1, 86 (1975).Google Scholar
- 3.D. I. Blokhintsev, Space and Time in the Microworld [in Russian], Nauka, Moscow (1970).Google Scholar
- 5.V. I. Noskov, On a certain possibility of geometrization of electrodynamics, Deposited at the All-Union Institute for Scientific and Technical Information, No. 4217-V90, Moscow (1990).Google Scholar
- 8.H. Rund, Differential Geometry of Finsler Spaces, Springer-Verlag (1959).Google Scholar
- 10.J. L. Synge, Relativity: The Special Theory, North-Holland, Amsterdam (1958).Google Scholar
- 11.M. A. Tonnelat, Les principes de la théori’e électromagnétique et de la relativité, Paris (1959).Google Scholar