Geodesic
The Possibility of Relativistic Finslerian Geometry
Contemporary Mathematics. Fundamental Directions, Geometry, Tome 22 (2007), pp. 73-99.

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Foundations of Finslerian geometry are investigated that are of interest for solving the problem of geometrization of classical electrodynamics in metric four-dimensionality. It is shown that parametrization of the interval — the basic aspect of geometry — is carried out non-relativistically. Relativistic way of parametrization is suggested, and the corresponding variant of the geometry is constructed. The equation for geodesic of this variant of geometry, aside from the Riemannian, has a generalized Lorentz term, connection contains an additional Lorentz tensorial summand, the first schouten is different from zero. Some physical consequences of the new geometry are considered: 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 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. 
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V. I. Noskov. The Possibility of Relativistic Finslerian Geometry. Contemporary Mathematics. Fundamental Directions, Geometry, Tome 22 (2007), pp. 73-99. http://geodesic.mathdoc.fr/item/CMFD_2007_22_a2/

[1] Asanov G. S., “Elektromagnitnoe pole kak finslerovo mnogoobrazie”, Izv. vuzov. Fizika, 1 (1975), 86

[2] Blokhintsev D. I., Prostranstvo i vremya v mikromire, Nauka, M., 1970 | Zbl

[3] Vladimirov Yu. S., Relyatsionnaya teoriya prostranstva-vremeni i vzaimodeistvii, MGU, M., 1998

[4] Matematicheskaya entsiklopediya, 5, Sovetskaya Entsiklopediya, M., 1984, 621

[5] Noskov V. I., Ob odnoi vozmozhnosti geometrizatsii elektrodinamiki, Dep. v VINITI No 4217-B90, M., 1990; Объединение электродинамики и гравитации на основе геометрии типа Вейля и Финслера, Дис. канд. физ.-мат. наук, М., 1997

[6] Rund Kh., Differentsialnaya geometriya finslerovykh prostranstv, Nauka, M., 1981 | MR | Zbl

[7] Alpatov V. G. et al., “The current stage of experiments on studying the influence of the temperature and gravity on the ${}^{109}$Ag gamma resonance”, Laser Physics, 10:4 (2000), 952

[8] Lichnerowicz A., Thiry Y., “Problémes de calcul des variations lies á la dynamique et á la théorie unitaire de champ”, C. R. Acad. Sci. Paris, 224 (1947), 529–531 | MR | Zbl

[9] Noskov V. I., “Relativistic version of finslerian geometry and an electromagnetic “redshift””, Grav. Cosmology, 7 (2001), 41 | MR | Zbl

[10] Randers G., “On an asymmetrical metric in the four-space of general relativity”, Phys. Rev., 59 (1941), 195–199 | DOI | MR | Zbl

[11] Stephenson G., Kilmister C. W., “A unified field theory of gravitation and electromagnetism”, Nuovo Cim., 10:3 (1953), 230 | DOI | MR | Zbl

[12] Synge J. L., Relativity: the special theory, North-Holland, Amsterdam, 1958

[13] Tonnelat M.-A., Les principes de la théorié électromagnétique et de la relativité, Paris, 1959 | Zbl