Abstract
The main ideas of the geometrization of classical electrodynamics based on the model of a supercontinuum (SC) are described in detail and the geodesic equation is derived. A relativistic Lagrangian equation is found for a free point particle in the SC. The affiliation of possible SC metric geometries to the class of Finsler geometries is analyzed. It is shown that they are not Finsler geometries, and Finsler geometries are unsuitable for the geometrization problem. Some physical consequences of the simplest metric version of SC geometry are discussed.
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References
V. I. Noskov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 85–91 (1991).
H. Rund, Differential Geometry of Finsler Spaces [Russian translation], Nauka, Moscow (1981).
V. I. Noskov, One Possibility for Geometrization of Electrodynamics [in Russian], VINITI, Moscow (1990).
Additional information
Institute of the Mechanics of Continuous Media, Ural Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 102–106, May, 1995.
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Noskov, V.I. Some aspects of the geometrization of classical electrodynamics based on the supercontinuum model. Russ Phys J 38, 528–532 (1995). https://doi.org/10.1007/BF00559311
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DOI: https://doi.org/10.1007/BF00559311