G.T. Tarabrin1

1 Volgograd State Technical University (Volgograd, Russia)

1 tageti@mail.ru

The mathematical description of processes in an electromagnetic field between a mutually moving emitter and receiver requires solving the problems of Maxwell's equations on the propagation of electromagnetic waves by the contrast method. It is necessary to compare the solutions of problems for cases when the emitter passes through a stationary receiver, when the receiver passes through a stationary emitter, as well as when two transceivers move one after the other and emit waves at each other. To investigate the quantities that make up the Doppler effect and compare the results of solving the problem of vehicles moving one after another with the May-Kelson-Morley experiments. Formulas for changing the wave period with mutual approach and distance of the receiver and the emitter are obtained, and formulas for the Doppler effect are derived. It is established that the obtained expression for the Doppler effect corresponds to the principle of relativity of motion, however, its components indicate that the principle of relativity is not fulfilled in the problems of Maxwell's equations. For pairs of transceivers, equal periods of waves received by them were obtained, which is consistent with the results of the Michelson–Morley experiments. Formulas for the distances passing through the waves in the direction of motion of the devices and in the opposite direction are obtained. The difference between these distances indicates that in Maxwell's equations, waves propagate through the ether. Analysis of the components of the Doppler effect and comparison of the results of the solution with the Michelson–Morley experiments lead to the conclusion that the mathematical model of the electromagnetic field created by Maxwell, as a development of Faraday's experimental theory, is based on the assumption that the electro-magnetic field is the product of the metamorphosis of a certain material substance called Ether. Deep space exploration poses challenges, in solving which the results of this work may be of practical importance.

Tarabrin G.T. Doppler effects and Michelson–Morley experiments in Cauchy problems of Maxwell equations // Electromagnetic waves and electronic systems. 2026. V. 31. № 4. P. 113−124. DOI: https://doi.org/10.18127/j15604128-202604-10

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