Deductive Formalism of Electrodynamics Part 1

The article develops the deductive formalism of electrodynamics based on the four-dimensional pseudo-Euclidean geometry proposed by H. Poincaré and H. Minkowski. Utilizing this formalism, the description of the electromagnetic field is extended, and its equations of motion are refined. The paper addresses and resolves issues concerning the violation of Newton's third law in electrodynamics, the magnetic dynamo phenomenon, and the infinite velocity problem in Gauss's law for the electric field. A new additional wave equation for electromagnetic field propagation is derived, which is tentatively interpreted as the photon equation. Furthermore, a wave equation for scalar longitudinal tension/compression waves of the electromagnetic field is obtained.