Quantum Solutions in Classical Electrodynamics and Its Connection with Geometrodynamics

Abstract

A quantum solution of the classical electrodynamics equations has been found. It is shown that all information on the multiparticle process of creation of scalar pairs of particles by a nonstationary self-acting electric field is contained in solutions of the d’Alembert single-particle equation. The existence of a quantum solution of the d’Alembert equation is determined by the Ehrenfest theorem. In this case, the corresponding solution is independent of the Planck constant. The process of conversion of thermal and acceleration energies into radiation has been investigated. It is demonstrated that a self-acting electric field exhibits elastic behavior. The connection of classical electrodynamics with geometrodynamics is established. The geometrodynamic justification of the appearance of the Hubble magnitude in classical electrodynamics is provided. The probabilities of creation of one-dimensional space and charge during tunneling in time of the effective Planck particle are determined. It has been shown that the fine structure constant α can be interpreted as the probability $$ \alpha ={e}^{-\frac{\pi^2\gamma }{2}} $$ of charge creation without charge and real mass. This implies that the so-called fine structure of mathematical constants can contain information on the interactions of matter, which can be used to solve the problem of information loss in black holes.