Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method

TL;DR

This paper critiques classical electrodynamics' traditional potentials, introduces a new approach based on separated potentials, and demonstrates that under certain conditions, accelerated charges do not radiate, challenging conventional views.

Contribution

It proposes a full-value solution to Maxwell equations using separated potentials, establishing a self-consistent electrodynamics framework that addresses previous inconsistencies.

Findings

Lie9nard-Wiechert potentials are inadequate.

Electrodynamics dualism concept is justified.

Accelerated charges may not radiate under certain conditions.

Abstract

The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons of the introduction of the so-called ``electrodynamics dualism concept" (simultaneous coexistence of instantaneous Newton long-range and Faraday-Maxwell short-range interactions) have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a self-consistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.