Space-time transformation properties of inter-charge forces and dipole radiation: Breakdown of the classical field concept in relativistic electrodynamics

TL;DR

This paper critically examines the transformation properties of inter-charge forces and radiation fields in relativistic electrodynamics, revealing errors in traditional treatments and questioning the classical field concept in the context of radiation and relativistic effects.

Contribution

It identifies errors in the classical relativistic treatment of electromagnetic fields and clarifies the non-classical nature of fields produced by moving charges, challenging standard assumptions.

Findings

Errors in traditional relativistic electromagnetism treatment

Fields from moving charges are not classical fields

Incorrect derivation of retarded potentials

Abstract

A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical electrodynamical theory. Important differences are found and serious errors are found in the traditional treatment of special-relativistic effects in classical electromagnetism. Fields associated with radiation processes are also considered and classical and quantum mechanical predictions are compared. An important, though trivial, mathematical error in the derivation of the retarded Li\'{e}nard-Wiechert retarded potentials is pointed out. It is also shown why electric and magnetic fields produced by moving source charges or current distributions are not `classical fields', and that they do not, in general, constitute an antisymmetic second-rank tensor, as is usually assumed.