On the validity of the LAD and LL classical radiation-reaction equations

TL;DR

This paper critically examines the classical radiation-reaction equations for charged particles, demonstrating that both the LAD and LL equations produce incorrect or incomplete results, highlighting ongoing challenges in defining the correct equations of motion.

Contribution

The paper provides a detailed analysis of the LAD and LL equations, revealing their limitations and contributing to the understanding of the correct radiation-reaction equations.

Findings

LAD and LL equations lead to incorrect or incomplete results

Analysis based on direct construction of electromagnetic self-potentials

Highlights unresolved issues in classical radiation-reaction theory

Abstract

The search of the correct equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field, the so-called \textit{radiation-reaction equation of motion}, remains elusive to date. In this paper we intend to point out why this is so. The discussion is based on the direct construction of the EM self-potentials produced by a charged spherical particle under the action of an external EM force. In particular we intend to analyze basic features of the LAD (Lorentz-Abraham-Dirac) and the LL (Landau-Lifschitz) equations. Both are shown to lead to incorrect or incomplete results.