Causality and Self-consistency in Classical Electrodynamics

TL;DR

This paper reviews classical electrodynamics issues, clarifies misconceptions about electron self-fields, and proposes that proper consideration of null terms resolves longstanding problems related to causality and energy conservation.

Contribution

It demonstrates that the electron self-field energy tensor is integrable without renormalization and resolves causality and energy conservation issues by including null terms.

Findings

Electron self-field energy tensor is integrable without renormalization.

Causality violation is resolved with proper term consideration.

Energy conservation holds when null terms are included.

Abstract

We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world-line but that give a non null contribution on its world-line. The electron self-field energy tensor is integrable without the use of any kind of renormalization; there is no causality violation and no conflict with energy conservation in the electron equation of motion, when its meaning is properly considered.