Consistency of a Causal Theory of Radiative Reaction with the Optical Theorem

TL;DR

This paper demonstrates that a causal, runaway-free theory of radiative reaction with finite charge distribution aligns with the optical theorem and Rayleigh scattering, resolving issues of causality and runaway solutions in classical electrodynamics.

Contribution

It introduces a finite charge distribution model that is consistent with the optical theorem and free from runaway solutions, improving upon the Abraham-Lorentz-Dirac equation.

Findings

Finite charge distribution theory is causal and free of runaway solutions.

The theory aligns with the optical theorem.

It matches the standard Rayleigh scattering cross section.

Abstract

The Abraham-Lorentz-Dirac equation for a point electron, while suffering from runaway solutions and an acausal response to external forces, is compatible with the optical theorem. We show that a theory of radiative reaction that allows for a finite charge distribution is not only causal and free of runaway solutions, but is also consistent with the optical theorem and the standard formula for the Rayleigh scattering cross section.