Thinking anew causality problems for the radiation reaction force

TL;DR

This paper revisits the radiation reaction force problem using a novel Lagrangian involving acceleration, demonstrating that pre-acceleration does not imply causality violation, contrary to common beliefs.

Contribution

It introduces a new Lagrangian formalism with acceleration dependence to analyze the Abraham-Lorentz force and clarifies the causality issue.

Findings

Conserved momentum includes acceleration terms.

Pre-acceleration is not causality-violating.

Provides new insights into radiation reaction force.

Abstract

In this work, we analyze a Lagrangian formalism recently proposed to approach the issue of the Abraham-Lorentz force. Instead of involving only position and velocity, as usual in Classical Mechanics, this Lagrangian involves the acceleration of the charge. We find the conserved momentum of the charge in the absence of any field and show that it contains an acceleration term. This enables us to re-visit the well-known pre-acceleration problem and show that, contrary to what has been widely believed, it is not related to any violation of causality.