Consistent Classical Radiation-Reaction Equation of Motion

Establish a consistent classical equation of motion for the radiation reaction of an accelerating point charge in classical electrodynamics that resolves the self-interaction problem and yields a physically acceptable dynamics.

Background

The paper reviews the historical difficulty of formulating radiation reaction in classical electrodynamics, noting that the Abraham–Lorentz–Dirac equation entails pathologies such as runaways and pre-acceleration, while the Landau–Lifshitz equation is a reduction-of-order approximation rather than a first-principles derivation.

Within this context, the authors introduce Tick–Tock dynamics as a finite-step, causal formulation designed to reproduce Landau–Lifshitz in the continuum limit and to provide transparent energy accounting. The initial framing emphasizes that, despite extensive paper, a definitive classical equation of motion incorporating radiation reaction has been regarded as an open question.