Consistent classical equation of motion for radiation reaction

Establish a consistent classical equation of motion that governs the radiation-reaction recoil force on an accelerated charge in a manner compatible with energy–momentum conservation.

Background

The paper reviews the historical difficulties in formulating a consistent classical radiation-reaction law, noting that the Abraham–Lorentz–Dirac equation exhibits runaways and pre-acceleration, while the Landau–Lifshitz equation is a reduction-of-order approximation. This longstanding issue is highlighted as an open question in classical electrodynamics.

The authors propose Tick–Tock (TT) dynamics as a discrete, causal alternative that reproduces Landau–Lifshitz in the continuum limit while avoiding pathologies and providing transparent energy bookkeeping. The explicit identification of the broader problem as an open question motivates their development of TT as a proposed resolution.