Lorentz-Dirac equation, solved!!

Preface The Lorentz–Dirac equation, describing the radiation reaction on a charged particle, has remained an unresolved problem in classical and modern physics for more than 85 years (from Abraham 1905 to Dirac 1938). Its standard formulation leads either to unphysical runaway solutions (a particle accelerating on its own) or to violations of causality (pre-acceleration). The present work demonstrates that by introducing the Smooth Uncertainty Regulator (SUR/JRN) – that is, by accepting infinity as an intrinsic part of the calculation rather than suppressing it – one obtains stable, causal, and finite solutions. The regulator removes the runaway pole, preserves the correct Newtonian limit, and is consistent with experimental observations (laser–electron interactions, synchrotron damping, crystal-based radiation reaction tests). This represents a new computational paradigm: infinity is not treated as an error, but as a fundamental element that must be regulated. With this approach, consistent and physically meaningful results emerge where classical methods failed. Thus, the work opens a path towards solving one of the most persistent problems in theoretical physics – and shows that embracing infinity can lead to results both mathematically robust and experimentally verified. Marek Ligocký, August 31, 2025