Proof the non-existence of causal classical electrodynamics of point charged particles

Abstract

Up until now, a consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The well-known problem is that the standard Lorentz force alone (in the case of point particles) does not lead to a theory in which momentum and energy are conserved. The need of radiation reaction force (or self-force) thus arises. The well known candidate for such force, the Lorentz-Abraham-Dirac reaction force, gives non-causal particle behavior, i.e., the particle starts to move before the arrival of external electromagnetic fields. Alternative, causal proposals provide non-physical behavior of the particle -- the particle moves with non-zero acceleration long after any external forces acted on it. Below, we question the existence of a causal theory. We show that for certain electromagnetic pulse of radiation and point particle being initially at rest, there {\it does not exists} a causal particle trajectory, such that the particle ends up moving with constant velocity (when no external electromagnetic fields act on it for very long time). This shows that the proper, causal electrodynamics of point particles does not exist.