Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics

Abstract

We consider the electromagnetic field of a charge moving with a constant acceleration along an axis. We find that this field obtained from the Li´enard–Wiechert potentials does not satisfy Maxwell equations if one considers exclusively a retarded interaction. We show that if and only if one takes into account both retarded interaction and direct interaction (so-called “instantaneous action at a distance”) the field produced by an accelerated charge satisfies Maxwell equations.