A speed-of-light barrier in classical electrodynamics

Abstract

Moving patterns created by changes in the distributions of macroscopic charges and currents act as sources of the electromagnetic field that have no inertia and so travel with an arbitrary velocity. It is shown that the retarded potential arising from such sources---though finite when the source moves either slower or faster than light---is divergent, at certain points within the source, when the source moves on a curved path with a speed equal to that of light. Independently of the speed-of-light barrier set up by the requirements of relativistic mechanics, therefore, it appears that there is a barrier stemming from the relativistic restrictions inherent in electrodynamics itself which forbids the accelerated motion of any localized charge-current distribution, whether with or without inertia, at the speed of light.