Classical electrodynamics of a point particle

Even for the simplest physical situations the Lorentz-Dirac equation, solved as an initial value problem, gives unphysical ‘run-away’ solutions. Dirac’s method for avoiding these unphysical solutions generates solutions which exhibit unphysical acausal pre-acceleration. A careful examination of the application of the conservation of momentum in the derivation of the Abraham self-force reveals a fundamental error concerning the force acting on the particle. This error, originally made by Abraham (1903), has been repeated by subsequent investigators. When corrected, a new equation of motion results. A discussion of the general properties of the new equation of motion is given, and solutions for several important special cases are presented. The behaviour of these solutions is causal, physically reasonable, and easily understood.