On the Classical Equations of Motion of Point Charges

Abstract

Recent attempts to obtain the force of radiative reaction in the classical equations of motion of point charges have proceeded from two different viewpoints. Each of these has to introduce one basic assumption in addition to Maxwell's equations, namely the conservation law for the electromagnetic energy-momentum tensor in field theory and the relation between the Lorentz force and the momentum of the particle in action-at-a-distance theory. In previous field-theoretical derivations the Lorentz-Dirac equations including radiation damping are obtained only if one takes the field produced by the particle to be the retarded field; but equations of motion without the damping term are obtained if one uses half the sum of retarded and advanced fields. On the other hand, the theory of action at a distance as developed by Wheeler and Feynman was able to obtain the radiation damping using fields symmetric in time. It is noted that the need for the exclusive use of retarded fields arose only in the field-theoretical derivations for the one-particle problem. The considerations of Wheeler and Feynman on the total field due to all particles of the universe are, however, applicable to field theory in the symmetric form as well as to action-at-a-distance theory. The acceptance of their condition of "complete absorption" again leads to the radiation damping term in the equations of motion of the many-body problem. Some implications of this result are discussed.