A Relativistic Cut-Off for Classical Electrodynamics

Ordinarily it is assumed that interaction between charges occurs along light cones, that is, only where the four-dimensional interval $s^2=t^2-r^2$ is exactly zero. We discuss the modifications produced if, as in the theory of F. Bopp, substantial interaction is assumed to occur over a narrow range of $s^2$ around zero. This has no practical effect on the interaction of charges which are distant from one another by several electron radii. The action of a charge on itself is finite and behaves as electromagnetic mass for accelerations which are not excessive. There also results a classical representation of the phenomena of pair production in sufficiently strong fields.