On the Classical Theory of the Electron

A classical theory of the electron, proposed by one of us several years ago and based on finite-difference equations, is discussed by considering the three possible following cases: radiating electron, absorbing electron and nonradiating, nonabsorbing electron. In particular the so-called transmission laws necessary to determine, in conjunction with the dynamical equations, the motion of a charged particle corresponding to given initial values of position and velocity are critically reconsidered. The general characteristics of the one-dimensional motion in the non-relativistic approximation are discussed in detail. It is found that in the case of the radiating electron the particle position tends asimptotically to the point of stable equilibrium. The present theory is, therefore, free from the unphysical phenomenon of runaway solutions. These general results are illustrated by studying the motion of a particle under the action of a restoring elastic force and under the action of purely time-dependent forces.