The Fundamental Equations of Electron Motion (Dynamics of High Speed Particles)

In work relating to the motion of electrons and other particles it is fairly common to assume that the particles obey the laws of Newtonian dynamics. T h a t is, briefly, it is assumed that the rectangular coordinates (x, y, z) of the particle under consideration satisfy the differential equations mx = X, my = Y, m'z = Z , where m is the mass of the particle (assumed constant), X, Y, and Z are the components of the applied force, and the dots indicate differentiation with respect to the time t. However, it is well recognized now that the above equations are not strictly correct, and that they merely represent an approximation which is adequate when the speed of the particle is sufficiently small compared with the speed of light. The system of dynamics based upon the correct equations 1 (which will be exhibited presently) is commonly called relativistic dynamics, not because any knowledge of the theory of relativity is essential to its understanding and use 2 , but because it is in agreement with the theory of relativity (which Newtonian dynamics is not), because it was first developed in connection with work on the theory of relativity, and because even yet virtually all of the expositions of the subject are to be found in books and papers dealing primarily with the theory of relativity. Just where the dividing line should be set between cases in which Newtonian dynamics is an adequate approximation and cases in which it is necessary to use relativistic dynamics is, of course, a rather vague question which cannot be answered simply and definitely.