RELATIVISTIC CLASSICAL-THEORY OF A FREE PARTICLE

By shifting the emphasis from the concept of trajectory to the concept of probability density it is possible to incorporate the uncertainty principle into classical mechanics. This amendment in the nonrelativis tic classical theory is sufficient to derive the Schrodinger equation for a general potential. In order to show that the approach has genera l validity it is necessary to show that it can be generalized to the c lassical relativistic dynamics. In this paper it is shown how this gen eralization is achieved for a free particle, and as a result the Dirac instead of the Klein-Gordon equation is obtained. It is shown that th e spin and the magnetic moment of charged particles are classical in c haracter because their correct values are calculated as the averages o ver the classical (relativistic) phase-space density, subject to the c onstraint imposed by the uncertainty principle. Since the Dirac equati on has direct connection to the classical (relativistic) dynamics the problem of the positive and negative energy states is discussed. (C) 1 997 American Institute of Physics.