Instantaneous and Asymptotic Conservation Laws for Classical Relativistic Mechanics of Interacting Point Particles

Abstract

The present article consists of two parts. First, we assume that the conservation laws for energy and linear momentum are valid and that these quantities are the sums of the energies and linear momenta of the individual particles, i.e., that there is no interaction energy and no interaction momentum. We then repeat a familiar argument and show that there can then be no interaction between the particles, that is, their world lines are straight. In the second part of the paper the interaction quantities for energy, linear and angular momenta, and the center-of-mass law are derived for the equations of motion proposed in an earlier paper. We then study these interaction quantities in the asymptotic region of collision processes, in order to arrive at asymptotic conservation laws. We find, in agreement with the earlier paper, that the interaction energy and the linear interaction momenta vanish asymptotically. This, however, is not true in general for the interaction angular momenta and center-of-mass motion. Asymptotic interaction angular momentum is present in all theories, such as classical electrodynamics, which lead to inverse-square-law forces.