Velocity distributions from relativistic boosts in one dimension

Abstract

Three methods are proposed for solving velocity distributions resulting from repeated relativistic velocity additions. In contrast to the usual situation where the velocities involved are definitely determined, we consider velocities coming from a distribution. Starting from velocity distributions corresponding to Gaussian and uniform rapidity distributions, we obtain explicit expressions for velocity distributions after N relativistic boosts, where N is any positive integer. The velocity distribution plots for the Gaussian case show a transition from a single peak profile (with a maximum at velocity zero) to a double peak profile.