Minimal information in velocity space

Abstract

Jaynes' transformation group principle is used to derive the objective prior for the velocity of a non-zero rest-mass particle. In the case of classical mechanics, invariance under the classical law of addition of velocities, leads to an improper constant prior over the unbounded velocity space of classical mechanics. The application of the relativistic law of addition of velocities leads to a less simple prior. It can however be rewritten as a uniform volumetric distribution if the relativistic velocity space is given a non-trivial metric.