BROWNIAN MOTION ON THE RELATIVISTIC VELOCITY SPACE

The Brownian motion on the relativistic velocity space was introduced in a fully relativistic invariant formalism in a seminal paper by R.M. Dudley. The idea that particles could follow a Brownian motion on the velocity space could prove interesting as the hypothesis is compatible with the equivalence principle. Here we review the results available and in particular show that the Brownian motion can be completely reduced from the frame bundle to the velocity space if a prescription is adopted that the driving Brownian motion Wigner rotates under Lorentz transformation. The asymptotic radial process on the velocity space is also considered showing that it gives rise to a constant outward average acceleration. The possibility of applying this result to the motion of distant galaxies so as to account for the observed acceleration of the universe is commented