Instability of quantum equilibrium in Bohm's dynamics

Samuel Colin, Antony Valentini

Published 2013-06-06, updated 2014-08-06Version 2

We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle Bohm's dynamics allows for 'extended' nonequilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended nonequilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation.