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Proc Math Phys Eng Sci. 2014 Nov 8;470(2171):20140288.

Instability of quantum equilibrium in Bohm's dynamics.

Author information

1
Department of Physics and Astronomy , Clemson University , Kinard Laboratory, Clemson, SC 29634-0978, USA ; Centre for Quantum Dynamics , Griffith University , Brisbane, Queensland 4111, Australia.
2
Department of Physics and Astronomy , Clemson University , Kinard Laboratory, Clemson, SC 29634-0978, USA.

Abstract

We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for 'extended' non-equilibrium, 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 non-equilibrium 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.

KEYWORDS:

de Broglie–Bohm; quantum equilibrium; stability

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