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Quantum equilibrium and the origin of absolute uncertainty
Authors:Detlef Dürr  Sheldon Goldstein  Nino Zanghí
Institution:(1) Department of Mathematics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Present address: Fakultät für Mathematik, Universität München, 8000 München 2, Germany;(3) Present address: Istituto di Fisica, Università di Genova, INFN, 16146 Genova, Italy
Abstract:The quantum formalism is a ldquomeasurementrdquo formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrödinger's equation for a system of particles when we merely insist that ldquoparticlesrdquo means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that anappearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by ldquorgr = ¦psgr¦ 2rdquo. A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.This paper is dedicated to the memory of J. S. Bell.
Keywords:Quantum randomness  quantum uncertainty  hidden variables  effective wave function  collapse of the wave function  the measurement problem  Bohm's causal interpretation of quantum theory  pilot wave  foundations of quantum mechanics
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