Quantum equilibrium and the origin of absolute uncertainty

Detlef Dürr, Sheldon Goldstein, Nino Zanghí

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416 Scopus citations


The quantum formalism is a "measurement" 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 "particles" 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 an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "ρ = |ψ|2". 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.

Original languageEnglish (US)
Pages (from-to)843-907
Number of pages65
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jun 1992

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Bohm's causal interpretation of quantum theory
  • Quantum randomness
  • collapse of the wave function
  • effective wave function
  • foundations of quantum mechanics
  • hidden variables
  • pilot wave
  • quantum uncertainty
  • the measurement problem


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