Journal of Statistical Physics

, Volume 67, Issue 5–6, pp 843–907 | Cite as

Quantum equilibrium and the origin of absolute uncertainty

  • Detlef Dürr
  • Sheldon Goldstein
  • Nino Zanghí


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 anappearance 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.

Key words

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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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Detlef Dürr
    • 1
  • Sheldon Goldstein
    • 1
  • Nino Zanghí
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew Brunswick

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