Foundations of Physics

, Volume 35, Issue 3, pp 449–467 | Cite as

On the Role of Density Matrices in Bohmian Mechanics

  • Detlef Dürr
  • Sheldon Goldstein
  • Roderich TumulkaEmail author
  • Nino Zanghí


It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the environment. A precise definition can be given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system.


Bohmian mechanics density matrix reduced statistical mixture conditional wave function spin 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Detlef Dürr
    • 1
  • Sheldon Goldstein
    • 2
  • Roderich Tumulka
    • 3
    Email author
  • Nino Zanghí
    • 3
  1. 1.Mathematisches Institut der Universität MünchenMünchenGermany
  2. 2.Departments of Mathematics, Physics, and Philosophy Hill Center, RutgersThe State University of New JerseyPiscatawayUSA
  3. 3.Dipartimento di Fisica and INFN sezione di GenovaUniversitá di GenovaGenovaItaly

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