On the role of density matrices in Bohmian mechanics

Detlef Dürr, Sheldon Goldstein, Roderich Tumulka, Nino Zanghí

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)449-467
Number of pages19
JournalFoundations of Physics
Issue number3
StatePublished - Mar 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


  • Bohmian mechanics
  • Conditional wave function
  • Density matrix
  • Reduced statistical mixture
  • Spin


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