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International Journal of Theoretical Physics

, Volume 36, Issue 9, pp 1973–1980 | Cite as

Formal existence and uniqueness of the Reichenbachian common cause on Hilbert lattices

  • Gábor Hofer-Szabó
Article

Abstract

The Reichenbachian definition of the common cause for two correlating events is formally generalized for the quantum case in two different ways. It is shown that (1) in the first quantum case, unlike in the classical case, there exists a common cause for any two correlating events, and (2) the common cause is not unique either in the classical or in both quantum cases.

Keywords

Conditional Probability Pure State Classical Case Quantum Case Boolean Lattice 
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References

  1. Bub, J. (1979). Conditional probabilities in non Boolean possibility structures, inThe Logico Algebraic Approach of Quantum Mechanics, Vol. II. Contemporary Consolidation, C. A. Hooker, ed., Reidel, Dordrecht, Holland.Google Scholar
  2. Hofer-Szabó, G. (1997a). Reichenbach's common cause definition on Hilbert lattices,International Journal of Theoretical Physics, submitted.Google Scholar
  3. Hofer-Szabó, G. (1997b). Can Reichenbach's common cause definition be generalized to non-commutative event structures?Foundations of Physics, submitted.Google Scholar
  4. Lüders, G. (1951). Über die Zustandsänderung durch den Messprozess,Annalen der Physik,8, 332–328.Google Scholar
  5. Reichenbach, H. (1956).The Direction of Time, University of California Press, Berkeley, California.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Gábor Hofer-Szabó
    • 1
  1. 1.Department of PhilosophyTechnical University of BudapestBudapestHungary

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