Foundations of Physics

, Volume 38, Issue 7, pp 591–609 | Cite as

The Limits of Common Cause Approach to EPR Correlation

  • Katsuaki Higashi


It is often argued that no local common cause models of EPR correlation exist. However, Szabó and Rédei pointed out that such arguments have the tacit assumption that plural correlations have the same common causes. Furthermore, Szabó showed that for EPR correlation a local common cause model in his sense exists. One of his requirements is that common cause events are statistically independent of apparatus settings on each side. However, as Szabó knows, to meet this requirement does not entail that different combinations of common cause events (e.g. meet and join in lattice-theoretic terminology) are statistically independent of measurement settings. This further condition is formulated in two ways. First, the apparatus settings are completely independent of such combinations. Second, the apparatus settings on each side are independent of such combinations. Does a common cause model which meets the former and the latter respectively exist? This problem is considered. In particular, the latter version is Szabó’s and Rédei’s open problem. Negative answers are given to both versions.


Common cause EPR correlation Classical probability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Maudlin, T.: Quantum Non-Locality and Relativity, 2nd edn. Blackwell, Malden (2002) Google Scholar
  2. 2.
    van Fraassen, B.C.: Quantum Mechanics: An Empiricist View. Oxford University Press, New York (1991) Google Scholar
  3. 3.
    Bub, J.: Interpreting the Quantum World. Cambridge University Press, Cambridge (1997) MATHGoogle Scholar
  4. 4.
    Rédei, M.: Reichenbach’s Common Cause Principle and Quantum Correlations. In: Placek, T., Butterfield, J. (eds.) Non-Locality and Modality, pp. 259–270. Kluwer, Dordrecht (2002) Google Scholar
  5. 5.
    Szabó, L.E.: Attempt to resolve the EPR-Bell paradox via Reichenbach’s concept of common cause. Int. J. Theor. Phys. 39, 901–911 (2000) MATHCrossRefGoogle Scholar
  6. 6.
    Reichenbach, H.: The Direction of Time. University of California Press, Berkeley (1956) Google Scholar
  7. 7.
    Arntzenius, F.: Reichenbach’s common cause principles. (2005)
  8. 8.
    Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems. Int. J. Theor. Phys. 43, 1819–1826 (2004) MATHCrossRefGoogle Scholar
  9. 9.
    Placek, T.: Is Nature Deterministic? A Branching Perspective on EPR Phenomena. Jagiellonian University Press, Kraków (2000) Google Scholar
  10. 10.
    Uffink, J.: The principle of the common cause faces the Bernstein paradox. Philos. Sci. 66, S512–S525 (1999) CrossRefMathSciNetGoogle Scholar
  11. 11.
    Gyenis, B., Rédei, M.: When can statistical theories be causally closed? Found. Phys. 32, 335–355 (2002) CrossRefMathSciNetGoogle Scholar
  12. 12.
    Pitowsky, I.: Quantum Probability-Quantum Logic. Springer, Berlin (1989) MATHGoogle Scholar
  13. 13.
    Clauser, J., Horn, M.: Experimental consequences of objective local theories. Phys. Rev. D 10, 526–535 (1974) CrossRefADSGoogle Scholar
  14. 14.
    Szabó, L.E.: Is quantum mechanics compatible with a deterministic Universe? Two interpretations of quantum probabilities. Found. Phys. Lett. 8, 421–440 (1995) CrossRefGoogle Scholar
  15. 15.
    Bana, G., Durt, T.: Proof of Kolmogorovian censorship. Found. Phys. 27, 1355–1373 (1997) CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Szabó, L.E.: Critical reflections on quantum probability theory. In: Rédei, M., Stöltzner, M. (eds.) John von Neumann and the Foundations in Quantum Physics, pp. 201–219. Kluwer, Dordrecht (2001) Google Scholar
  17. 17.
    Bell, J.: The theory of local beables. Dialectica 39, 86 (1985). Reprinted in Speakable and Unspeakable. Cambridge University Press, Cambridge (1987) Google Scholar
  18. 18.
    Hofer-Szabó, G., Rédei, M., Szabó, L.: Common-causes are not common common-causes. Philos. Sci. 69, 623–636 (2002) CrossRefMathSciNetGoogle Scholar
  19. 19.
    Gräshoff, G., Portmann, S., Wüthrich, A.: Minimal assumption derivation of a bell-type inequality. Br. J. Philos. Sci. 56, 663–680 (2005) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Tokyo Metropolitan UniversityHachiouji-shiJapan

Personalised recommendations