Foundations of Physics

, Volume 27, Issue 10, pp 1309–1321 | Cite as

Reichenbach's common cause principle and quantum field theory

  • Miklós Rédei


Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V1) andA(V2) pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events inA(V1) andA(V2) have a genuinely probabilistic common cause, then the local algebrasA(V1) andA(V2) must be statistically independent in the sense of C*-independence.


Statistical Independence Spacetime Region Local Algebra Split Property Maximal Violation 
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  1. 1.
    N. Belnap and L. E. Szabó, “Branching space-time analysis of the GHZ theorem,”Found. Phys. 26, 989–1002 (1996).CrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Butterfield, “David Lewis meets John Bell”,Philos. Sci. 59, 26–43 (1992).CrossRefMathSciNetGoogle Scholar
  3. 3.
    J. Butterfield, “Vacuum correlations and outcome dependence in algebraic quantum field theory”, inFundamental Problems in quantum Theory, D. M. Greenberger and A. Zeilinger, eds.,Ann. New York Acad. Sci. 755, 768–785 (1994).Google Scholar
  4. 4.
    M. Florig and S. J. Summers, “On the statistical independence of algebras of observables,”J. Math. Phys. 3, 1318–1328 (1997).CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    R. Haag,Local Quantum Physics. Fields, Particles, Algebras (Springer, Berlin, 1992).zbMATHGoogle Scholar
  6. 6.
    G. Hellman, “Stochastic Einstein-locality and the Bell theorem”,Synthese 53, 461–504 (1982).CrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Horuzhy,Introduction to Algebraic Quantum Field Theory (Kluwer Academic, New York, 1990).zbMATHGoogle Scholar
  8. 8.
    F. Muller and J. Butterfield, “Is algebraic relativistic quantum field theory stochastic Einstein local?,”Philos. Sci. 61, 457–474 (1994).MathSciNetGoogle Scholar
  9. 9.
    M. Rédei, “Bell's inequalities, relativistic quantum field theory and the problem of hidden variables,”Philos. Sci. 58, 628–638 (1991).CrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Rédei, “Are prohibitions of superluminal causation by stochastic Einstein-locality and by absence of Lewisian probabilistic counterfactual causation equivalent?,”Philos. Sci. 60, 608–618 (1993).CrossRefMathSciNetGoogle Scholar
  11. 11.
    M. Rédei, “Is there counterfactual Superluminal causation in relativistic quantum field theory?”, InPerspectives on Quantum Reality: Relativistic, Non-Relativistic and Field Theoretic, R. Clifton, ed. (Kluwer Academic, Dordrecht, 1996), pp. 29–42.Google Scholar
  12. 12.
    M. Rédei, “Logical independence in quantum logic,”Found. Phys. 25, 411–422 (1995).CrossRefMathSciNetGoogle Scholar
  13. 13.
    H. Reichenbach,The Direction of Time (University of California Press, Los Angeles, 1956).Google Scholar
  14. 14.
    H. Roos, “Independence of local algebras in quantum field theory,”Commun. Math. Phys.,16, 238–246 (1970).CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    S. Schlieder, “Einige Bemerkungen über Projektionsoperatoren,”Commun. Math. Phys. 13, 216–225 (1969).CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    S. J. Summers and R. Werner, “The vacuum violates Bell's inequalities,”Phys. Lett. A 110, 257–279 (1985).CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    S. J. Summers and R. Werner, “Maximal violation of Bell's inequalities is generic in quantum field theory,”Commun. Math. Phys. 110, 247–259 (1987).CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    S. J. Summers and R. Werner, “Bell's inequalities and quantum field theory, I. General Setting,”J. Math. Phys. 28, 2440–2447 (1987).CrossRefADSMathSciNetGoogle Scholar
  19. 19.
    S. J. Summers and R. Werner, “Bell's inequalities and quantum field theory, I. Bell's inequalities are maximally violated in the vacuum,”J. Math. Phys. 28, 2448–2456 (1987).CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    S. J. Summers and R. Werner, “Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions,”Ann. Inst. Henri Poincaré—Phys. Theor. 49, 215–243 (1988).MathSciNetGoogle Scholar
  21. 21.
    S. J. Summers, “On the independence of local algebras in quantum field theory,”Rev. Math. Phys. 2, 201–247 (1990).CrossRefMathSciNetGoogle Scholar
  22. 22.
    S. J. Summers, “Bell's inequalities and quantum field theory,” inQuantum Probability a Applications V (Lecture Notes in Mathematics No. 1441, Springer, 1990), pp. 393–413.Google Scholar
  23. 23.
    S. J. Summers and R. Werner, “On Bell's inequalities and algebraic invariants,”Lett. Math. Psys. 33, 321–334 (1995).CrossRefMathSciNetGoogle Scholar
  24. 24.
    G. Szabó, “Reichenbach's common cause definition on Hilbert lattice,” submitted.Google Scholar
  25. 25.
    B. C. Van Fraassen, “When is a correlation not a mystery?,” inSymposium on the Foundations of Modern Physics, P. Lahti and P. Mittelstaedt, eds. (World Scientific, Singapore, 1985), pp. 113–128.Google Scholar
  26. 26.
    B. C. Van Fraassen, “The Charybdis of Realism: Epistemological Implications of Bell's inequality,” inPhilosophical Consequences of Quantum Theory, J. Cushing and E. McMullin eds. (University of Notre Dame Press, Notre Dame, 1989), pp. 97–113.Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Miklós Rédei
    • 1
  1. 1.Faculty of Natural SciencesLoránd Eötvös UniversityBudapestHungary

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