Abstract
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.
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References
N. Belnap and L. E. Szabó, “Branching space-time analysis of the GHZ theorem,”Found. Phys. 26, 989–1002 (1996).
J. Butterfield, “David Lewis meets John Bell”,Philos. Sci. 59, 26–43 (1992).
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).
M. Florig and S. J. Summers, “On the statistical independence of algebras of observables,”J. Math. Phys. 3, 1318–1328 (1997).
R. Haag,Local Quantum Physics. Fields, Particles, Algebras (Springer, Berlin, 1992).
G. Hellman, “Stochastic Einstein-locality and the Bell theorem”,Synthese 53, 461–504 (1982).
S. Horuzhy,Introduction to Algebraic Quantum Field Theory (Kluwer Academic, New York, 1990).
F. Muller and J. Butterfield, “Is algebraic relativistic quantum field theory stochastic Einstein local?,”Philos. Sci. 61, 457–474 (1994).
M. Rédei, “Bell's inequalities, relativistic quantum field theory and the problem of hidden variables,”Philos. Sci. 58, 628–638 (1991).
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).
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.
M. Rédei, “Logical independence in quantum logic,”Found. Phys. 25, 411–422 (1995).
H. Reichenbach,The Direction of Time (University of California Press, Los Angeles, 1956).
H. Roos, “Independence of local algebras in quantum field theory,”Commun. Math. Phys.,16, 238–246 (1970).
S. Schlieder, “Einige Bemerkungen über Projektionsoperatoren,”Commun. Math. Phys. 13, 216–225 (1969).
S. J. Summers and R. Werner, “The vacuum violates Bell's inequalities,”Phys. Lett. A 110, 257–279 (1985).
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).
S. J. Summers and R. Werner, “Bell's inequalities and quantum field theory, I. General Setting,”J. Math. Phys. 28, 2440–2447 (1987).
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).
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).
S. J. Summers, “On the independence of local algebras in quantum field theory,”Rev. Math. Phys. 2, 201–247 (1990).
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.
S. J. Summers and R. Werner, “On Bell's inequalities and algebraic invariants,”Lett. Math. Psys. 33, 321–334 (1995).
G. Szabó, “Reichenbach's common cause definition on Hilbert lattice,” submitted.
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.
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.
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Rédei, M. Reichenbach's common cause principle and quantum field theory. Found Phys 27, 1309–1321 (1997). https://doi.org/10.1007/BF02551514
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DOI: https://doi.org/10.1007/BF02551514