Reichenbach's common cause principle and quantum field theory
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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.
KeywordsStatistical Independence Spacetime Region Local Algebra Split Property Maximal Violation
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- 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
- 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
- 13.H. Reichenbach,The Direction of Time (University of California Press, Los Angeles, 1956).Google Scholar
- 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
- 24.G. Szabó, “Reichenbach's common cause definition on Hilbert lattice,” submitted.Google Scholar
- 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.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