Abstract
Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different experimental setups, the choice of which obeys a classical distribution.
Similar content being viewed by others
References
L. Accardi and A. Fedullo, “On the statistical meaning of the complex numbers in quantum mechanics,”Nuovo Cimento 34, 161 (1982).
A. Aspect, P. Dalibard, and G. Roger, “Experimental tests of realistic local theories via Bell's theorem,”Phys. Rev. Lett. 47, 460 (1981).
J. S. Bell, “On the EPR paradox,”Physics 1, 195 (1964).
J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,”Phys. Rev. D. 10, 526 (1974).
T. Durt, “Three Interpretations of the violation of Bell's inequalities,”Found. Phys. 27(3), 415 (1995).
T. Durt, “From quantum to classical, a toy model.,” Doctoral thesis, V.U.B., January 1996 (1996a).
T. Durt, “Why God might play dice,”Int. J. Theor. Phys. 35, 2271 (1996b).
S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,”J. Math. Mech. 17, 59 (1967).
I. Pitowsky,Quantum Probability. Quantum Logic (Lecture Notes in Physics321) (Springer, Berlin, 1989).
L. E. Szabó, “Quantum mechanics in an entirely deterministic universe,”Int. J. Theor. Phys. 34, 1751–1766 (1995a).
L. E. Szabo, “Is quantum mechanics compatible with a deterministic universe? Two interpretations of quantum probabilities,”Found. Phys. Lett. 8, 421–440 (1995b).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bana, G., Durt, T. Proof of Kolmogorovian censorship. Found Phys 27, 1355–1373 (1997). https://doi.org/10.1007/BF02551517
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02551517