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By Feynman R.P., Leighton R.B., Sands M.
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Formula (13) in Bell's '64 paper) is true almost everywhere. Proof. Follows from Lemma (1) with the choice f = Sx , g = Si'. Summing up: if you want to compare the predictions of a hidden variable theory with quantum theory in the EPR experiment (so that at least we admit the validity of the singlet law) then the hidden assumption, of realizability of all the random variables in (3) in the same probability space, (without which Bell's inequality cannot be proved) implies the same conclusion of the counterfactual argument.
38 References 1. J. S. Bell, Physics 1, 195 (1964). 2. F. Selleri, Le grand debat de la mcanique quantique (Champs Flammarion, Paris, 1986). 3. A. Aspect, Nature 398, 189 (1999). 4. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935). 5. D. Bohm, Phys. Rev. 85, 166 (1952). 6. D. Greenberger, M. Home, A. Shimony and A. Zeilinger, Am. J. Phys. 58, 1131 (1990). 7. A. Bohm, Quantum Mechanics, Foundations and applications (SpringerVerlag, New York, 1979). 8. J. S. Bell, in Proceedings of the international School of physics 'Enrico Fermi', course IL: Foundations of quantum mechanics (Academic, New York, 1971), p.
8. J. S. Bell, in Proceedings of the international School of physics 'Enrico Fermi', course IL: Foundations of quantum mechanics (Academic, New York, 1971), p. 171. 9. J. S. Bell, Epistemological Letters, p. 2 (July, 1975). 10. J. F. Clauser, M. A. Home, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969). 11. B. d'Espagnat, Veiled Reality: An Analysis of Present Day Quantum Mechanical Concepts, (Addison-Wesley, 1995). 12. B. d'Espagnat, http://arXiv/abs/quant-ph/9802046. 13. A. Aspect, J.