Foundations of Physics

, Volume 22, Issue 6, pp 807–817 | Cite as

Bell-type inequalities in the nonideal case: Proof of a conjecture of bell

  • Geoffrey Hellman
Part II. Invited Papers Dedicated To Henry Margenau


Recently Bell has conjectured that, with “epsilonics,” one should be able to argue, à la EPR, from “almost ideal correlations” (in parallel Bohm-Bell pair experiments) to “almost determinism,” and that this should suffice to derive an approximate Bell-type inequality. Here we prove that this is indeed the case. Such an inequality—in principle testable—is derived employing only weak locality conditions, imperfect correlation, and a propensity interpretation of certain conditional probabilities. Outcome-independence (Jarrett's “completeness” condition), hence “factorability” of joint probabilities, is not assumed, but rather an approximate form of this is derived. An alternative proof to the original one of Bell [1971] constraining stochastic, contextual hidden-variables theories is thus provided.


Locality Condition Conditional Probability Joint Probability Alternative Proof Weak Locality 
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  1. 1.
    J. S. Bell, “On the Einstein-Podolski-Rosen paradox,”Physics 1, 195–200 (1964).Google Scholar
  2. 2.
    G. Hellman, “EPR, Bell, and collapse: a route around ‘stochastic’ hidden variables,”Philos. Sci. 54, 558–576 (1987).Google Scholar
  3. 3.
    J. Jarrett, “On the physical significance of the locality conditions in the Bell arguments,”Noûs 18, 569–589 (1984).Google Scholar
  4. 4.
    J. S. Bell, “Introduction to the hidden variables question,” in B. d'Espagnat, ed.,Foundations of Quantum Mechanics (Academic Press, New York, 1971), pp. 171–181.Google Scholar
  5. 5.
    J. F. Clauser and M. A. Horne, “Experimental consequences of objective local theories,”Phys. Rev. D 10, 526–535 (1974).Google Scholar
  6. 6.
    J. F. Clauser and A. Shimony, “Bell's theorem: Experimental tests and implications,”Rep. Prog. Phys. 41, 1881–1927 (1978).Google Scholar
  7. 7.
    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,”Phys. Rev. Lett. 23, 880–884 (1969).Google Scholar
  8. 8.
    F. Selleri, “Generalized EPR paradox,”Found. Phys. 12(1), 645–659 (1982).Google Scholar
  9. 9.
    G. Hellman, “Stochastic Einstein locality and the Bell theorems,”Synthese 53(3), 461–504 (1982).Google Scholar
  10. 10.
    A. Aspect, J. Dalibard, and G. Roger, “Experimental tests of Bell's inequalities using time-varying analyzers,”Phys. Rev. Lett. 49, 1804–1807 (1982).Google Scholar
  11. 11.
    D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell's theorem without inequalities,”Am. J. Phys. 58(12), 1131–1143 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Geoffrey Hellman
    • 1
  1. 1.Department of PhilosophyUniversity of MinnesotaMinneapolis

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