Bell-type inequalities in the nonideal case: Proof of a conjecture of bell
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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  constraining stochastic, contextual hidden-variables theories is thus provided.
KeywordsLocality Condition Conditional Probability Joint Probability Alternative Proof Weak Locality
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