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Journal of Physics A Mathematical and General

Is the Clauser–Horne model of Bell's theorem completely stochastic?

H. Razmi

Published Apr 6, 2005• 1 citation
Publisher

Abstract

The stochastic Clauser–Horne (CH) model of Bell's theorem [1] is considered and by applying the locality condition it is shown that this (local) model, as far as applied to the singlet-state and without using quantum mechanical formalism, is not completely stochastic (i.e. there are possible configurations for which the model is deterministic).

DOI
10.1088/0305-4470/38/16/013

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The stochastic Clauser–Horne (CH) model of Bell's theorem [1] is considered and by applying the locality condition it is shown that this (local) model, as far as applied to the singlet-state and without using quantum mechanical formalism, is not completely stochastic (i.e. there are possible configurations for which the model is deterministic).
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The claim that the Clauser-Horne inequality $S(\ensuremath{\phi})<~1$ is valid for all local theories is criticized. The criticism is based on the author's proof that this universality claim is incompatible with the conservation law of angular momentum. There exists an infinity of counterexamples to the universality claim made for $S(\ensuremath{\phi})<~1$. So Clauser and Horne offer no valid proof of the nonlocality of the quantum formalism; consequently experiments like Aspect's cannot be said to refute Einsteinian locality.
I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation does not favour locality over completeness. (4) If we prohibit all superluminal causation, then the violation of the Bell inequality teaches us a lesson, besides quantum mechanics' familiar ones that quantities can lack precise values and that pairs of quantities can lack joint probabilities: namely, some pairs of events are not screened off by their common past.