Where Lies the Mistake in the Clauser and Horne Proof of Bell’s Theorem?

Gordon Watson

Thomas D. Angelidis

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.

Justo Pastor Lambare

H. Razmi

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).

W. vanDam, Richard David Gill, P.D. Grunwald

There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments. Statistical considerations show that the amount of evidence should be measured by the Kullback-Leibler (KL) or relative entropy divergence. The statistical strength of the following proofs is determined: Bell's original proof and Peres' optimized variant of it, and proofs by Clauser, Horne, Shimony, and Holt (CHSH), Hardy, Mermin, and Greenberger, Horne, and Zeilinger (GHZ). The GHZ proof is at least four and a half times stronger than all other proofs, while of the two-party proofs, the one of CHSH is the strongest.

Gordon Watson