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Communications in Theoretical Physics

Local-Realism Violation in Non-Idealized Experiment

Wu Xiao-Hua

Published Oct 30, 1998• 0 citations
Publisher

Abstract

Santos argued that quantum mechanical states which do violate the Bell inequalities are not physically realizable and local hidden-variable theories for quantum mechanics are still possible. We discuss the non-idealized experiment given by Santos, and show local-realism violation in such an experiment without requiring high efficiencies of the detectors and the polarization analyzers.

DOI
10.1088/0253-6102/30/3/321

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Santos argued that quantum mechanical states which do violate the Bell inequalities are not physically realizable and local hidden-variable theories for quantum mechanics are still possible. We discuss the non-idealized experiment given by Santos, and show local-realism violation in such an experiment without requiring high efficiencies of the detectors and the polarization analyzers.
Recent experiments of Gröblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Gröblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Gröblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class.
The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables level”. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell’s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell’s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment.