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American Journal of Physics

Bell inequalities and quantum mechanics

Joseph H. Eberly

Published Mar 1, 2002• 27 citations
Publisher

Abstract

We employ an arrangement of polarization analyzer loops to derive several simple Bell inequalities and then discuss the violation of one of them in light of quantum and classical interpretations of the data recorded.
DOI
10.1119/1.1427311

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Louis Sica derived Bell's inequalities from the hypothesis that the time series of outcomes observed in one station does not change if the setting in the other (distant) station is changed. This derivation is based on arithmetical properties only. It does not involve the controversial definitions of Locality and Realism, it does not require the definition of probabilities, and is valid for series of any length. In this paper, Sica's approach is extended to series with non ideal efficiency and to the actual time structure of experimental data. The first extension leads to an interesting relationship, involving the entanglement parameter SCHSH and efficiency, that places the so-called 'detection loophole' under new light. The second extension makes visible that measuring with different settings unavoidably means recording series at different times. It replaces 'Local Realism' (as the assumption necessary for the validity of Bell's inequalities), with the assumption that the recorded series can be arbitrarily reordered. Violation of this latter assumption is, in my opinion, more acceptable to intuition than violation of Local Realism. The second extension also shows that the observation of a violation of Bell's inequalities implies that Sica's hypothesis is not valid, i.e., that the series in one station is different if the setting in the other station is changed. This result gives precise meaning to 'quantum non-locality', and also explains why it cannot be used for sending messages. Finally, it is demonstrated that a series of outcomes, even if it violates Bell's inequalities, can be always embedded in a set of factual and counter-factual data in which Sica's hypothesis is valid. In consequence, factual universe may be quantum (non-classical) or not, but the union of factual and counter-factual universes is always classical.