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International Journal of Theoretical Physics

Ideals in ortholattices, Bell inequalities, and simultaneously definite properties

Sylvia Pulmannová, Karl Svozil

Published Jul 1, 1997• 1 citation
Publisher
DOI
10.1007/bf02435755

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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.

arXiv:2403.03236•Mar 5, 2024•1 citation
Abstract. Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or “loopholes ” in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a “loophole-free ” or “definitive ” Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. ar X iv
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or 'loopholes' in available experiment tests, local realist theories can reproduce the data from these experiments. This paper reviews such loopholes, what effect they have on Bell inequality tests, and how to avoid them in experiment. Avoiding all these simultaneously in one experiment, usually called a 'loophole-free' or 'definitive' Bell test, remains an open task, but is very important for technological tasks such as device-independent security of quantum cryptography, and ultimately for our understanding of the world. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
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.