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The experimental violation of Bell's inequality [as predicted by quantum mechanics]: A contribution to the study of its meaning

Bertrand Hespel

Published Jan 1, 2001• 0 citations
OpenAlex

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Entanglement is a prediction of quantum mechanics that suggests that our physical laws cannot be described by a local causal model. This has led to much debate, including Einstein's famous suggestion that quantum mechanics is an incomplete theory, and we may one day discover a deeper theory that can be described by a locally causal model. However, loophole free violations of Bell inequalities demonstrate that this is not the case. Bell's theorem is independent of quantum mechanics, and it shows that any theory attempting to supplant quantum mechanics must be somehow nonlocal. Since then, there have been many experimental violations of Bell inequalities using different physical systems, culminating in three loophole-free experiments [1-3].

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Violations of Locality Beyond Bell's Theorem

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Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.

arXiv:quant-ph/0307143•Jul 20, 2003•1 citation
We analyze anomalies in data to test the violation of Bell's inequality for the EPR-Bohm experiment. We found that the experimental correlations for photon polarization have an intriguing property. In the experimental data there are visible non-negligible deviations of probabilities $P_{++}^{\rm{exp}}(α, β), P_{+-}^{\rm{exp}}(α, β), P_{-+}^{\rm{exp}}(α, β), P_{--}^{\rm{exp}}(α, β) $ from the predictions of quantum mechanics, namely, P++(α,β)=P−−(α,β)=1/2cos⁡2(α−β)P_{++}(α, β)=P_{--}(α, β)= {1/2}\cos^2(α-β)P++​(α,β)=P−−​(α,β)=1/2cos2(α−β) and P+−=P−+(α,β)=1/2sin⁡2(α−β).P_{+-}=P_{-+}(α, β)={1/2}\sin^2(α-β).P+−​=P−+​(α,β)=1/2sin2(α−β). However, in some mysterious way those deviations compensate each other and finally the correlation Eexp(α,β)=P++exp(α,β)−P+−exp(α,β)−P−+exp(α,β)+P−−exp(α,β)E^{\rm{exp}}(α, β)= P_{++}^{\rm{exp}}(α, β)- P_{+-}^{\rm{exp}}(α, β)- P_{-+}^{\rm{exp}}(α, β)+ P_{--}^{\rm{exp}}(α, β)Eexp(α,β)=P++exp​(α,β)−P+−exp​(α,β)−P−+exp​(α,β)+P−−exp​(α,β) is in the complete agreement with the QM-prediction, namely, E(α,β)=P++(α,β)−P+−(α,β)−P−+(α,β)+P−−(α,β)=cos⁡2(α−β).E(α, β)= P_{++}(α, β)- P_{+-}(α, β)- P_{-+}(α, β)+ P_{--}(α, β)= \cos 2(α-β).E(α,β)=P++​(α,β)−P+−​(α,β)−P−+​(α,β)+P−−​(α,β)=cos2(α−β). Therefore such anomalies play no role in the Bell's inequality framework. Nevertheless, other linear combinations of experimental probabilities do not have such a compensation property. There can be found non-negligible deviations from predictions of quantum mechanics. Thus neither classical nor quantum model can pass the whole family of statistical tests given by all possible linear combinations of the EPR-Bohm probabilities. Does it mean that both models are wrong?
Entanglement is a prediction of quantum mechanics that suggests that our physical laws cannot be described by a local causal model. This has led to much debate, including Einstein's famous suggestion that quantum mechanics is an incomplete theory, and we may one day discover a deeper theory that can be described by a locally causal model. However, loophole free violations of Bell inequalities demonstrate that this is not the case. Bell's theorem is independent of quantum mechanics, and it shows that any theory attempting to supplant quantum mechanics must be somehow nonlocal. Since then, there have been many experimental violations of Bell inequalities using different physical systems, culminating in three loophole-free experiments [1-3].
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.