Anomalies in experimental data for the EPR-Bohm experiment: Are both classical and quantum mechanics wrong?

Abstract

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, $P_{++}(α, β)=P_{--}(α, β)= {1/2}\cos^2(α-β)$ and $P_{+-}=P_{-+}(α, β)={1/2}\sin^2(α-β).$ However, in some mysterious way those deviations compensate each other and finally the correlation $E^{\rm{exp}}(α, β)= P_{++}^{\rm{exp}}(α, β)- P_{+-}^{\rm{exp}}(α, β)- P_{-+}^{\rm{exp}}(α, β)+ P_{--}^{\rm{exp}}(α, β)$ is in the complete agreement with the QM-prediction, namely, $E(α, β)= P_{++}(α, β)- P_{+-}(α, β)- P_{-+}(α, β)+ P_{--}(α, β)= \cos 2(α-β).$ 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?