In the present paper a robustness stress-test of the CHSH experiments for
Einstein locality and causality is designed and employed. Random A and B from
dice and coins, but based on a local model, run "parallel" to a real
experiment. We found a local causal model with a nonzero probability to violate
the CHSH inequality for some relevant quartets $\mathcal{Q}$ of settings in the
series of trials.Comment: 2 pages, accepted for publicatio
Here, we consider the Bell experiment for a system described by multipartite states in the case where n-dichotomic observables are measured per site. If n is two, we consider a two-setting Bell experiment. If n is three, we consider a three-setting Bell experiment. Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment. Three-setting model is an explicit local realistic model for the values of a correlation function, given in a three-setting Bell experiment. In the non-contextual scenario, there is not the difference between three-setting model and two-setting model. And we cannot classify local realistic theories in this case. This says that we can construct three-setting model from two-setting model. Surprisingly we can discuss incompleteness in the Bell theorem using non-contextual model. On the other hand, in the contextual scenario, there is the difference between three-setting model and two-setting model. This says that we must distinguish three-setting model from two-setting model. And we can classify local realistic theories in this case.
In the paper it is demonstrated that a concrete inconsistency occurs in experimental conclusions concerning quantum foundation. This inconsistency is similar to concrete mathematical incompleteness. We would like to stress that in the derivations there are no physics assumptions. Nevertheless the basic physics requirements of a local model are fulfilled.
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