Non-Kolmogorov probability models and modified Bell’s inequality

Source abstract

We analyze the proof of Bell’s inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics from 1933. We found a (numerical) statistical correction to Bell’s inequality. Such an additional term εφ on the right-hand side of Bell’s inequality can be considered as a probability invariant of a quantum state φ. This is a measure of nonreproducibility of hidden variables in different runs of experiments. Experiments to verify Bell’s inequality can be considered as just experiments to estimate the constant εφ. It seems that Bell’s inequality could not be used as a crucial reason to deny local realism. We consider deterministic as well as stochastic hidden variables models.