Classical probability model for Bell inequality

Emergent Quantum Mechanics 2013

物理学;力学

Khrennikov, Andrei^1

Intl. Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, School of Mathematics, Linnaeus University, S-35195 Vaxjo, Sweden^1

关键词: Bell inequalities;    Bell's inequality;    Classical probabilities;    Measurements of;    Polarization beam splitters;    Probabilistic framework;    Probability spaces;    Statistical datas;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/504/1/012019/pdf
DOI  :  10.1088/1742-6596/504/1/012019

学科分类：力学，机械学

来源: IOP

【 摘 要 】

We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction "Kolmogorovization" of contextuality. This construction of common probability space is applied to Bell's inequality. It is well known that its violation is a consequence of collecting statistical data in a few incompatible experiments. In experiments performed in quantum optics contexts are determined by selections of pairs of angles (θi, θ'j) fixing orientations of polarization beam splitters. Opposite to the common opinion, we show that statistical data corresponding to measurements of polarizations of photons in the singlet state, e.g., in the form of correlations, can be described in the classical probabilistic framework. The crucial point is that in constructing the common probability space one has to take into account not only randomness of the source (as Bell did), but also randomness of context-realizations (in particular, realizations of pairs of angles (θi, θ'j)). One may (but need not) say that randomness of "free will" has to be accounted for.