dorsal/arxiv
View SchemaEinstein and Bell, von Mises and Kolmogorov: reality and locality, frequency and probability
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0006016 |
| URL | https://arxiv.org/abs/quant-ph/0006016 |
| Journal | Foundations of Physics, 32, N. 7, 1159-1174, 2002 |
Abstract
We perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of frequencies for physical observables. If, nevertheless, micro-parameters are also statistically stable, then violations of Bell's inequality and its generalizations may be a consequence of dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, the frequency approach implies totally different interpretation of dependence. It is not dependence of events, but it is dependence of collectives. Such a dependence may be induced by the same preparation procedure.
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"abstract": "We perform frequency analysis of the EPR-Bell argumentation. One of the main\nconsequences of our investigation is that the existence of probability\ndistributions of the Kolmogorov-type which was supposed by some authors is a\nmathematical assumption which may not be supported by actual physical quantum\nprocesses. In fact, frequencies for hidden variables for quantum particles and\nmeasurement devices may fluctuate from run to run of an experiment. These\nfluctuations of frequencies for micro-parameters need not contradict to the\nstabilization of frequencies for physical observables. If, nevertheless,\nmicro-parameters are also statistically stable, then violations of Bell\u0027s\ninequality and its generalizations may be a consequence of dependence of\ncollectives corresponding to two different measurement devices. Such a\ndependence implies the violation of the factorization rule for the simultaneous\nprobability distribution. Formally this rule coincides with the well known BCHS\nlocality condition (or outcome independence condition). However, the frequency\napproach implies totally different interpretation of dependence. It is not\ndependence of events, but it is dependence of collectives. Such a dependence\nmay be induced by the same preparation procedure.",
"arxiv_id": "quant-ph/0006016",
"authors": [
"Andrei Khrennikov"
],
"categories": [
"quant-ph"
],
"journal_ref": "Foundations of Physics, 32, N. 7, 1159-1174, 2002",
"title": "Einstein and Bell, von Mises and Kolmogorov: reality and locality, frequency and probability",
"url": "https://arxiv.org/abs/quant-ph/0006016"
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