Bell-Boole inequality: nonlocality or probabilistic incompatibility of random variables?
type: Item
instance of: scholarly article
title: Bell-Boole inequality: nonlocality or probabilistic incompatibility of random variables?
zbMATH Open document ID: 1179.94047
published in: Entropy
publication date: 2010-01-29T00:00:00Z
review text: Summary: The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras). The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous Bell's inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and ``death of reality'' which are typically linked to Bell's type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in Bell's type inequalities statistical data from a number of experiments performed under different experimental contexts.
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 60A05
zbMATH DE Number: 5664127
zbMATH Keywords: Bell's inequality
zbMATH Keywords: nonlocality
zbMATH Keywords: ``death of reality''
zbMATH Keywords: probabilistic incompatibility of random variables
zbMATH Keywords: boole's necessary condition
zbMATH Keywords: vorobjev theorem
zbMATH Keywords: contextual description of the EPR-Bohm experiment
zbMATH Keywords: parameters of measurement devices
zbMATH Keywords: fluctuations of hidden variables of source
author: Andrei Khrennikov
MaRDI profile type: Publication
full work available at URL: entropy-e10020019
OpenAlex ID: W1969941437
DOI: 10.3390/ENTROPY-E10020019
Recommended article: Q3085692
Recommended article: Bell’s inequalities versus teleportation: What is nonlocality?
Recommended article: Is nonlocality responsible for the violation of Bell's inequalities?
Recommended article: Bell's nonlocality in a general nonsignaling case: Quantitatively and conceptually
Recommended article: Bell inequality, nonlocality and analyticity
Recommended article: Buonomano against Bell: Nonergodicity or nonlocality?
Recommended article: Q3001383
Recommended article: Q5324463
Recommended article: Quantum locality, rings a Bell?: Bell's inequality meets local reality and true determinism
Recommended article: Bell non-locality and Kochen-Specker contextuality: how are they connected?
description: scientific article; zbMATH DE number 5664127