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Bell Could Become the Copernicus of Probability
Linnaeus University, Faculty of Technology, Department of Mathematics. (International Center for Mathematical Modeling in Physics and Cognitive Sciences)ORCID iD: 0000-0002-9857-0938
2016 (English)In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, no 2, 1650008Article in journal (Refereed) Published
Abstract [en]

Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell's inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born's rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model - the first example of the non-Euclidean model of geometry. This is the "probability model" interpretation of the violation of Bell's inequality. We also criticize the standard interpretation - an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test. © 2016 World Scientific Publishing Company.

Place, publisher, year, edition, pages
2016. Vol. 23, no 2, 1650008
National Category
Probability Theory and Statistics Computational Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-56120DOI: 10.1142/S1230161216500086ISI: 000382850400001Scopus ID: 2-s2.0-84982802729OAI: oai:DiVA.org:lnu-56120DiVA: diva2:964785
Available from: 2016-09-08 Created: 2016-08-31 Last updated: 2016-10-06Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
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More styles
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  • de-DE
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