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Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories

Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow for an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical probabilities we show that a class [Formula: see text] of theor...

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Autor principal: Garola, Claudio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7831124/
https://www.ncbi.nlm.nih.gov/pubmed/33477572
http://dx.doi.org/10.3390/e23010121
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author Garola, Claudio
author_facet Garola, Claudio
author_sort Garola, Claudio
collection PubMed
description Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow for an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical probabilities we show that a class [Formula: see text] of theories can be selected in which probabilities are introduced as classical averages of Kolmogorovian probabilities over sets of (microscopic) contexts, which endows them with an epistemic interpretation. The conditions characterizing [Formula: see text] are compatible with classical mechanics (CM), statistical mechanics (SM), and QM, hence we assume that these theories belong to [Formula: see text]. In the case of CM and SM, this assumption is irrelevant, as all of the notions introduced in them as members of [Formula: see text] reduce to standard notions. In the case of QM, it leads to interpret quantum probability as a derived notion in a Kolmogorovian framework, explains why it is non-Kolmogorovian, and provides it with an epistemic interpretation. These results were anticipated in a previous paper, but they are obtained here in a general framework without referring to individual objects, which shows that they hold, even if only a minimal (statistical) interpretation of QM is adopted in order to avoid the problems following from the standard quantum theory of measurement.
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spelling pubmed-78311242021-02-24 Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories Garola, Claudio Entropy (Basel) Article Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow for an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical probabilities we show that a class [Formula: see text] of theories can be selected in which probabilities are introduced as classical averages of Kolmogorovian probabilities over sets of (microscopic) contexts, which endows them with an epistemic interpretation. The conditions characterizing [Formula: see text] are compatible with classical mechanics (CM), statistical mechanics (SM), and QM, hence we assume that these theories belong to [Formula: see text]. In the case of CM and SM, this assumption is irrelevant, as all of the notions introduced in them as members of [Formula: see text] reduce to standard notions. In the case of QM, it leads to interpret quantum probability as a derived notion in a Kolmogorovian framework, explains why it is non-Kolmogorovian, and provides it with an epistemic interpretation. These results were anticipated in a previous paper, but they are obtained here in a general framework without referring to individual objects, which shows that they hold, even if only a minimal (statistical) interpretation of QM is adopted in order to avoid the problems following from the standard quantum theory of measurement. MDPI 2021-01-18 /pmc/articles/PMC7831124/ /pubmed/33477572 http://dx.doi.org/10.3390/e23010121 Text en © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Garola, Claudio
Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title_full Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title_fullStr Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title_full_unstemmed Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title_short Kolmogorovian versus Non-Kolmogorovian Probabilities in Contextual Theories
title_sort kolmogorovian versus non-kolmogorovian probabilities in contextual theories
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7831124/
https://www.ncbi.nlm.nih.gov/pubmed/33477572
http://dx.doi.org/10.3390/e23010121
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