Cargando…
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...
Autor principal: | |
---|---|
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 |
_version_ | 1783641571183296512 |
---|---|
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. |
format | Online Article Text |
id | pubmed-7831124 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT garolaclaudio kolmogorovianversusnonkolmogorovianprobabilitiesincontextualtheories |