Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts
Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/9/1285 |
| _version_ | 1797488667593277440 |
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| author | Karl Svozil |
| author_facet | Karl Svozil |
| author_sort | Karl Svozil |
| collection | DOAJ |
| description | Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason’s theorem. |
| first_indexed | 2024-03-10T00:05:36Z |
| format | Article |
| id | doaj.art-b91ab9c157f941f786cdb7d7782ec2d5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T00:05:36Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-b91ab9c157f941f786cdb7d7782ec2d52023-11-23T16:09:07ZengMDPI AGEntropy1099-43002022-09-01249128510.3390/e24091285Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of ContextsKarl Svozil0Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, AustriaKolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason’s theorem.https://www.mdpi.com/1099-4300/24/9/1285value indefinitenessKolmogorov axioms of probability theoryPitowsky’s logical indeterminacy principlequantum mechanicsGleason theoremKochen–Specker theorem |
| spellingShingle | Karl Svozil Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts Entropy value indefiniteness Kolmogorov axioms of probability theory Pitowsky’s logical indeterminacy principle quantum mechanics Gleason theorem Kochen–Specker theorem |
| title | Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts |
| title_full | Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts |
| title_fullStr | Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts |
| title_full_unstemmed | Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts |
| title_short | Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts |
| title_sort | extending kolmogorov s axioms for a generalized probability theory on collections of contexts |
| topic | value indefiniteness Kolmogorov axioms of probability theory Pitowsky’s logical indeterminacy principle quantum mechanics Gleason theorem Kochen–Specker theorem |
| url | https://www.mdpi.com/1099-4300/24/9/1285 |
| work_keys_str_mv | AT karlsvozil extendingkolmogorovsaxiomsforageneralizedprobabilitytheoryoncollectionsofcontexts |