Quantum Probability’s Algebraic Origin
Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1196 |
| _version_ | 1797550092726566912 |
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| author | Gerd Niestegge |
| author_facet | Gerd Niestegge |
| author_sort | Gerd Niestegge |
| collection | DOAJ |
| description | Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions. |
| first_indexed | 2024-03-10T15:23:36Z |
| format | Article |
| id | doaj.art-5b3f0edc23c54e378f5aec9c6c63e152 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:23:36Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-5b3f0edc23c54e378f5aec9c6c63e1522023-11-20T18:13:25ZengMDPI AGEntropy1099-43002020-10-012211119610.3390/e22111196Quantum Probability’s Algebraic OriginGerd Niestegge0Freelance Researcher, 48683 Ahaus, GermanyMax Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions.https://www.mdpi.com/1099-4300/22/11/1196quantum mechanicsprobabilityquantum logicuncertainty relationBell-Kochen- Specker theorem |
| spellingShingle | Gerd Niestegge Quantum Probability’s Algebraic Origin Entropy quantum mechanics probability quantum logic uncertainty relation Bell-Kochen- Specker theorem |
| title | Quantum Probability’s Algebraic Origin |
| title_full | Quantum Probability’s Algebraic Origin |
| title_fullStr | Quantum Probability’s Algebraic Origin |
| title_full_unstemmed | Quantum Probability’s Algebraic Origin |
| title_short | Quantum Probability’s Algebraic Origin |
| title_sort | quantum probability s algebraic origin |
| topic | quantum mechanics probability quantum logic uncertainty relation Bell-Kochen- Specker theorem |
| url | https://www.mdpi.com/1099-4300/22/11/1196 |
| work_keys_str_mv | AT gerdniestegge quantumprobabilitysalgebraicorigin |