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Quantum probability's algebraic origin

Niestegge, Gerd (2020) Quantum probability's algebraic origin. Entropy 2020, 22, 1196. ISSN 1099-4300

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Abstract

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. While 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.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Niestegge, Gerdgerd.niestegge@web.de0000-0002-3405-9356
Keywords: quantum mechanics, probability, quantum logic, uncertainty relation, Bell-Kochen-Specker theorem
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Dr. Gerd Niestegge
Date Deposited: 26 Oct 2020 03:08
Last Modified: 26 Oct 2020 03:08
Item ID: 18314
Journal or Publication Title: Entropy 2020, 22, 1196
DOI or Unique Handle: 10.3390/e22111196
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 23 October 2020
ISSN: 1099-4300
URI: http://philsci-archive.pitt.edu/id/eprint/18314

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