Article
Version 1
Preserved in Portico This version is not peer-reviewed
Quantum Probability's Algebraic Origin
Version 1
: Received: 17 September 2020 / Approved: 20 September 2020 / Online: 20 September 2020 (14:01:11 CEST)
A peer-reviewed article of this Preprint also exists.
Niestegge, G. Quantum Probability’s Algebraic Origin. Entropy 2020, 22, 1196. Niestegge, G. Quantum Probability’s Algebraic Origin. Entropy 2020, 22, 1196.
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 lat- ter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the gen- eral definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further 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' un- certainty 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.
Keywords
quantum mechanics; probability; quantum logic; uncertainty relation; Bell-Kochen-Specker theorem
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment