Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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.


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.


quantum mechanics; probability; quantum logic; uncertainty relation; Bell-Kochen-Specker theorem


Physical Sciences, Quantum Science and Technology

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.