Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Revisiting Born’s rule through Uhlhorn’s and Gleason’s theorems

Abstract : In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that are accessible to a quantum system, and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason's theorem was emphasized, with the argument that CSM provides a physical justification for Gleason's hypotheses. Here we extend this result by showing that an essential one among these hypotheses - the need of unitary transforms to relate different contexts - can be removed and is better seen as a necessary consequence of Uhlhorn's theorem.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal-iogs.archives-ouvertes.fr/hal-03455462
Contributor : Fatima Pereira Connect in order to contact the contributor
Submitted on : Monday, November 29, 2021 - 4:30:03 PM
Last modification on : Tuesday, January 4, 2022 - 6:09:30 AM

File

2111.10758.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03455462, version 1
  • ARXIV : 2111.10758

Collections

Citation

Alexia Auffèves, Philippe Grangier. Revisiting Born’s rule through Uhlhorn’s and Gleason’s theorems. 2021. ⟨hal-03455462⟩

Share

Metrics

Les métriques sont temporairement indisponibles