Publication : t11/035

Importance of Reversibility in the Quantum Formalism

David F. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
In this letter I stress the role of (causal) reversibility, together with causality and locality, in the justification of the quantum formalism. Firstly, in the algebraic quantum formalism, I show that the assumption of reversibility implies that the observables of a quantum theory form a real C*-algebra, and can be represented as an algebra of operators on a real Hilbert space. The restriction to standard complex C*-algebras and complex Hilbert spaces is recalled to come from the constraints of locality and separability. Secondly, in the quantum logic formalism, I emphasize which axioms (existence of an orthocomplementation and the covering property) derive from reversibility. Here again, assuming locality ensures that the lattice of propositions can be represented as projectors on a complex Hilbert space, and leads to the standard representation of the quantum formalism.
Année de publication : 2011
Revue : Phys. Rev. Lett. 107 180401 (2011)
DOI : 10.1103/PhysRevLett.107.180401
Preprint : arXiv:1103.3454v3
Lien :
Langue : Anglais

Fichier(s) à télécharger :
  • PhysRevLett.107.180401.pdf
  • letter-reversibility-4.pdf


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