Abstract:Année de publication : 2011
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.