Consistent histories and relativistic invariance in the modal interpretation of quantum mechanics

Modal interpretations of quantum mechanics assign definite properties to physical systems and specify single-time joint probabilities of these properties. We show that a natural extension, applying to properties at several times, can be given if a decoherence condition is satisfied. This extension defines "consistent histories" of modal properties. We suggest a new form of the modal scheme, that offers prospects of a more general applicability of the histories concept. Finally, we discuss a possible way of applying these ideas to relativistic quantum field theory.Comment: 13 pages, no figure

Scopes and Limits of Modality in Quantum Mechanics

We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular structure, contextuality remains a central feature of quantum systems.Comment: 9 pages, no figure

Semilattices global valuations in the topos approach to quantum mechanics

In the framework of the topos approach to quantum mechanics a kind of global valuation is introduced and studied. It allows us to represent certain features related to the logical consequences of properties about quantum systems when its phase space is endowed with an intuitionistic structureFil: Freytes Solari, Hector Carlos. Università di Cagliari; Italia. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: de Ronde, Christian. Universidad de Buenos Aires. Facultad de Filosofía y Letras. Instituto de Filosofía "Dr. Alejandro Korn"; Argentina. Center Leo Apostel; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Domenech, Graciela. Center Leo Apostel; Bélgica. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A Topological Study of Contextuality and Modality in Quantum Mechanics

Kochen-Specker theorem rules out the non-contextual assignment of values to physical magnitudes. Here we enrich the usual orthomodular structure of quantum mechanical propositions with modal operators. This enlargement allows to refer consistently to actual and possible properties of the system. By means of a topological argument, more precisely in terms of the existence of sections of sheaves, we give an extended version of Kochen-Specker theorem over this new structure. This allows us to prove that contextuality remains a central feature even in the enriched propositional system.Comment: 10 pages, no figures, submitted to I. J. Th. Phy