The Contextual Character of Modal Interpretations of Quantum Mechanics

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.Comment: 21 pages, no figures, preprint submitted to SHPM

Two-valued states on Baer ∗^*-semigroups

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer $^*$-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer $^*$-semigroups.Comment: Reports on mathematical physics (accepted 2013

A discussion on particle number and quantum indistinguishability

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schroedinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept.Comment: 46 pages, no figures. Accepted by Foundations of Physic

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

Q-spaces and the foundations of quantum mechanics

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a labeltensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics.Fil: Domenech, Graciela. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Holik, Federico Hernan. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Krause, Décio. Conselho Nacional de Desenvolvimiento Científico y Tecnológico; Brasi

Modalidad y no-individualidad en la teoría cuántica

La revolución en los fundamentos de la física de comienzos del siglo XX se enmarca en la crisis que sacudió las bases del pensamiento clásico. Por una parte, la teoría de la relatividad dio lugar a un concepto de espacio diferente al presupuesto por la mecánica newtoniana mientras que por otra, la teoría atómica cuestionó la visión clásica del mundo en términos de objetos entrando en conflicto con los principios de la lógica aristotélica.. En particular, el principio de identidad encuentra severas limitaciones en relación a las llamadas "partículas idénticas", dicho en un lenguaje más preciso "partículas indistinguibles"

Physical properties as modal operators in the topos approach to quantum mechanics

In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties