Contextuality, non-locality and indistinguishability: a modal ontology of properties

OLIMPIA LOMBARDI

Rio de Janeiro

Congreso; 4th World Congress and School on Universal Logic, Workshop: Logical Quantum Structures; 2013

Universidad Federal de Rio de Janeiro

In previous papers (Lombardi & Castagnino 2008, Ardenghi & Lombardi 2011) a new member of the “modal family” of interpretations of quantum mechanics (see Dieks & Vermaas 1998, Dieks & Lombardi 2012) has been proposed. In that paper, the contextuality of quantum mechanics is addressed by means of a modal ontology of of type-properties, whose modal nature consists in the fact that they only set the possible case-properties of a quantum system, but not its actual case-properties: a quantum system is conceived as a bundle of type-properties. This view is immune to the challenge represented by contextuality, since the Kochen-Specker theorem imposes no constraint on type-properties but only on the assignment of case-properties. However, in that paper the problem of indistinguishability was only superficially treated. This question has been specifically addressed in a recent work (da Costa, Lombardi & Lastiri 2012), where “identical particles” are indistinguishable because bundles of instances of the same type-properties: to the extent that they are strictly bundles, there is no principle of individuality that permits them to be subsumed under the ontological category of individual. By beginning from atomic bundles (corresponding to irreducible representations of the Galilean group, see Ardenghi, Castagnino & Lombardi 2009, Lombardi, Castagnino & Ardenghi 2010), that last work faces the question of indistinguishability from a bottom-up viewpoint. Nevertheless, from a top-down perspective, the problem of indistinguishability leads us to consider the features of the new “composite” bundle as a whole: it is a structure with an internal symmetry (see Narvaja, Córdoba & Lombardi 2012). Therefore, the resources supplied by logic and mathematics, in particular, the concepts of invariance and rigidity (Krause & Coelho 2005; da Costa & Rodrigues 2007), may be useful to discuss the problem. The purpose of this work is to apply these concepts to the picture of a modal ontology of properties.