The contextual and modal character of quantum mechanics : a formal and philosophical analysis in the foundations of physics

Abstract

This doctoral dissertation contains four main elements:

1. We put forward an interpretational map of quantum mechanics in general and of the modal interpretation in particular based on metaphysical and anti-metaphysical stances.

2. In contraposition to what we characterize as the anti-metaphysical and classical metaphysical

stances we collect arguments in favor of a constructive metaphysical stance.

3. We analyze the meaning of contextuality and possibility in quantum theory in general, and in the modal interpretation in particular.

4. Finally, we end up with a proposal for the development of a possible constructive metaphysical scheme based on the notion of potentiality.

Although some of these problems are well known in the literature we attempt to cast new light on the discussion through the analysis of the concepts involved and their relation to the formalism. We attempt to make explicit the tension in between the theoretical conditions and the conceptual structure of the theory, in order to discuss and disclose the metaphysical ideas involved within the different interpretational problems of quantum mechanics. We believe that this analysis can help us to understand much of the implicit background of such theoretical conditions.

The dissertation centers itself on the modal and contextual character of quantum mechanics. On the one hand, we discuss the contextual character of quantum possibility through the development of a Modal Kochen-Specker theorem, and on the other hand, we analyze the contextual character of quantum correlations through the distinction of properties. In the last part we discuss some more speculative ideas related to the possible metaphysical developments of quantum mechanics based on the notion of potentiality.