The metaphysics of quantum mechanics: Modal interpretations

Christian DE RONDE, Wim Christiaens

Bas C. van Fraassen

Christian DE RONDE

In this paper we discuss the relation of quantum theory to the problem of metaphysics.Based on metaphysical and anti-metaphysical stances, we put forward an 'interpretational map' of quantum mechanics in general and of the modal interpretation in particular.Thus, within the modal interpretation, we distinguish between: Modal Interpretations (which start from) the Mathematical Formalism (MIMF) and Modal Interpretations (which start from) Metaphysical Principles (MIMP).Finally, we argue for a middle path in between metaphysical principles and the formal conditions imposed on quantum mechanics.

Guido Bacciagaluppi

Christian DE RONDE

This doctoral dissertation contains four main elements: \n \n1. 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. \n \n2. In contraposition to what we characterize as the anti-metaphysical and classical metaphysical \n \nstances we collect arguments in favor of a constructive metaphysical stance. \n \n3. We analyze the meaning of contextuality and possibility in quantum theory in general, and in the modal interpretation in particular. \n \n4. Finally, we end up with a proposal for the development of a possible constructive metaphysical scheme based on the notion of potentiality. \n \nAlthough 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. \n \nThe 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.

Vladislav Terekhovich

Some interpretations of quantum mechanics use notions of possible states and possible trajectories. I investigate how this modal approach correlates with several metaphysical conceptions of a transition from potential to actual existence. The comparison is based on a discussion in contemporary analytical metaphysics of modality. I also consider an analogy between Leibniz's theory of the possibilities striving towards existence, wave mechanics of Schrodinger, and Feynman path integral.