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arXiv:0705.1660

The Contextual Character of Modal Interpretations of Quantum Mechanics

Graciela Domenech, Héctor Freytes, Christian DE RONDE

Published May 11, 2007• 2 citations
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Abstract

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.

DOI
10.48550/arxiv.0705.1660

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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.
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.
We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
Many world interpretations (MWIs) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MIs) which state that quantum mechanics does not provide an account of what “actually is the case,” but rather deals with what “might be the case,” i.e., with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why—even though both interpretations share the same formal structure—MI fall pray of Kochen–Specker-type contradictions while MWI escape them.