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The Metaphysical Mismatch in Modal Interpretations of Quantum Mechanics: Beyond Necessary Equivalence

M. Coelen

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

The measurement problem is one of the major philosophical problems in the Philosophy of Quantum Mechanics. Modal Interpretations of Quantum Mechanics aim to overcome the measurement problem, however, not always without a hitch: other problems arise. That is, some Modal Interpretations claim that a property Q, considered in a subsystem , is a di erent property while considered in the composite physical system , this while both situations are empirically indistinguishable: a non-empirical mismatch ensues. The mismatch, that seems to manifest at the metaphysical level, implies that empirically equivalent propositions like \\the left-hand side of the table is green" (subsystem) and \\the table is green at the left-hand side" (composite system) are metaphysically di erent. Although such a conclusion is clearly at odds with our everyday idea of properties, in my thesis, I question why metaphysical equivalence should (directly) ensue from empirical equivalence. The goal is to provide an explanation why the mismatch can been seen as a correct representation. Furthermore, I question what is exactly ment by metaphysical. As it turns out, under certain circumstances, by using an injective non-surjective function f that sends ordered pairs of operators to quantitative properties, in all possible worlds, the mismatch appears to be a correct representation. Nevertheless, since there are good reasons to renounce the mismatch, I question the level of activity and I invoke a more ne-grained version of metaphysics, i.e hyperintensional metaphysics. A relation between two entities is considered as hyperintensional from the very moment the relation is more ne-grained than necessary equivalence: beyond necessary equivalence. Finally, I claim that the mismatch must be understood in terms of beyond necessary equivalence and should be seen as a correct representation of the relation between language and reality in all hyperintensional worlds.

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The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.

arXiv:quant-ph/0610121•Oct 15, 2006•1 citation
The measurement problem is one of the major philosophical problems in the Philosophy of Quantum Mechanics. Modal Interpretations of Quantum Mechanics aim to overcome the measurement problem, however, not always without a hitch: other problems arise. That is, some Modal Interpretations claim that a property Q, considered in a subsystem , is a di erent property while considered in the composite physical system , this while both situations are empirically indistinguishable: a non-empirical mismatch ensues. The mismatch, that seems to manifest at the metaphysical level, implies that empirically equivalent propositions like \the left-hand side of the table is green" (subsystem) and \the table is green at the left-hand side" (composite system) are metaphysically di erent. Although such a conclusion is clearly at odds with our everyday idea of properties, in my thesis, I question why metaphysical equivalence should (directly) ensue from empirical equivalence. The goal is to provide an explanation why the mismatch can been seen as a correct representation. Furthermore, I question what is exactly ment by metaphysical. As it turns out, under certain circumstances, by using an injective non-surjective function f that sends ordered pairs of operators to quantitative properties, in all possible worlds, the mismatch appears to be a correct representation. Nevertheless, since there are good reasons to renounce the mismatch, I question the level of activity and I invoke a more ne-grained version of metaphysics, i.e hyperintensional metaphysics. A relation between two entities is considered as hyperintensional from the very moment the relation is more ne-grained than necessary equivalence: beyond necessary equivalence. Finally, I claim that the mismatch must be understood in terms of beyond necessary equivalence and should be seen as a correct representation of the relation between language and reality in all hyperintensional worlds.
Starting with a more philosophical review, I discuss how modal interpretations describe reality. Firstly, it is shown that they describe states of affairs which need not be observable. Secondly, I underpin my position that in order to be metaphysically tenable, interpretations need only to satisfy the criteria of Consistency and Internal Completeness. Thirdly, I analyse how properties, states and measurement outcomes are related to one another within the modal descriptions of reality. Finally, I show how modal interpretations recover the standard formulation of quantum mechanics if one defines, in addition to the true states, so-called effective states of systems. Noumenal states of affairs The aim of an interpretation of quantum mechanics is, as I said in the introduction, to provide a description of what reality would be like if quantum mechanics were true. This formulation underlines two aspects of interpretations. Firstly, interpretations intend to construe quantum mechanics in terms of a description of reality and not merely in terms of the outcomes of measurements. Secondly, this description need not be correct. The objective is only to prove that there exists a construal of quantum mechanics which yields an acceptable description of reality. And because it is already difficult enough to give such a proof of existence, it is not (yet) the aim of interpretations to provide the one and only correct description of reality. The above formulation, however, disregards another aspect of interpretations of quantum mechanics, namely that they describe states of affairs which need not always be observable.
In this final part I analyse the modal interpretations from a more philosophical point of view. In Chapter 12 I start by arguing that modal interpretations describe noumenal states of affairs and that therefore metaphysically tenable interpretations need only to meet the criteria of Consistency and Internal Completeness. Then I analyse the relations between properties, states and outcomes of measurements in the modal description of reality. I end by discussing how modal interpretations, when restricted to the description of measurement outcomes, recover the standard formulation of quantum mechanics. Chapter 13 concerns the relations between the properties ascribed to composite systems and subsystems. I show that the property ascriptions of the bi and spectral modal interpretations can be characterised as holistic and non-reductionistic, whereas the property ascription of the atomic modal interpretation is non-holistic and to a large extent reductionistic. I argue that notwithstanding the lack of reductionism, the bi and spectral modal interpretations are empirically adequate and metaphysically tenable. I also discuss the possibility of saving the metaphysical tenability of the atomic modal interpretation by taking holistic properties as dispositional properties. In Chapter 14 I give a survey of the possibilities and impossibilities of modal interpretations and in Chapter 15 I end with general conclusions.
This article sits at a point of intersection between the philosophy of physics and the metaphysics of modality. There are clear similarities between Everettian quantum mechanics and various modal metaphysical theories, but there have hitherto been few attempts at exploring how the two topics relate. In this article, I build on a series of recent papers by Wilson ([2011], [2012], [2013]), who argues that Everettian quantum mechanics’ connections with traditional modal metaphysics are vital in defending it against objections. I show that Wilson’s preferred version of Everettian quantum mechanics has two problems. First, it is unable to account for the contingency of various intuitively contingent modal claims. Second, it fails to yield intuitive truth values on modal claims about the number of branches in a given Everettian multiverse. Since modal claims about branch number are instrumental in decision-theoretic solutions to Everettian quantum mechanics’ problem(s) with probability, this second problem has wider dialectical implications. I suggest amendments to the underlying metaphysics that overcome these problems. The result is a more robust version of Everettian quantum mechanics.
In this essay I make use of the resources of ‘naturalized ontology’ in order to determine what quantum mechanics implies about answers to fundamental metaphysical questions. Naturalized ontology is a methodology for metaphysics influenced by the philosopher Willard Van Orman Quine which makes explicit reference to our best scientific theories in order to answer questions which have traditionally been reckoned to belong solely to the realm of philosophy such as ‘What is the nature of reality in the most general sense?’ Quantum mechanics faces a unique interpretational problem known as the ‘measurement problem’ which makes determining the answer to such general metaphysical questions on this view especially problematic; nevertheless, naturalized ontology interprets and evaluates the various responses to this problem via measures of ‘theoretical virtue’, and ultimately concludes that the best interpretation of quantum mechanics—and thus reality—is absurd.
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.
The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties.