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Constructive Empiricism, Partial Structures and the Modal Interpretation of Quantum Mechanics

Otávio Bueno

Published Jan 14, 2014• 24 citations

Abstract

Van Fraassen's modal interpretation of non-relativistic quantum mechanics is articulated to support an anti-realist account of quantum theory. However, given the particular form of van Fraassen's anti-realism (constructive empiricism), two problems arise when we try to make it compatible with the modal interpretation: one difficulty concerns the tension between the need for modal operators in the modal interpretation and van Fraassen's skepticism regarding real modality in nature; another addresses the need for the truth predicate in the modal interpretation and van Fraassen's rejection of truth as the aim of science. After examining these two problems, I suggest a formal framework in which they can be accommodated – using da Costa and French's partial structures approach – and indicate a variant of van Fraassen's modal interpretation that does not face these difficulties. Quanta 2014; 3: 1–15.

DOI: 10.12743/quanta.v3i1.19

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Van Fraassen's modal interpretation of non-relativistic quantum mechanics is articulated to support an anti-realist account of quantum theory. However, given the particular form of van Fraassen's anti-realism (constructive empiricism), two problems arise when we try to make it compatible with the modal interpretation: one difficulty concerns the tension between the need for modal operators in the modal interpretation and van Fraassen's skepticism regarding real modality in nature; another addresses the need for the truth predicate in the modal interpretation and van Fraassen's rejection of truth as the aim of science. After examining these two problems, I suggest a formal framework in which they can be accommodated – using da Costa and French's partial structures approach – and indicate a variant of van Fraassen's modal interpretation that does not face these difficulties. Quanta 2014; 3: 1–15.

Bas van Fraassen in [4] has recently tried to use modal logic to solve the measurement problem of quantum mechanics. His model is based on a method of expressing quantum states developed by Hugh Everett [1] called the “relative state formulation.” Unfortunately, Everett's mathematics cannot be generalized as van Fraassen requires. The difficulty itself is elementary enough. But a revision of van Fraassen's postulates (such as the one he adopted on p. 341 after he had been told of the problem) can save the mathematics only on pain of making the whole study irrelevant to the physics. I shall explain the dilemma in this note. In a later paper [5], van Fraassen avoids this dilemma by developing an abstract modal interpretation which does not rely on any expression for quantum states.

Although there has been some discussion in the literature of Bas van Fraassen's modal interpretation of Quantum Mechanics, it has for the most part been concentrated on difficulties that van Fraassen's viewpoint shares with those of some other authors, including Kochen, Dieks, and Healey. van Fraassen's approach has, however, some problems of its own; in this note we want to focus on what seems to us to be one of the most serious of these. The difficulty concerns immediately repeated non-disturbing measurements of the same observable on a single system. As is well known, von Neumann's Projection Postulate guarantees that such measurements will always give the same outcome; likewise, in the approaches of the “modalists” mentioned above, such ‘consilience of repeated measurements’ is in one way or another built into the formalism. By contrast, we shall argue, van Fraassen's modal interpretation neither guarantees this result nor adequately explains why it is unnecessary to do so.

In the present paper I describe a general formal semantic scheme for the interpretation of quantum mechanics (QM) , and on the basis of this scheme I examine the modal interpretation of QM — both the Copenhagen and the anti-Copenhagen variants — proposed by van Fraassen [19, 20, 21], This is intended to be a fragment of a larger work [12] which additionally investigates a number of closely related interpretations, including ones proposed by Bub and Demopoulos [1, 2, 3, 4], Fine [5, 6], and Krips [16, 17]. Formal semantically speaking (see, e.g., Thomason [18]), a logic L may be characterized as an ordered pair <SYN,SEM>, where SYN is the underlying syntax (language) of L, and SEM is the semantics of L, which consists of a class of semantic assignments on SYN.

Two conceptions of the contemporary philosophy of science are taken under consideration: scientific realism and constructive empiricism. Scientific realism presupposes 1) the conception of truth as the correspondence of knowledge to reality, 2) the real existence of entities postulated by a theory. The constructive empiricism puts forward the idea of empirical adequacy: science aims to give us the theories which are empirically adequate and acceptance of the theory involves as belief only that it is empirically adequate. To compare methodological resources of these two positions in the philosophy of science the problem of the interpretation of quantum mechanics is involved. As a methodological realization of scientific realism the ensemble interpretation of quantum mechanics is taken under consideration. K.Popper’s version