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Van Fraassen's Modal Interpretation of Quantum Measurement

Wan Xiao-lon

Published Jan 1, 2002• 0 citations
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Abstract

B. C. van Fraassen s Modal Interpretation of Quantum Mechanics is not only the core of his philosophy of Quantum Mechanics, but also the thinking fundament in his philosophy of science, constructive experimenta-lism. In this article, the author introduces van Fraassen's Modal Interpretation of Quantum Measurement from these aspects: interpretation problems of Quantum Mechanics, the main content of Modal Interpretation, and the significance of Modal Interpretation.

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B. C. van Fraassen s Modal Interpretation of Quantum Mechanics is not only the core of his philosophy of Quantum Mechanics, but also the thinking fundament in his philosophy of science, constructive experimenta-lism. In this article, the author introduces van Fraassen's Modal Interpretation of Quantum Measurement from these aspects: interpretation problems of Quantum Mechanics, the main content of Modal Interpretation, and the significance of Modal Interpretation.
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.
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.
There is no such thing as “The Quantum Logical Interpretation of Quantum Mechanics”. Rather, there is a cluster of interpretations, all of which can be described as “quantum logical”. Here I provide a general framework for discussing interpretations of this kind, and then locate various suggestions within it. The presentation owes much to van Fraassen (see, in particular, van Fraassen 1974 ); his “modal interpretation” is one of those I discuss, along with those of Jauch, Putnam and Kochen. I begin by rehearsing some orthodox quantum theory. Within quantum mechanics we deal with a set 0 of measurable quantities, orobservables(position, momentum, components of spin and so on). Experiment can determine the value of an observable for a given system: the values so determined will be real numbers. A maximal amount of information about what the result would be for a given system, whatever experiment we chose to perform on it, is available once we know thestateof the system.