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A Note on Van Fraassen's Modal Interpretation of Quantum Mechanics

Published online by Cambridge University Press:  01 April 2022

Stephen Leeds  and
Richard Healey
Stephen Leeds*
Affiliation:
Department of Philosophy University of Colorado
Richard Healey
Affiliation:
Department of Philosophy University of Arizona
*
†Send reprint requests to S. Leeds, Department of Philosophy, University of Colorado-Boulder, 169 Hellems, Campus Box 232, Boulder, CO 80309.
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Extract

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.

Type
Research Article
Information
Philosophy of Science , Volume 63 , Issue 1 , March 1996 , pp. 91 - 104
Copyright
Copyright © 1996 by the Philosophy of Science Association

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References

1 In van Fraassen, Bas C. Quantum Mechanics: An Empiricist View; Oxford: Clarendon Press, 1991.

2 Dieks, D. “Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior”, Physical Review A, 49 (1994): 2290–2300; Healey, R. The Philosophy of Quantum Mechanics: an Interactive Interpretation; Cambridge: Cambridge University Press, 1989; Kochen, S. “A New Interpretation of Quantum Mechanics”, in Lahti, P. and Mittelstaedt, P. (eds.), Symposium on the Foundations of Modern Physics 1985; Singapore: World Scientific, 1985.

3 There is, a referee urges, yet another possible reading. To quote the referee: “… what vF is saying here is that the answer to a question regarding the outcomes of the first two measurements can be predicted if we consider the question to be about a third measurement situation which determines whether the first two agreed. In that sense vF can talk about the probability of two measurements agreeing but only within the confines of the theory itself which gives us only probabilities of measured outcomes.”

It is of course true that, if by ‘QM’ one means only the linear QM dynamics together with the algorithm for assigning probabilities to measurement outcomes, then the only way QM can give the answer to a question about consilience of measurement outcomes is to make a prediction about the result of a third measurement. But QM, thus conceived, should be carefully distinguished from what van Fraassen is trying to present, namely, an interpretation of QM: that is, a story about what actually happens in the world which, if true, would show us what underlies the predictive success of QM. QM, conceived only as a predictive instrument, can make no distinctions between ‘The measurements agreed!’ and ‘The agreement-measurement says Yes!’, but a given interpretation of QM may well allow us to make this distinction. And van Fraassen's is exactly such an interpretation: since it speaks of systems as possessing definite values as various times for various observables, it gives us enough ideology to pose the question, whether or not it is generally the case that on occasions where the agreement-measurement says Yes, the same value was in fact possessed by both systems (and the same value was read on both measurement devices). What we argue in the text is that, having given sense to this question, van Fraassen's interpretation is then obliged to answer it.

4 van Fraassen, Bas C. The Scientific Image; Oxford: Oxford University Press, 1980.

5 In his ‘The Einstein-Podolsky-Rosen Paradox’, Synthese 29(1974): 291–309.

6 Leggett discusses these in his “Quantum Mechanics at the Macroscopic Level”, in The Lesson of Quantum Theory, J. de Boer, E. Dal and O. Ulfbeck (eds.); Amsterdam: Elsevier Science Publishers B. V. (1986) and elsewhere.

7 The results of one impressive recent quantum tunnelling experiment are reported in Martinis, J. M., Devoret, M. H. and Clarke, J. “Experimental Tests for the Quantum Behavior of a Macroscopic Degree of Freedom: the Phase Difference Across a Josephson Junction”, Physical Review B, 35 (1987): 4682–4698. In this particular experiment, the role of ‘position’ variable was played by the phase difference across a Josephson junction rather than the approximate flux through a SQUID ring.

8 Coleman does offer a derivation of the Born rules in the style of Hartle and others. However, he offers this not to show why measurement outcomes actually conform to these rules (on his view there are no outcomes of non-trivial measurements!), but rather to explain why our own quantum nature inevitably makes us think they do. Unfortunately, it is hard to see how any such derivation can account for the fact that what we take to be our experiences of relative frequencies of outcomes in finite sequences of non-trivial quantum measurements squares so well with the Born rules.

9 Our argument against (B) leaves a few small openings through which van Fraassen might choose to slip. The heart of our argument is the claim that, if we were in the position of just having repeated an “interesting” measurement, then our usual procedure in the case of single measurements would compel us to trust our apparent recollection that the two measurements had exhibited consilience, and we would then need to account for this consilience. One might agree to all this, but deny that we are thereby committed to saying that if in fact there are, or will be, such measurements, then they did or will exhibit consilience: there is a gap between ‘If I believed P, I would then believe Q’ and ‘If P then Q’. Our suspicion is that van Fraassen would not wish to take advantage of this gap; it is too similar to gaps which, in other contexts, he does want to bridge.

However, there remains another gap: it is possible to accept our argument, deny that there have been or ever will be any repeated “interesting” measurements, and refuse to believe that if there had been any such measurements, they would have exhibited consilience. Indeed, a committed empiricist might claim not even to understand the counterfactual in the last claim, prior to settling on an interpretation of quantum mechanics. This is not a very attractive position: if one takes this line, one would have to hope that all the experimentalists who we take to be at least close to the goal of performing repeated “interesting” measurements of a quantum observable will never succeed, since it is clear that if they do achieve this goal, the reported result will be consilience. But the gap is there, and it may take some more experimental results to close it.