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arXiv:quant-ph/9909071 · The British Journal for the Philosophy of Science

Counting Marbles with 'Accessible' Mass Density: A Reply to Bassi and Ghirardi

R. Clifton, Bradley Monton

Published Mar 1, 2000• 22 citations

Abstract

In a previous article (cf. quant-ph/9905065) we argued that, while Lewis is correct that the enumeration principle fails in dynamical wavepacket reduction theories, one need not following Lewis in rejecting these theories. Because the dynamical reduction process itself prevents the failure of enumeration from ever becoming manifest, and because one can treat the semantics for dynamical reduction theories as not adding anything of ontological import to them, it is reasonable to accept these theories notwithstanding Lewis's counting anomaly. In their response to our paper (cf. quant-ph/9907050), Bassi and Ghirardi reject our criticisms of their own response to Lewis, as well as our argument against Lewis that dynamical reduction precludes failures of enumeration from ever becoming manifest. Our intention here is to demonstrate that Bassi and Ghirardi's responses to us do not succeed.

DOI: 10.1093/bjps/51.1.155

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•Jan 1, 2002•0 citations

In a previous article (cf. quant-ph/9905065) we argued that, while Lewis is correct that the enumeration principle fails in dynamical wavepacket reduction theories, one need not following Lewis in rejecting these theories. Because the dynamical reduction process itself prevents the failure of enumeration from ever becoming manifest, and because one can treat the semantics for dynamical reduction theories as not adding anything of ontological import to them, it is reasonable to accept these theories notwithstanding Lewis's counting anomaly. In their response to our paper (cf. quant-ph/9907050), Bassi and Ghirardi reject our criticisms of their own response to Lewis, as well as our argument against Lewis that dynamical reduction precludes failures of enumeration from ever becoming manifest. Our intention here is to demonstrate that Bassi and Ghirardi's responses to us do not succeed.

Peter Lewis ([1997]) has recently argued that the wavefunction collapse theory of GRW (Chirardi, Rimini and Weber [1986]) can only solve the problem of wavefunction tails at the expense of predicting that arithmetic does not apply to ordinary macroscopic objects. More specifically, Lewis argues that the GRW theory must violate the enumeration principle: that 'if marble 1 is in the box and marble 2 is in the box and so on through marble n, then all n marbles are in the box' ([1997], p. 321). Ghirardi and Bassi ([1999]) have replied that it is meaningless to say that the enumeration principle is violated because the wavefunction Lewis uses to exhibit the violation cannot persist, according to the GRW theory, for more than a split second ([1999], p. 709). On the contrary, we argue that Lewis's argument survives Ghirardi and Bassi's criticism unscathed. We then go on to show that, while the enumeration principle can fail in the GRW theory, the theory itself guarantees that the principle can never be empirically falsified, leaving the applicability of arithmetical reasoning to both micro- and macroscopic objects intact.

A few years ago, I argued that according to spontaneous collapse theories of quantum mechanics, arithmetic applies to macroscopic objects only as an approximation. Several authors have written articles defending spontaneous collapse theories against this charge, including Bassi and Ghirardi, Clifton and Monton, and now Frigg. The arguments of these authors are all different and all ingenious, but in the end I think that none of them succeeds, for reasons I elaborate here. I suggest a fourth line of response, based on an analogy with epistemic paradoxes, which I think is the best way to defend spontaneous collapse theories, and which leaves my main thesis intact.

The aim of this article is twofold. Recently, Lewis has presented an argument, now known as the "counting anomaly", that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that the composition principle, which holds true in standard quantum mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of such interpretations. Once this flaw is uncovered, the anomaly vanishes.

The aim of this paper is two-fold. Recently, Lewis has presented an argument, now known as the `counting anomaly', that the spontaneous localization approach to quantum mechanics, suggested by Ghirardi, Rimini, and Weber, implies that arithmetic does not apply to ordinary macroscopic objects. I will take this argument as the starting point for a discussion of the property structure of realist collapse interpretations of quantum mechanics in general. At the end of this I present a proof of the fact that the composition principle, which holds true in Standard Quantum Mechanics, fails in all realist collapse interpretations. On the basis of this result I reconsider the counting anomaly and show that what lies at the heart of the anomaly is the failure to appreciate the peculiarities of the property structure of collapse interpretations. Once this flaw is uncovered, the anomaly vanishes.