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Abstract
David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the world supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws.
Notes
1 Roughly, an individual's intrinsic properties are ones that, in contrast to extrinsic or relational properties, are logically and metaphysically independent of other, wholly distinct individuals [Lewis Citation1983].
2 I take ‘traditional’ reductionism to treat the intrinsic properties of wholes as supervening on the intrinsic properties and arrangements of parts. I am not directly concerned with attempts at part-on-whole ‘reduction’, in which some wholes are taken to be more fundamental than their supervening parts—as in, for instance, CitationSchaffer [2010].
3 CitationTeller [1989: 214] puts it this way: ‘Unless one takes a starkly instrumentalist attitude toward quantum theory, quantum theory tells us … that we must endorse what I call Relational Holism’, the thesis that there are non-supervening entanglement relations. Schaffer endorses the non-supervenience described in Metaphysical Holism and cites Lewis's Humean supervenience as a contemporary example of the ‘Democritean pluralism’ that ‘cannot provide an adequate basis for entangled systems’ [2010: 53]. Richard Healey is more measured in his assessment of the quantum threat to reductionism. He points out that a hidden variables theorist might avoid holism, but he does not fill in the details—and he seems to think that the Bohmian interpretation fails to count as a version of realism about quantum mechanics ‘itself’ [1991: 417fn].
4 To every vector there corresponds a projection operator onto the one-dimensional subspace (or ray) spanned by that vector. We thus can swap our formal representation by vectors with a representation in terms of projection operators, with the advantage that we can expand the mathematical space of representations to include not only projection operators (familiar pure states) but weighted sums of projection operators—with the weights non-negative real numbers adding up to one. These density matrices equip us to formally represent the states of individual entangled particles [Hughes Citation1989: 136–49].
5 CitationMaudlin [2007] focuses his presentation of the non-separability argument on spin states. While I am drawing on his example of particles entangled with respect to spin, I have offered a formulation of the argument that speaks in terms of wave functions in general, rather than focusing only on spin states in particular, since spin will play a less central role in the coming discussion of Bohmian mechanics (§3). Nothing deeper hinges on my choice.
6 Maudlin's [2007: 55–60] singlet pair has spin state, (1/√2)|z↑>l|z↓>r – (1/√2)|z↓>l|z↑>r, and his corresponding triplet pair has state (1/√2) |z↑>l|z↓>r + (1/√2)|z↓>l|z↑>r. There is some direction, x (in particular, with |z↑> = (1/√2)|x↑> + (1/√2)|x↓> and |z↓> = (1/√2)|x↑> – (1/√2)|x↓>), such that, when we express the singlet and triplet states in terms of x-spin, we see that we should expect differing pairwise outcomes on x-spin measurements. The singlet state becomes (1/√2) |x↓>ll|x↑>r – (1/√2)|x↑>l|x↓>r, and the triplet state becomes (1/√2) |x↑>l|x↑>r − (1/√2)|x↓>l|x↓>r.
7 There is a debate among holists as to the philosophical import of these non-supervening relations. Some, such as CitationTeller [1989], take entangled pairs to be made up of fundamental particles connected by an entanglement relation. Others may take pairs to be more fundamental, understanding individual particles as derivative aspects. CitationSchaffer [2010] thinks of the entire cosmos as the single most fundamental object, and treats all cosmic subsystems as derivative.
8 Thanks to Bradford Skow for mentioning the case of velocity boost.
9 Granted, (i) is stronger than the holist needs. He needs claim only that the (type-c) difference in the wave functions of singlet and triplet pairs marks a difference in their intrinsic properties. I take (i) to reveal the more general presupposition behind this particular claim. The Bohmian profiled here will deny (i) and deny that there is a difference in the intrinsic properties of our particular singlet and triplet pairs.
10 This assumption makes the argument much cleaner but is not necessary; without it, one can arrive at the same conclusion by adding premises to the effect that the intrinsic properties of non-point-sized particles are to supervene on the intrinsic properties of and spatio-temporal relations among their point-sized parts.
11 For a detailed exposition of Bohmian mechanics, see CitationDürr, Goldstein, and Zanghì [1992]; for a helpful general overview, see Dürr, CitationGoldstein, Tumulka, and Zanghì [2009]. I draw on both of these here.
12 Since the Bohmian theory supplements the quantum wave function with particle positions, the standard specification of a system's wave function is an under-specification of the system's state. However, a consequence of the Bohmian account is that we, as epistemic agents, are unavoidably ignorant of any information about a system that is not in a sense already contained within the wave function of that system [Dürr, Goldstein, and Zanghì Citation1992].
13 Particle masses may also be intrinsic according to the Bohmian, in which case facts about particle masses can count among the fundamental facts as well.
14 A clarification concerning the way in which at least Bohmian particles—if not the pilot wave—seem to be at home in a separable metaphysics: the Bohmian has a mosaic or field of points of space-time of a sort that Lewis describes. Then facts about particles can bottom out in facts about patterns in the points’ intrinsic states of ‘occupation’ or ‘unoccupation’, or we can add to the space-time points particles that can stand in occupation relations to points based on their spatio-temporal arrangement.
15 For the most part I use ‘pilot wave’ or ‘guiding wave’ when talking about some physical thing described by the mathematical universal wave function. Confusingly, it is common in this sort of discussion to use ‘universal wave function’ to name both the mathematical and the physical things.
16 Esfeld and his co-authors suggest that Bohmian mechanics may be combined with a Humean account of laws, but it is not clear from their discussion exactly how they expect this to go and, especially, whether they take this to be a realist treatment of the Bohmian pilot wave. My proposal may be read as a suggestion in a similar Humean spirit, one that fleshes out a (distinct, explicitly realist) Humean treatment of the pilot wave by way of an analogy to a Humean account of objective chance and that offers this treatment as a response to the non-separability argument. Thanks to Zee Perry, who, along with Harjit Bhogal, has been developing a similar Humean treatment of entanglement, for helpful comments encouraging me to distinguish between the present proposal and the sort of nomological account mentioned by Esfeld and his co-authors.
17 Thanks to Hartry Field and Ned Hall (who also suggested the narcissist case) for pressing this concern.
18 I am indebted to Ned Hall for many helpful discussions about this paper and its contents. I am grateful, also, to Sharon Berry, Harjit Bhogal, Meghan Dupree, John Heil, Barry Loewer, Richard Moran, Zee Perry, Mark Richard, Bradford Skow, Zeynep Soysal, members of the Harvard M&E Workshop, participants in the 2013 Columbia–NYU Graduate Conference in Philosophy, and anonymous reviewers from the LMU-Munich 2013 Foundations of Physics Conference and from this Journal.
