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La Bohume

Abstract

This paper critically assesses whether quantum entanglement can be made compatible with Humean supervenience. After reviewing the prima facie tension between entanglement and Humeanism, I outline a recently-proposed Humean response, and argue that it is subject to two problems: one concerning the determinacy of quantities, and one concerning its relationship to scientific practice.

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Notes

  1. Lewis (1994, p. 474).

  2. Teller (1986), Maudlin (2007).

  3. To be strictly accurate, there are good reasons for thinking that Humean supervenience, at least on the letter of the above, is inconsistent with classical physics. However, one can get around this by (roughly speaking) taking “local qualities” to be intrinsic properties of infinitesimally small spacetime regions, rather than spacetime points per se (see Butterfield 2006). I will ignore this subtlety for the purposes of this essay.

  4. Esfeld (2014) claims that the proposed rescue of Humean Supervenience is available to any “primitive-ontology” approach to quantum mechanics, not just Bohmian mechanics. It’s not my intention to examine this claim in this essay: in the interests of brevity, I will focus on the specific case of Bohmianism (though see fn. 11).

  5. See e.g. Loewer (1996), Albert (1996).

  6. Darby (2012).

  7. My presentation of Bohmian mechanics here follows that of Dürr et al. (1992) and Dürr and Teufel (2009).

  8. That said, we will later touch upon relativistic quantum mechanics, where (as a referee observed) spin is more essential. So what I really mean here is that although I only explicitly discuss spinless particles, extending the analysis to particles with spin should not pose any problems of principle.

  9. Miller (2014), Callender (2015), Bhogal and Perry (2017), Esfeld et al. (2014). Dickson (2000) also prefigures some of the relevant ideas.

  10. That is, the spin quantum number of the particles; not the projection of the spin along some axis, which cannot plausibly be interpreted as a property of the particle rather than the wavefunction (see e.g. Dürr and Teufel 2009, §8.4).

  11. Note that doing so is not entirely straightforward: see Brown et al. (1996). Esfeld (2014) observes that other primitive ontologies could be used to provide alternative austere supervenience bases; it’s not so clear that other primitive ontologies are so amenable to forming the richer bases discussed here, however. For example, if the mass of a particle is to be localised by being taken as a property of the particle, then the primitive ontology for that particle will have to be a point-sized occupant of some spatial point (at each time), as is the case in Bohmian mechanics. In GRWm or GRWf, by contrast, the primitive ontology of the particle is either a region-sized occupant, or else a point-sized occupant of multiple spatial points at each time (and in the case of flashes, sometimes an occupant of no point)—so treating mass as a property of a particle with that primitive ontology would not mean that mass was a local quality.

  12. Bhogal and Perry (2017) use a best system which postulates a space Q (with the structure of \(X^N\)) and a particle \(\omega \) moving around within Q (whose location at any time is exactly correlated with the configuration of the N particles); the wavefunction is then postulated as a function assigning a complex number to each point of Q, which then acts on \(\omega \) via the guidance equation. If Q here is intended to simply be defined as \(X^N\) (i.e., as the space consisting of N-tuples of points of X), then I take their system and this system to be essentially the same. If not—that is, if the idea is to stipulate Q’s structure separately and then put it into appropriate correspondence with N-tuples of points of X—then it seems to me that the system outlined here will be considerably simpler, at no cost in strength. (I’m grateful to Zee Perry for discussion of this point.)

  13. See Dürr et al. (1992) for a more detailed discussion of the role of the QEH in Bohmian mechanics. I assume that the Bohumean should include the QEH in the best system, given the role that it plays in the deriving the Born rule within Bohmian mechanics; I thank an anonymous referee for suggesting it.

  14. Presumably, this will involve understanding probabilities in a Humean fashion; as a referee pointed out, this will plausibly require expanding the criteria for best-system-hood to include fit. I will put this complication aside.

  15. Callender, in particular, discusses this in detail.

  16. If the wavefunction \(\Psi \) did refer to anything in the basis, then we would instead be dealing with something like the Albert/Loewer/Darby strategy.

  17. Albeit one which—as they observe—is prefigured by Lewis (1994)’s discussion of chance, and Hall (2009)’s discussion of mass and charge.

  18. Bhogal and Perry (2017, p. 78).

  19. Huggett (2006, p. 50).

  20. Stevens (2015), Stevens (2017).

  21. Pooley (2013).

  22. Brown (2005), Brown and Pooley (2006).

  23. Slightly more carefully, which agree on an arbitrarily small region around that trajectory.

  24. My presentation of this example follows Belot (2011), although the example goes back (at least) to Einstein (1953): see Myrvold (2003).

  25. Thanks to a referee for stressing this. In principle, the Bohumean could choose to deny that the best system asserts the wavefunction to be determinate (by omitting the claim 3, that the wavefunction takes the form of a complex-valued field on spacetime, from their best system). But the wavefunction would then be a vague and indeterminate sort of thing; and this looks to be in tension with Bohumeanism’s pretensions to be a means of reconciling a commitment to locality with realism about quantum mechanics.

  26. Given that the best system includes the QEH, it is already bound to impose some constraints on admissible wavefunctions beyond mere consistency with the supervenience basis: for instance, this will rule out any wavefunction with a zero at the actual location of the Bohmian particles. (Thanks to a referee for this observation.) In general, though, it remains the case that there are several wavefunctions consistent with the particles’ actual trajectories and the QEH.

  27. See, in particular, Dürr et al. (1997) and Callender (2015) for defences of the claim that the wavefunction may be considered lawlike.

  28. Albert (2015, p. 23).

  29. Hall (2015, §17.5.2) also discusses this problem. One can amend the best-systems account to get around this, either by adjusting the criteria for a system’s being “best”, or by insisting that only certain kinds of statements in the best system (e.g. general statements) count as lawlike. But the onus will be on the Humean to explain why the modified account is preferable to the original, if this is not to be a merely ad hoc fix.

  30. Huggett (2006, §3.2).

  31. Huggett (2006, p. 60).

  32. Huggett (2006, p. 70). Of course, it is true quite generally that the laws alone fail to determine the values of quantities: the point here is that the laws together with the facts about the supervenience basis should determine the values of the supervenient quantities (as is the case for regularity relationalism, but not for Bohumeanism).

  33. Lewis (1983, p. 367).

  34. Lewis (1986, p. 123).

  35. The first guiding idea is the proposal that the relevant standards are, in particular, those of simplicity and strength. Hall argues convincingly that we should take the second guiding idea as the core proposal, with the first guiding idea being a substantive (epistemic-cum-sociological) proposal about what the standards of science in fact are.

  36. Hall (2015, p. 266).

  37. Huggett (2006, p. 48).

  38. “[...] in physics the only observations we must consider are position observations, if only the positions of instrument pointers.” (Bell 1987, p. 166).

  39. Of course, even our knowledge of the probability densities is somewhat indirect. But the point being made here is just that it is nevertheless more direct than whatever knowledge we might have about trajectories.

  40. Huggett (2006, p. 49).

  41. See Wallace (2016).

  42. My thanks to an anonymous referee for raising this concern.

  43. Indeed, in the literature on the philosophy of quantum mechanics one sometimes sees the view that orthodox quantum mechanics is so muddled and incoherent as to fail to have any content at all—which would surely guarantee that it is not the best system, regardless of whether scientists have adopted it or not. But this just seems to me to be a reason to be very sceptical of that claim about the content of orthodox quantum mechanics; indeed, one of the most striking features of quantum physics is the extraordinary empirical success it has enjoyed despite the absence of any widely agreed account of its foundations. Compare the discussion in Wallace (2012) of the role decoherence plays in making the measurement problem “a philosophical rather than a practical problem” (p. 4586).

  44. Bhogal and Perry (2017, p. 91).

  45. I’m grateful to an anonymous referee for this way of formulating the argument, and for suggesting that Bhogal and Perry should be interpreted as making this argument rather than the direct argument.

  46. See Struyve (2010) for a survey.

  47. I thank a referee for pressing me on this point.

  48. See Maudlin (2007) for a particularly biting critique.

  49. That is, according to those accounts of quantum mechanics in which there are non-local physical phenomena.

  50. Indeed (as a referee to this paper pointed out), it is precisely such aggregation that Humeans rely upon to make sense of the notion of patterns in the mosaic.

  51. This isn’t to say that locality isn’t still desirable, and worth pursuing where there is not a significant cost to so doing; it is just that we should not contort ourselves or our theories in order to obtain it.

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Acknowledgements

I’m very grateful to Harjit Bhogal, John Dougherty, Niels Martens, Elizabeth Miller, Zee Perry, Chip Sebens, David Wallace and several anonymous referees, for discussion and comments on previous drafts. I’m also grateful to George Darby for his patience in the editorial process for this manuscript. This work was supported by an AHRC Doctoral Studentship (Grant No. 1336589), and latterly by a Procter Fellowship.

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Dewar, N. La Bohume. Synthese 197, 4207–4225 (2020). https://doi.org/10.1007/s11229-018-1800-1

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Keywords

  • Humean supervenience
  • Quantum entanglement
  • Quantum mechanics