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Quantum monism: an assessment

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Monism is roughly the view that there is only one fundamental entity. One of the most powerful argument in its favor comes from quantum mechanics. Extant discussions of quantum monism are framed independently of any interpretation of the quantum theory. In contrast, this paper argues that matters of interpretation play a crucial role when assessing the viability of monism in the quantum realm. I consider four different interpretations: modal interpretations, Bohmian mechanics, many worlds interpretations, and wavefunction realism. In particular, I extensively argue for the following claim: several interpretations of QM do not support monism at a more serious scrutiny, or do so only with further problematic assumptions, or even support different versions of it.

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  1. A different, yet related argument is presented in Ismael and Schaffer (2016: §3.2.2). Such an argument deserves an independent scrutiny. Relevantly, it also addresses some of the issues I raise in this paper—especially those I deal with in Sect. 3. Ismael and Schaffer suggest two different fundamental ontologies for QM that would be consistent with their basic idea of “common ground explanation”: Spacetime State Realism—the view that the fundamental ontology is that of the whole spacetime bearing a density operator, and Wave Function Realism. I address the latter in Sect. 3.4.

  2. Only the dependence relation is crucially taken to be well-founded. The so called Gunk Argument for priority monism depends upon considering non-well founded mereological structures.

  3. He challenges these assumptions himself in Schaffer (2012a).

  4. For more details see, e.g. Schaffer (2010: 50–57).

  5. The following passage should help grasping what minimal realism about the quantum state amounts to: “Standard quantum mechanics assigns to physical systems—single particles or collections of particles—formal representations, wave functions, in mathematical (Hilbert) spaces. The elements of, or vectors in, such a space yield, according to the standard statistical algorithm of quantum theory, functions from possible measurement outcomes to probabilities. To say that a particle has some wave function, or is properly represented by some vector in a given space, is, at least, to say something about how it is likely to behave in certain experimental settings. In so far as we think that a system’s probabilistic experimental dispositions manifest some underlying physical states, we also may take ourselves to be describing the particle’s real physical properties by associating it with a wave function” (Miller 2013: 570).

  6. I use ‘determine’ intentionally, so as not to take any stance towards any particular account of such determination relation. It was customary to cash this out in terms of supervenience. Recently it has been suggested that we should use a stronger notion such as e.g. grounding.

  7. The following is a mathematically precise and concise way to put all this: the Cartesian product space is a proper subset of the tensor product space used to describe the composite system.

  8. It follows from well-foundedness that something has to be fundamental simpliciter.

  9. For a different critique of the argument see e.g. Morganti (2009), and Calosi (2014).

  10. McDaniel (2008). McDaniel is explicit in using ‘supervenience’ as the determination relation in question.

  11. The following passage is explicit: “(I have argued) that quantum entanglement is a case of emergence” (Schaffer 2010: 55, italics added).

  12. See among others, Spekkens (2007), Harrigan and Spekkens (2010), Fuchs (2003) and Bub and Pitowski (2010).

  13. See Rovelli (1996), and Laudisa and Rovelli (2013). Schaffer acknowledges this in Schaffer (2015: 31–32).

  14. See e.g. Ghirardi et al. (1986). Schaffer himself entertains the thought the collapse theories might pose some problems for his argument, in e.g. Schaffer (2015: 32). I suspect things might be more complicated than that. There is plenty of residual entanglement in collapse theories, as witnessed by the “problem of tails”, and it might be thought that any entanglement is enough for Schaffer's argument to get off the ground. I will leave the question of the fate of monism in collapse theories aside.

  15. This is actually the core of the argument of Schaffer’s I presented in Sect. 2.

  16. I cannot make justice to the subtlety of Earman’s paper here. The interested reader is referred to Earman (2015) and references therein.

  17. Earman does not discuss Monism, but it is clear that his arguments have bearings on the issue.

  18. Thanks to an anonymous referee here.

  19. I am using “Wavefunction Realism” in a much stricter sense than e.g. Ney (2013a: 37). She uses it to characterize all those interpretations of quantum mechanics that give an ontological reading of the wavefunction, independently of the details of such an interpretation. Thus, orthodox quantum mechanics, many-world interpretations and what I call more restrictedly ‘wavefunction realism’ count as wavefunction realisms.

  20. One particular interpretation which is arguably interesting in the present context, and one which I will not consider, is the one put forward in Wallace and Timpson (2010). They call it “State-space realism”. The fundamental ontology of such a picture is given by different spacetime regions with intrinsic properties assigned to them by looking at the Hilbert space representation. This is interesting because Ismael and Schaffer (2016) argues that a variant of such a view represents one of the most-hospitable ontological setting for monism. As I said in footnote 1, this deserves an independent scrutiny.

  21. The modal interpretations stemmed from some works by Van Frassen which led eventually to his mature formulation in Van Frassen (1991). For an introduction see Lombardi and Dieks (2012), and for a more detailed exposition Dieks and Veermas (1998).

  22. Hence the term “modal”.

  23. The following passage is clear: “Modal interpretations are a class of interpretations of quantum mechanics which, roughly speaking, do not take the quantum state of a system to specify completely the properties of the system […] but take the quantum state itself […] to prescribe or at least constraint the possible range of properties of the system […] modal interpretations are related to other approaches which take some preferred observable as having a definite value” (Bacciagaluppi and Dickson 1999: 1165–1166, italics added).

  24. The discussion follows—albeit not rigidly—Vermaas (1998).

  25. But see Vermaas (1998).

  26. As Arntzenius (1999) puts it: “The central idea of Kochen’s interpretation is that in state \(\sum {c_{i} |a_{i} \rangle |b_{i} \rangle }\) the observable A has some definite value ‘witnessed’ by the measuring apparatus. In a given state not all observable are witnessed, and only the witnessed observable have values” (Arntzenius 1999: 242). In the passage above \(|a_{i} \rangle\)s are the eigenvectors of the observable A, whereas \(|b_{i} \rangle\)s are the eigenvectors of the measuring apparatus observable B.

  27. They apply to Kochen’s interpretation as well.

  28. In Calosi (2017) I argue that failure of property decomposition speaks in favor of the possibility of submergence. This in turn favors the pluralistic case.

  29. Actually, things might not be exactly symmetrical. That is because Kochen’s modal interpretation is still available. And there is an asymmetry there: “There are no perspective on the universe, but from certain perspectives certain things are true about the parts of the universe. It can be true of the universe that half of it is green” (Arntzenius 1999: 245, italics added).

  30. The technical reason for this is that in the previous variants it is possible to define a joint property ascription in terms of joint probability iff the systems to which such properties are ascribed are disjoint.

  31. “This version would adopt a preferred factorization of the Hilbert space for the universe and assign modal algebras of possible properties directly only to those subsystems corresponding to atomic factors in the preferred factorization […]. All other subsystems inherit properties from these “atomic” subsystems by the principle of property composition: if two subsystems \(\alpha\) and \(\beta\), possess the properties \(P_{m}^{\alpha }\) and \(P_{n}^{\beta }\), then the system composed of \(\alpha\) and \(\beta\) possesses the property \(P_{m}^{\alpha } \otimes P_{n}^{\beta }\)” (Bacciagaluppi and Dickson 1999: 1169, italics added).

  32. See Schaffer (2010: 61–65).

  33. The original proposal is in Bohm (1952). See also Bohm and Hiley (1993), and Goldstein (2012).

  34. Given this structure Bub (1997) considers BM as a particular modal interpretation of QM in which the value state is given by the specification of positions.

  35. To be fair there is another way to understand these equations, i.e. the Schrödinger’s equation, and the guiding equation. This is due to Albert (1996, 2013). As Ney (2013a: 42) puts it: “It is possible to read both these equations as being about entities in 3N-dimensional configuration space. We may start by interpreting the wavefunction realistically, as a field in configuration space. Then we may interpret what the guidance equation describes not as a configuration of many-particles in a separate three-dimensional space, but as one particle representing the whole configuration. According to this view, the guidance equation is about the evolution over time of one world particle”. This is strikingly similar—if not straightforwardly the very same thing—to what I will discuss in Sect. 3.4, so I will defer the discussion.

  36. See Goldstein and Zanghì (2013: 92).

  37. Suppose someone was to insist that particles and positions are indeed fundamental but the way they are related is holistically determined. If positions are fundamental and bearers of fundamental properties are themselves fundamental, pluralism would still follow—at least if there are at least two particles. To put it in a different way, the view that is being considered here is holism, not wholism.

  38. “You should think of the wavefunction as describing a law, not as some sort of physical reality” (Goldstein and Zanghì 2013: 97).

  39. One might see reasons to regard some other properties, e.g. spin, as dispositional properties of physical systems: these dispositional properties are grounded—so to speak—in the position of the system, its initial wavefunction, and the Hamiltonian that governs the evolution of the system through the interaction with a measurement apparatus—yielding e.g. a spin-up measurement. For a detailed discussion, see e.g. Clifford (1996: 376–177).

  40. Thanks to an anonymous referee for pushing this point.

  41. As Lewis put it, Humean Supervenience “says that all else supervenes on the spatiotemporal arrangement of local qualities throughout all history” (Lewis 1994: 474).

  42. For arguments against Humean Supervenience in the quantum realm see Maudlin (2007), Darby (2012), and Calosi and Morganti (2016).

  43. For an introduction see Barrett (1999, 2014), Saunders (2010) and Wallace (2013). For a detailed, recent defense see Wallace (2012).

  44. Some classic difficulties are the so called preferred basis problem, the interpretation of probabilities, and the seeming violation of conservation laws.

  45. Wallace (2012) could be a more complicated case. This is sometimes known as ‘decoherence interpretation’.

  46. Saunders is explicit about worlds: “The claim is that the worlds are dynamically robust patterns in the wavefunction, obeying approximately classical equations”. (Saunders 2010: 5). Wallace extends the pattern ontology from worlds to material objects. See e.g. Wallace (2003).

  47. For a critique of the possibility of defining macroscopic objects—and presumably worlds—in terms of patterns in the wavefunction see Ney (2013b).

  48. Besides being related (naturally) via dependence.

  49. Significantly Ney (2013a) refers to these interpretations collectively with “Wavefunction Monism”.

  50. See Dennet (1991).

  51. This might be the starting point to develop yet another version of monism, perhaps along the line of Guigon (2012). This is an interesting suggestion that deserves an independent scrutiny.

  52. It might be objected that WR is not an interpretation of QM. Rather it provides an ontology for QM. Several interpretations might posit such an ontology—e.g. the so called bare GRW and the Many Worlds Interpretation. Granted. But WR seems exactly the kind of ontology that is indeed hospitable to monism. I take this to be enough to warrant a discussion of WR in the present context.

  53. See, e.g. Albert (2015).

  54. The first articulated formulation is Albert (1996). Its most recent defense is in Albert (2013, 2015), Ney (2013b), and North (2013). See also Lewis (2016). For a criticism see Monton (2006, 2013).

  55. See also Albert (1996: 278).

  56. I am not considering the possibility in which material objects are simply identified with ‘propertied-regions of a particular space’, as in certain varieties of super-substantivalism. It should be noted that, in any event, this is not the traditional kind of super-substantivalism, where objects are identical to regions of four-dimensional spacetime. Rather it is a different kind of super-substantivalism where objects are identical with regions of configuration space.

  57. Ney (2012) makes a convincing case for this clam.

  58. Or the theory of extension.

  59. Formulation might slightly disagree—e.g. whether expansivity should be phrased using proper part rather than part. This does not play any crucial role here.

  60. “What is to be a table or a chair […] is—at the end of the day—to occupy a certain relation in the causal map of the world” (Alber 2013: 54).

  61. There might be yet another candidate, namely other wavefunction-fields. Yet it is controversial that fields have a mereological structure of their own. Usually the mereological structure is not ascribed to fields themselves but rather to the spaces they are defined on.

  62. Though it is unclear—at least to me, I must confess—whether he provides any argument for this contention.

  63. Schaffer (2015: 63—footnote 18) agrees as well, albeit with no argument. Schaffer criticizes Horgan and Potrc’s blobjectivism in Schaffer (2012b).

  64. This seems to be the option preferred by wavefunction realists themselves. North writes: “For example, there being a table in three-space consists in nothing but the wave function’s having a certain shape in its high-dimensional space. […] and is itself a real fact” (North 2013: 198, italics added). Here is Ney: “There really are material objects, even if their three-dimensionality is a mirage, and they are ultimately grounded in the behavior of the wavefunction in configuration space” (Ney 2012: 252, italics added).

  65. One might argue that those who are inclined to follow this line of thought, and go for some sort of broadly functional/causal account of material objects would be deflationist about the parthood relation. They would then argue that on such a deflationist understanding, material objects do have mereological structure. I actually believe this is exactly what they should say. Parthood relations will hold between less fundamental entities, but not between the only fundamental entity and the less fundamental ones.


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For comments and suggestions I am grateful to J. Schaffer, M. Morganti, S. French, J. Saatsi, F. Ceravolo, J. Wilson, A. Ney, N. Emery, C. Conroy, G. Bacciagaluppi, F. Muller and to everyone at eidos. I would also like to thank an anonymous referee of this journal, for very helpful suggestions on previous drafts of the paper. This work was generously founded by Swiss National Science Foundations, Project Numbers BSCGIo_157792, and 100012_165738.

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Calosi, C. Quantum monism: an assessment. Philos Stud 175, 3217–3236 (2018).

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