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Wave-functionalism

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Abstract

In this paper I present a new perspective for interpreting the wavefunction as a non-material, non-epistemic, non-representational entity. I endorse a functional view according to which the wavefunction is defined by its roles in the theory. I argue that this approach shares some similarities with the nomological account of the wave function as well as with the pragmatist and epistemic approaches to quantum theory, while avoiding the major objections of these alternatives.

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Notes

  1. de Broglie (1927), Bohm (1952).

  2. Ghirardi et al. (1986).

  3. Everett (1957).

  4. See Albert and Ney (2013) for a review of the different approaches to it.

  5. See most notably Albert (1996, 2015), Ney (2021), North (2013), and references therein.

  6. See Albert (2015) and Ney (2021) for two different approaches on this.

  7. Ney (2021) and references therein.

  8. “It seems a little paradoxical to construct a configuration space with the coordinates of points which do not exist.” de Broglie (1928) translated in Bacciagaluppi and Valentini (2009, p. 380).

  9. Monton (2013), Allori (2013).

  10. See Wallace and Timpson (2010), Myrvold (2015).

  11. See Chen (2019) and references therein for more objections.

  12. One view considers the wavefunction as a three-dimensional poly-wave or multi-field which assigns values to regions of points (Belot, 2012; Chen, 2017; Forrest, 1988; Hubert & Romano, 2018). Another possibility is primitivism: the wavefunction represents an unanalyzable, nonlocal, material field (Maudlin, 2019). Others have tried to reformulate quantum theory only in terms of local ‘beables’ (Norsen, 2010), while spacetime state realism associates to each system a determinate property represented by a reduced density matrix (Wallace and Timpson, 2010).

  13. Alllori (2018) has objected that the multi-field view is unable to account for symmetries, while primitivism looks unnecessarily mysterious and dismissive (Allori, 2020). Theories of local beables face serious technical challenges (Norsen, 2010), and Maudlin (2019) has objected that the reduced density matrix proposed by spacetime state realists inverts the usual relation between parts and wholes because it is not separable.

  14. Allori et al. (2008), Allori (2013).

  15. Dürr et al. (2013), Goldstein and Zanghì (2013).

  16. Alllori (2013).

  17. Brown and Wallace (2005).

  18. Dürr et al. (1997), Goldstein and Teufel (2001), Goldstein and Zanghì (2013).

  19. Wallace, p.c.; Albert, p.c.

  20. Callender (2015).

  21. Maudlin, p.c. See also Sect. 3.5, objection 3. For more objections, see Belot (2012), Callender (2015), Esfeld et al. (2014), Suarez (2015).

  22. These proposals have been developed in a Humean framework (see Bhogal & Perry, 2017; Callender, 2015; Esfeld, 2014; Miller, 2014). A connected nomological approach is to think of the wavefunction as a dispositional property, or more generally as a property of the primitive ontology (Monton, 2013; see also Esfeld et al., 2014; Suarez, 2015 for the development of this approach in the framework of Bohmian mechanics). Other approaches that seems to belong to the same camp are structuralist accounts (North, 2013).

  23. Many find the Humean accounts wanting, partly because they find Humeanism with respect to laws misguided for other reasons. Moreover, some others consider find the property approach to the wavefunction objectionable, given that the wavefunction does not behave like a traditional property (Suarez, 2015). Finally, structuralist accounts seem at the moment to be underdeveloped or too vague, as it is unclear what structure is in this context.

  24. Epistemic approaches can be distinguished into neo-Copenhagen accounts, and hidden variables ones. Einstein’s original statistical interpretation (1949) is an example of a hidden variable epistemic approach.

    In fact, it states that quantum theory is fundamentally incomplete, as it does not specify hidden variables describing the reality under the phenomena, whose behavior is statistically well described by the wavefunction. For a more modern approach, see Spekkens (2007). In contrast, the neo-Copenhagen approaches reject that the above-mentioned hidden variables exist or are needed. Traces of this can be found for example in Heisenberg (1958). Neo-Copenhagen approaches include the information-theoretic approach (Bub, 2015; Bub & Pitowsky, 2010), Bayesian approaches (Fuchs, 2010), and relational ones (Rovelli, 1996). See Dunlap (2015) for a comparison between the primitive ontology approach and the information-theoretic interpretation.

  25. Pusey et al. (2012).

  26. See Leifer (2014), Gao (2017), Maudlin (2019), and references therein, for a discussion of objections and replies.

  27. Bub and Pitowsky (2010). See also Fuchs (2010) for a discussion of how quantum Bayesianism is a realist approach.

  28. For more on the constructive/principle distinction in this context, see Bub and Pitowsky (2010). Also, for a more general discussion of this distinction, see Flores (1999), Balashov and Janssen (2003), Brown and Pooley (2004), Brown (2005), Brown and Timpson (2006), Felline (2011), van Camp (2011).

  29. Healey (2015, 2017a, b, 2020) and references therein. See also Friederich (2015).

  30. A pragmatist view is one in which, as held by the pragmatist school of philosophy, to understand a concept, such as the wavefunction, is to understand its functions, rather than what it represents. Instead a view can be called pragmatic when it focuses on the macroscopic domain, aiming at reproducing our experiences, rather than providing the microscopic description giving rise to the macroscopic data. I thank an anonymous referee for pointing this out to me.

  31. Notice the PBR theorem proves that the wavefunction has to be non-epistemic. Traditionally this has been taken to mean that the wavefunction has to be ontic, in the sense that the wavefunction represents something independently of any observer. Nonetheless, the epistemic-ontic distinction so understood is a false dichotomy, as it is not necessarily the case that if the wavefunction is not epistemic has to be ontic in this way. In fact, the following are all possible state of affairs: (1) the wavefunction represents a physical object (as wavefunction realism proposes); (2) the wavefunction represents a nomological fact (as the primitive ontologists claim); but also (3) the wave function is defined in terms of the functions it plays in the theory. While in the first two cases the wavefunction is ontic strictly speaking (being representational), in the third option the wavefunction is non-representational, but nonetheless it is non-epistemic. This fact alone allows to bypass the PBR theorem.

  32. See e.g. Jansson (2020), Lewis (2020) and references therein for criticisms, and Healey (2020) for a defense. See also Brown and Timpson (2006) for a criticism of the information-theoretic interpretation as not explanatory.

  33. Or, as Forrest Gump’s mother used to say: “Stupid is as stupid does”.

  34. Starting from Putnam (1960).

  35. Ney (2021) provides a criticism and discusses her own alternative.

  36. For a review of spacetime emergence in quantum gravity see e.g., Huggett and Wüthrich (2013, forthcoming), Crowther (2016), Le Bihan and Linnemann (2019), and references therein.

  37. For a discussion on the role of functionalism in the emergence of spacetime, see Le Bihan (2019). See also Lam and Esfeld (2013), and Yates (forthcoming).

  38. Barrett (1999), Maudlin (2007) and Ney (2015) discuss the issue of empirical incoherence in the framework of quantum mechanics, while Huggett and Wüthrich (2013) address it in quantum gravity. For related considerations, see also Healey (2002).

  39. Indeed, the wavefunction is as a ray in Hilbert space, namely an equivalence class of objects which differ from a phase, because each element in the class generates the same empirical results.

  40. Allori et al. (2008).

  41. In the context of the pilot-wave theory, the wavefunction can be taken as a force or a potential, but one does not think of it as material either (even if Belousek, 2003 argues otherwise).

  42. Healey (2017a).

  43. Indeed, at least initially, the pilot-wave theory was described in terms of the quantum potential, containing the wavefunction, and acting on matter, made of particles, as another interaction.

  44. See also Sect. 3.5, objection 4.

  45. I have in mind Esfeld's super-Humeanism (2014), or Bhogal and Perry's version of Humeanism (2017). They relax the condition, proper of the more traditional Lewisian Humeans, that fundamental laws should mention only perfectly natural properties in the Humean mosaic. Lewisians instead may resist this view. In fact, their best system would include the Schrödinger equation as an axiom, and this would mention the wavefunction, which therefore should be part of the Humean mosaic.

    Thank you for an anonymous reviewer for pressing me on this point.

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Acknowledgements

I am especially grateful to Mario Hubert for his thoughtful comments on a previous version of this paper and in particular for the suggestion of the name of the view. Also, I wish to thank four anonymous reviewers as well as the participants of the 2020 Central APA meeting, the 2020 PSA meeting, and the Harvard Foundations of Physics Workshop (June 2020) for their insightful suggestions.

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    Valia Allori

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Allori, V. Wave-functionalism. Synthese 199, 12271–12293 (2021). https://doi.org/10.1007/s11229-021-03332-z

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