On The Methodological Arguments for Wave−Function Realism

ABSTRACT

The paper explores a particular line of objection against wave-function realism. This view, advocated by Bell (1987) and presently defended by Albert (1996), North (2013) and Ney (2016), claims that the quantum wave function is a high-dimensional physical field. Normally, wave-function realism has been criticized for its ontological commitments, which are regarded as empirically unsupportable in principle and as violating empirical coherence. In this paper, I investigate whether there are any methodological arguments for endorsing such an ontology and whether they are sound. In particular, I home in on and discuss three arguments that may be used to support wave-function realism: (i) the argument from laws; (ii) the argument from the complete information of the system; (iii) the argument from explanation. My conclusion is that these arguments do not provide any good methodological grounds for inferring the existence of a high-dimensional physical field from quantum theory.

KEYWORDS:

• Wave-function realism
• Configuration Space
• Laws of Nature
• Locality
• Methodological Arguments

Acknowledgements

It is with deep and genuine gratitude that I dedicate this article to Professor Renato Pettoello, on the occasion of his retirement. If this work has produced any good fruits, he was the gardener who planted the tree. I am also thankful to the two anonymous referees who reviewed this paper, and to Jonas Werner for his insightful comments.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 For a comprehensive and detailed historical perusal of the different views on the status of the quantum wave function at the birth of quantum mechanics, see (Bacciagaluppi and Valentini 2009).

2 See (Monton 2006), for the same historical considerations.

3 In this paper, I use the expression ‘wavefunction realism’ as is used in (Albert 2013), (Ney 2015), (Wallace and Timpson 2010), (Wallace 2017). Another way would be to use the expression ‘wavefunction realism’ to denote any views that take wavefunction to represent a piece of physical reality (for instance, three-dimensional ‘multi-fields’ (Hubert and Romano 2018; Romano 2021).

4 Albert (2013) for instance, has offered a functionalist account of emergence.

5 For a discussion of the Hamiltonian as a nomological entity, see (Goldstein and Zanghì 2013), (Sole’ and Hoefer, in Cordero 2019, p. 125).

6 Bear in mind, however, that also Humeans, who endorse a fundamental 3D ontology, can avoid this.

7 Colyvan (2001) spells out the notion of indispensability by referring to the best theory, instead of the best regimentation. However, in this paper we reformulate his notion in line with the notion of indispensability used by Quine and Putnam, who refer to regimentation.

8 A primitivist of nomological entities, for instance, would deny that laws need something to make them true. For the primitivist, laws are brute facts that are not analysable in terms of deeper truths. See (Maudlin 2007b).

9 See for instance Valentini (2009); Lewis (2004) considers this as a motivation for wave function realism.

10 This was discussed in Myrvold’s presentation What is the WFR? For the workshop “The World in the Wave-function” organized by the University of Geneva.

11 Claims that the 3ND wavefunction is coordinate-dependent (Lewis 2004), and breaks Earman’s symmetry principle (Rivat 2016) are not sufficient to reject that the wavefunction is not a mathematical structure, since, as North makes it clear, mathematical structures can be coordinate-dependent or symmetry-variant (North 2021).

12 This is of course not entirely true. However, let’s grant it for the moment, for the sake of the dialectic of the paper.

13 This is the example that Maudlin himself uses in order to delineate the difference between the informationally complete representation and the ontologically complete representation of the system (Maudlin 2007a).

14 The explanatory role of the wavefunction and its space is for instance mentioned in Lewis:“The wavefunction figures in quantum mechanics in much the same way that particle configurations figure in classical me­chanics; its evolution over time successfully explains our observations. Realists, then, should regard the wavefunction as part of the basic furniture of the world. [I] t is the wavefunction that plays the central explanatory […] role.” (2004, p. 714). Similar considerations may be found in Valentini (2009), who explicitly refer to the explanation that the wavefunction provides for an entangled system.

15 Of course this is a debatable claim. See Lange (2002) for an argument supporting this claim, but see (Hartenstein and Hubert 2021; Lazarovici 2018) for the opposite claim. For a discussion on the reality of electromagnetic fields, see Hesse (1961).