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Wavefunction Realism and Fundamentality

Nina Emery, Gabrielle Kerbel

Published May 28, 2026• 0 citations
OpenAlex

Abstract

Wavefunction realism is an account of quantum ontology according to which the wavefunction represents a field in a high-dimensional space. We present a novel version of wavefunction realism that differs from the standard version when it comes to which features of the ontology are fundamental. We argue that our version should be taken just as seriously as the standard version. Along the way we show that the choice between the two turns on substantive commitments regarding the nature of grounding, supervenience, locality, and explanation.

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Wavefunction realism is an account of quantum ontology according to which the wavefunction represents a field in a high-dimensional space. We present a novel version of wavefunction realism that differs from the standard version when it comes to which features of the ontology are fundamental. We argue that our version should be taken just as seriously as the standard version. Along the way we show that the choice between the two turns on substantive commitments regarding the nature of grounding, supervenience, locality, and explanation.
The phrase “Wave Function Realism” (WFR) has come to be used for a family of views according to which quantum theory motivates us to think that quantum wave functions are fields on a space of extremely high dimension, which is in some sense more fundamental that ordinary three-dimensional space or four-dimensional spacetime. With an aim at gaining clarity about the nature of the project, I distinguish between varieties of Wave Function Realism that one might hold. I focus on two axes of distinction. One has to do with the nature of the project. Is it an Interpretive project, one of accepting standard quantum theory pretty much as we have it, and exploring its implications for ontology? Or is it a Constructive project, which finds standard quantum theory wanting in crucial aspects, and seeks to construct a new theory that will satisfy some set of metaphysical constraints? The other has to do with how radical the claims are that are made about the nature of spacetime. Does the fundamental space on which the wave functions of WFR are defined have intrinsic structure corresponding to the low-dimensional spacetime structure? I call versions of WFR on which this is so “Mild” versions, as on such a view any sense in which the low-dimensional spatial structure is non-fundamental would be at best a highly attenuated one. A more radical view, which I call “Spicy,” has it that the fundamental space has no intrinsic structure corresponding to our low dimension spacetime, and that such structure is emergent from the structure and evolution of certain sort of wave functions. Judging from what they say about the view, it seems that proponents of WFR intend it to be Interpretive and Spicy. I will argue that there can be no such position. Standard quantum mechanics makes such heavy use of low-dimensional spacetime structure that an Interpretive version of WFR must be Extremely Mild. A Spicy but Constructive version has yet to be formulated.
What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. We argue that: • Strictly speaking, it is not possible to interpret quantum theories as theories about the wave function; • Even if the wave function is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously; • All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time.
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.
This paper investigates the tenability of wavefunction realism, according to which the quantum mechanical wavefunction is not just a convenient predictive tool, but is a real entity figuring in physical explanations of our measurement results. An apparent difficulty with this position is that the wavefunction exists in a many-dimensional configuration space, whereas the world appears to us to be three-dimensional. I consider the arguments that have been given for and against the tenability of wavefunction realism, and note that both the proponents and the opponents assume that quantum mechanical configuration space is many-dimensional in exactly the same sense in which classical space is three-dimensional. I argue that this assumption is mistaken, and that configuration space can be taken as three-dimensional in a relevant sense. I conclude that wavefunction realism is far less problematic than it has been taken to be. 1. Introduction 2. Non-separability 3. The instantaneous solution 4. The dynamical solution 5. Invariance 6. What is configuration space, anyway? 7. Conclusion