Physicists like Sean Carroll argue not only that quantum mechanics is not only a valuable way of interpreting the world, but actually describes reality, and that the central equation of quantum mechanics – the wave function – describes a real object in the world. But philosophers Raoni Arroyo and Jonas R. Becker Arenhart warn that the arguments for wave-function realism are deeply confused. At best, they show only that the wave function is a useful element inside the theoretical framework of quantum mechanics. But this goes no way whatsoever to showing that this framework should be interpreted as true or that its elements are real. The wavefunction realists are confusing two different levels of debate and lack any justification for their realism. The real question is: does a theory need to be true to be useful?

1. Wavefunction realism

Quantum mechanics is probably our most successful scientific theory. So, if one wants to know what the world is made of, or how the world looks at the fundamental level, one is well-advised to search for the answers in this theory. What does it say about these problems? Well, that is a difficult question, with no single answer. Many interpretative options arise, and one quickly ends up in a dispute about the pros and cons of the different views. Wavefunction realists attempt to overcome those difficulties by looking directly at the formalism of the theory: the theory is a description of the behavior of a mathematical entity, the wavefunction, so why not think that quantum mechanics is, fundamentally, about wavefunctions? The view that emerges is, as Alyssa Ney puts it, that

Reality isn’t fundamentally a collection of objects—particles, atoms—spread out in three-dimensional space or even four-dimensional spacetime, but instead, reality is fundamentally a wave function, a field-like object that exists in some higher-dimensional quantum reality.

This view is quite appealing to those philosophers keen to have a closer connection between science and philosophy, the naturalists.

For naturalist philosophers, having our image of the world directly anchored to science is not just a preference, it is the whole game plan. Wavefunction realism promises to make that plan easier to achieve. The main advantage is the idea that we can “read off,” as it were, the ontology directly from our mature science—in this case, quantum mechanics. We can thereby furnish the inventory of the world in the most scientific way possible. That would seem to bypass the many messy interpretative difficulties that typically arise with quantum ontology, namely, when trying to say what quantum mechanics is really about.

___

For a small price, the prize seems large: wavefunction realism would offer a direct path to closing the traditional epistemic gap in the metaphysics of science, that is, the gap betwen how theories say the world is and how reality actually is.

___

But then, the natural question is: why wavefunctions? Here, the traditional indispensability argument becomes very attractive. The point is simple: commitment to wavefunctions is widespread and transversal across the most famous formulations of quantum mechanics; all of them rely, in one way or another, on this mathematical entity to function properly. So, just as philosophers of mathematics sometimes argue that we should be ontologically committed to whatever mathematical entities are indispensable to the success of empirical science, one could try to apply the same reasoning to quantum mechanics. If wavefunctions are indispensable to scientific practice, then—so the argument goes—we should accept an ontological commitment to them. In the case of wavefunction realism, this means granting full reality to the wavefunction itself. We reify the mathematical entity, the wavefunction, but for a good reason, it seems.

From this perspective, for a small price, the prize seems large: wavefunction realism would offer a direct path to closing the traditional epistemic gap in the metaphysics of science, that is, the gap between how theories say the world is and how reality actually is. Just look at the theory and you will find the answer in its indispensable ingredients.

2. Layers of realism

The difficulties, however, come from two sources: “wavefunction” and “realism.” The status of the wavefunction as a physical entity is a well-charted problem. Because the wavefunction lives in a very high-dimensional space, it does not fit smoothly into our ordinary, manifest picture of the world, and there is an entire ecosystem of proposals trying to make the two line up.

But the second component—the “realism” part—has not been discussed thoroughly in connection to wavefunction realism. Where, exactly, is the realism supposed to be in wavefunction realism? Roughly, to be a realist about something simply means to believe in its independent existence, where “independence” means “independent from our thoughts and language.” To be a realist about mathematics, for example, means believing that mathematical entities genuinely exist—not just as useful fictions, not just as a language. In the same spirit, to be a scientific realist means believing in the entities—observable or not—that our best science posits. When we say “wavefunctions exist,” or “black holes exist,” we are expressing this kind of ontological confidence.

___

If all one has in favor of wavefunction realism are pragmatic factors—such as simplicity, elegance, or intuitive appeal—then one should be reminded that these are not generally considered to be truth-conducive theoretical virtues.

___

Being a realist about our best scientific theories involves at least two distinct layers: an ontological thesis and a metaontological thesis. The ontological thesis is straightforward: we should be realists (that is, believe in the existence of) the entities postulated by our best scientific theories. Those theories often come with a catalogue of entities they commit us to. In quantum mechanics, wavefunctions may be part of that catalogue: wavefunction realists argue that the wavefunction is simply one more element in the theory’s inventory. But there is also a metaontological thesis in play here: the claim that this theory, with this inventory, is the true theory—which is to say that the theory’s inventory is (or coincides with) the inventory of nature, so to speak. It is the metaontological thesis that enables one to go from within the theory to reality itself, and claim that the theory somehow mirrors reality.

To recall Rudolf Carnap’s famous distinction, the ontological thesis is internal to a framework. The relevant thesis here would be that within quantum mechanics, there are wavefunctions that behave in a certain way. The metaontological thesis is external to the framework: it says about the description provided by quantum mechanics that it is true of external reality. The issue at stake here is not merely that of saying that such an entity exists within a theoretical model. The realist wants to know whether that entity exists in reality, i.e., whether the framework truly describes what is out there. Belief in the truth of our best theories is the distinguishing trait that separates scientific realists from their non-realist cousins.

So how does wavefunction realism behave under such a demand? At first glance, it looks promising: it seems we can appeal to indispensability and declare that the existence of the wavefunction is granted by quantum mechanics itself. But this does not automatically secure the metaontological level. In fact, the indispensability argument fails: there are formulations of quantum mechanics that don’t appeal to wavefunctions, Heisenberg’s matrix mechanics being one prominent example.

3. Wavefunction pragmatism

What now? Maybe there are some other reasons one can appeal to in order to ensure that a world with wavefunctions is nicer than a world without them. For instance, we could appeal to a kind of intuitive continuity—the idea that something like the wavefunction preserves precious aspects of the classical picture (for example, some sense of locality). However, if all one has in favor of wavefunction realism are pragmatic factors—such as simplicity, elegance, or intuitive appeal—then one should be reminded that these are not generally considered to be truth-conducive theoretical virtues since the seminal work of Thomas S. Kuhn. These virtues might count for theory choice in several ways to help us navigate whenever we face a plurality of theoretical options, but they do not, on their own, tip the balance toward the stronger claim that such-and-such a theory is literally true in the sense of interest for scientific realists. The world might not be simple after all. Simplicity is a theoretical virtue concerning us and how we evaluate theories, but has nothing to do, ipso facto, with truth—with how the world truly is. In other words: we prefer to choose simple theories, but that does not imply that simpler theories are closer to the truth—that link is still missing.

In fact, some versions of wavefunction realism recognize the limits of their naturalistic project of extracting (or reading off) the ontology from science, along with the troubles it causes for the corresponding metaontological argument. They even explicitly adopt a (Carnapian) stance of tolerance toward other interpretations of quantum mechanics that do not involve wavefunctions at all. These versions of wavefunction “realism” are not compatible with scientific realism in the strong sense. They do not commit to the idea that there is a single true ontology provided by the theory. Instead, they look much more like versions of empiricism or pragmatism: the view that the task of science is not to tell us how the world actually is, but only how it might possibly be, among other plausible options. For these versions of wavefunction realism, it would be more accurate—and certainly more honest—to use names like “wavefunction empiricism” or “wavefunction pragmatism.”

Nobody seems to want those labels, of course, but—as is often said—“the shoe fits.”

For more details, see Arroyo, R., Arenhart, J. R. B. “Antirealism in Sheep’s Clothing.” Found Phys 55, 70 (2025).