The central mystery of quantum mechanics is that quantum particles move like waves but hit and leave effects like localized particles. This is true of elementary particles, atoms, molecules, and increasingly larger objects, possibly macroscopic ones. It’s even true of collections of entangled particles, no matter how separated the particles may have become.
People have been arguing about how to interpret this for almost a century. A key question in an interpretation is, how should we regard the wave function, the tool used to model and predict the evolution of the wave? Is it modeling something real? Or is it just a convenient fiction, a mathematical contrivance that is really just modeling probabilities? Are quantum particles really ever waves?
As many of you know, on this question, I fall into the realist camp. We have the wave function because of empirical data showing interference effects. And too much quantum phenomena, like tunneling, electron orbitals, or the Aharonov-Bohm effect, just make a lot more sense in terms of waves, but are spooky when viewed with a strict particle ontology.
So I think the waves are real and we have to deal with the implications. But I’ve generally been uncommitted on the nature of that realness. It’s not clear that we can know how much of it is a substance of some kind, and how much is modeling relations between substances. The structures seem real, but what the structures are structures of seems beyond the current boundary of knowability.
And there’s the whole issue that the wave function seems to operate in 3N dimensions, where N is the number of particles being modeled. In an observable universe of 1080 particles, that’s a lot of dimensions.
These, and other issues, make most physicists resistant to accept full wave function realism. Even many Everettians (many-worlders), like David Wallace, are reluctant to sign on. However, there are people who support it. This week I came across an interesting article by Alyssa Ney advocating for exactly this type of realism (warning: possible paywall). In her view, the wave function is fully real, in the sense that it represents a physical wave in a field operating in a higher dimensional space.
My initial reaction to this was to wonder how much this is actually saying. A lot hinges here on what we mean by words like “physical”, “wave”, “field”, “dimension”, or “space”. Taking “physical” to mean working according to rules or laws, “wave” as a topological category of processes, “field” to mean a field of something, “dimension” as a degree of freedom, and “space” as configuration space, it’s not clear we’ve moved much.
Poking around in her book, The World in the Wave Function, by “physical”, Ney seems to mean res, or substance. But even here we still run into the fact that substances we commonly think of, such as the wood in furniture, is ultimately a series of structures, patterns, of processes. Do we hit ultimate substance with quantum fields? Or just a new boundary of structure and processes?
So the question for me is, what does buying this ontology get us? Ney has an answer: locality. Now, locality in quantum mechanics is usually broken up into two components: causal locality and separability.
Causal locality is the one most of us think of when we think about locality. It’s the principle that you can’t have action at a distance, instantaneous (or faster than light) effects from causes that are distant in time and space. The evolution of the wave function is usually considered to be causally local, at least until a physical collapse, if in fact there are collapses. So it’s not clear what benefits full wave function realism provides here.
Separability just means that, for a system distributed over multiple spacetime regions, there’s nothing in the accounting of the system as a whole that isn’t contained in the accounting of its components. Most physicists, including most Everettians, accept that this is violated by the correlations in entangled particles.
Ney’s assertion is that accepting wave function realism provides separability. Here, I think I’ll just quote the key passage from her book.
It is separable because all states of the wave function, including the entangled states we have been considering, are completely determined by localized assignments of amplitude and phase to each point in the higher-dimensional space of the wave function.
Ney, Alyssa. The World in the Wave Function (p. 87). Oxford University Press. Kindle Edition.
This might be true for the individual value assignments of the wave function. But it’s not clear to me that the relations themselves can be accounted for separately, at least not in the bra-ket notation I’m familiar with. On the other hand, David Deutsch claims to demonstrate separability using Heisenberg matrices, which seems to resonate with Ney’s assertion here.
Ney admits that this only provides separability in terms of the higher dimensional reality. If we restrict our view to 3D space, then we’re still faced with non-separable phenomena, just with that non-separability rooted in a separable reality in the higher dimensions.
What does seem clear to me, which hadn’t before, is that the correlations, even if non-local, are fully accounted for and encoded in the wave function. And it seems easier to think about that accounting in some higher dimensional framework. So I don’t know if it necessarily demonstrates separability, but it does make understanding how the entangled correlations exist and persist easier than when trying to map them into 3D space, at least for me. That seems true as much for qubit circuits in quantum computers as it is for particles separated by light years.
Ney works hard to avoid making this about any specific interpretation of the measurement problem. Obviously wave function realism sits most easily with the Everett many-worlds approach, and Ney admits that’s where her sympathies lie. But she also spends a lot of time discussing the implications for Bohmian mechanics (pilot-wave theories) and objective collapse models (mostly focusing on GRW, although she does mention Penrose’s version in an endnote).
Interestingly, she notes that wave function realism doesn’t necessarily sit that well with Bohmian mechanics. The reason is that Bohmians, while regarding the wave function as real in some sense, tend to relegate it into some kind of ghostly secondary ontology, with the particle itself only having primary ontology. (Many Everettians regard the Bohmain approach as many-worlds in denial, relegating the other worlds to that secondary ontology.)
She also makes the case that the spontaneous collapses in GRW don’t, strictly speaking, violate causal locality. Since the collapse is spontaneous with no external cause, there’s no action at a distance, just a whole bunch of spontaneous actions throughout the extent of the field. Not entirely sure I buy this one, but it’s an interesting point.
Ney’s wave function realism is something that exists in a higher dimensional configuration space. (At least in the non-relativistic version. She does address the relativistic version, but I haven’t attempted to parse that section of the book. My QFT is too limited.) It’s worth noting that this is somewhat in contrast to Sean Carroll’s wave function realism, where he asserts that reality is a ray in Hilbert space. Ney doesn’t find this view compelling and I have to agree. Reality may end up summing up to a ray in Hilbert space, but saying it is just that ray, doesn’t seem productive. (To be fair, I haven’t attempted to navigate Carroll’s paper on this.)
Ney, at the end of her book, discusses the issue of the incredulous stare, the reaction that wave function realism is simply absurd and should be rejected, without trying to find a logical reason to do so. She obviously doesn’t think this is a valid reaction. I agree with her. The wave function obviously works with all its infinite dimensions, which means that simply dismissing aspects we don’t like is really just flinching from what the data seem to be telling us, taking the blue pill rather than the red.
On the other hand, I’m not sure if Ney’s argument has moved me from my original position. I’ll have to give it more thought. I do think it provides a good way of thinking about the wave function, which, at least for me, seems like progress. But I still leave room for the underlying reality to be something very different. That said, I suspect any hope that underlying reality would be less bonkers than what we’re already looking at is likely to be forlorn.
What do you think of wave function realism? Are there aspects you think are more likely to be real than others? Or do you go for a full epistemic view? If so, where do you see the interference effects coming from?