The problem of wave function ontology

Disclaimer: I’m neither a physicist, nor a philosopher of physics. Moreover, I don’t play either role on television! Nonetheless, I’m fascinated by physics, as well as by debates amongst physicists, or between physicists and philosophers. So I perked up when a couple of weeks ago the regular colloquium at the Philosophy Program of CUNY’s Graduate Center was scheduled to be by Nina Emery, of Brown University, who gave an unusually lucid talk (given the topic) entitled “Against radical quantum ontologies.”

We have all heard of the wave function, hopefully from a real physicist rather than, say, from Deepak Chopra. It is a fundamental concept in quantum mechanics, being a description of the quantum state of a system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. Okay, you may ask, but what is a wave function, physically — rather than mathematically or statistically — speaking? Hell if I know. And apparently, hell if anyone else knows either.

Which is where Nina’s talk comes in. I’m going to follow her handout from now on, adding a few comments here and there. Near the end of the post I will get to why the issue may be of broader interest than “just” understanding what the wave function actually is.

To begin with, Nina introduced wave function realism as the view that all that exists at the fundamental level is a field defined in a highly dimensional physical space, the configuration space, where none of its physical dimensions correspond to the standard three spatial and one temporal ones we are all familiar with. There are two types of wave function realism out there: wave function monism, which claims that all that exists is a field in configuration space, which gives rise directly to our everyday experience of the world; and wave function fundamentalism, which says that what exists at the fundamental level is a field in configuration space, which then gives rise to ordinary objects in 3D space, which in turn we then somehow perceive (i.e., fundamentalists allow for additional transitions when compared to monists).

What Nina set out to do was to build an argument against wave function realism, based on something she calls the minimal divergence norm, which states: “insofar as we have two empirically adequate theories (i.e., two theories that both accurately predict the phenomena we observe), we ought to choose the one that minimizes the difference between how the theory says the world is and the way the world appears to be (to us).

To use the classical distinction famously introduced by philosopher Wilfrid Sellars, the minimal divergence norm says that we should try to minimize the distance between the scientific and the manifest images of the world.

Nina explained that we should care about this for a couple of reasons: first, because wave function realism is taken increasingly seriously by a number of philosophers and physicists; second, because the minimum divergence norm may be helpful in metaphysics against what she amusingly called “incredulous stare arguments” (i.e., arguments based on some sophisticated version of “are you f**ing kidding me?”).

Nina’s argument can be summarized in the following way:

P1: wave functional realism (either of the monist or the fundamentalist type) violates the minimal divergence norm.

P2: we should accept the minimal divergence norm.

C: therefore, we should reject wave function realism.

The argument is valid, which means that the only way to reject it is to doubt one or the other of the two premises (i.e., to question its soundness). Accordingly, Nina proceeded to defend her premises. Before doing that, however, she cautiously added a few caveats, which I’m going to briefly examine here.

First, she explained that her focus is on ontologies compatible with Everett-type (so-called “many-worlds”) interpretations of quantum mechanics, but that the argument applies also (straightforwardly, she said) to Bohmian-type dynamics. Don’t ask, I can’t tell.

Second, she distinguished between her proposed minimal diverge norm and a similar, but more restrictive, no-divergence norm. The latter says that we should not endorse a scientific theory that says that the world is significantly different from the way it appears to us.

This is crucial, and of high interest to me. Basically, while the minimal divergence norm attempts to put a leash on scientific theories and keep them as close as empirically and theoretically possible to the manifest image, the no-divergence norm says that, no matter what, priority should go to the manifest image. The first one is, I think, a reasonable attempt to remind us that scientific theories are human constructions, not god’s eye-views of the world, and so that one of their virtues is to make the world understandable to us. The second norm, however, is basically what flat-earthers and creationists happily support: no matter what science tells me, what I see is what I get. Clearly, the minimal divergence norm is a (debatable, for sure) reasonable constraint on science, while the no-divergence norm quickly degenerates into a rejection of science and possibly a support of pseudoscience.

Nina’s third caveat was that she wasn’t going to propose any positive account of the ontology of the wave function, since that’s a much more complex issue, on which there simply isn’t any agreement, either among physicists or among philosophers.

Caveats duly put out there and set aside, Nina proceeded to defend her first premise, that wave function realism violates the minimal divergence norm. To do that, she identifies one possible alternative to wave function realism, mass-density ontology, according to which what exists fundamentally is a mass-density field in 3D space. (Just like wave function realism, mass-density ontology comes in two flavors, monism and fundamentalism, but the difference is irrelevant here.)

Nina claims that wave function realism diverges more from the manifest image than mass-density ontology, for instance because mass-density ontology at the least includes objects in 3D space, which wave function realism does not.

The general idea is that neither wave function realism nor mass-density ontology contradict the manifest image (because they both somehow recover the appearance of everyday objects), but they both go beyond the manifest image. The difference is that wave function realism goes further beyond when compared to mass-density ontology. We could say that it is a less parsimonious departure from the manifest image.

Nina then turns to her defense of the second premise, that we should accept the minimal divergence norm. This, for me, is the more crucial point, and one that has far wider applications than this particular issue in fundamental (meta)physics.

Her move is interesting, though certainly controversial. She claims that the minimal divergence norm is the chief — indeed te only — reason that keeps our theorizing theorizing from sliding inot so-called radical metaphysical notions. Here are some examples of the latter:

* Solipsistic idealism, the notion that I don’t have a physical body and brain, and that all that exists is my mental states.

* Brain-in-a-vat hypothesis. My brain is floating in a vat, receiving sensorial inputs indirectly. The physical world is nothing like what it appears to be.

* Bostrom simulation hypothesis. The physical universe is nothing like physics describes it, it is, rather, a simulation in someone else’s computer.

* Boltzmann brain hypothesis. My brain formed spontaneously in an empty region of space, as a result of a number of coincidences. Again, the physical universe is nothing like what it appears to be.

At first I thought that Nina’s claim that these radical metaphysical hypotheses are incompatible with science was a bit too strong, and that it would have sufficed to say that they are in no way entailed by the current scientific worldview. But upon further reflection I think she is right. Notice the recurrence above of a specification along the lines of “… and the world is nothing like it appears to be.” If any of the radical metaphysical hypotheses were true (and it is possible that one of them is!), then it would not just be the manifest image that would be incorrect, but also the scientific one. When physicists talk about electrons, quarks, strings, and what not, they most certainly do mean that these things are physical components of fundamental aspects of our reality. Which would be false if any of the above scenarios actually held.

Further, Nina makes clear two additional points to be considered insofar as this discussion is concerned: i) while it is true that the radical metaphysical hypotheses can be designed so as to present a number of extra-empirical virtues (such as simplicity, elegance, etc.), this is irrelevant unless one also has a reasonable story to explain how those virtues are acquired by scientists and why they should be deployed in a way that favors the metaphysically radical scenarios; ii) her argument for the second premise goes through even if one limits the radical scenario to just the fundamental level, for instance by saying that the Bostrom simulation hypothesis claims that what exists fundamentally is a computer simulation, which is then capable of giving rise to a world of 3D objects.

Nina’s conclusion, which seems reasonable to me, is that “anyone who rejects the minimal divergence norm must either take seriously the radical metaphysical scenarios, or give up a plausible story about how they are ruled out.”

Obviously, there is plenty of room for disagreement with Nina’s argument and conclusions, though I find them quite plausible. Nevertheless, the reason this is very interesting — other than its application to the ontology of quantum mechanical concepts such as the wave function — is because of the broader issue I mentioned earlier: the difference (and tension) between Sellars’ manifest and scientific images of the world.

Indeed, I have been invited to contribute a chapter to a forthcoming book on the common sense tradition in philosophy, to be published by Oxford University Press. My chapter will be on the challenges posed by science to such tradition. As a scientist and philosopher, of course, I wholly realize that science has introduced and will continue to introduce notions that will depart from “common sense,” or from the manifest image. But as I said above, I also think that science is a human-centered activity that never had, nor ever will, achieve a god’s eye-view of things. Science, in other words, isn’t just in the neutral business of discovering how the world works, it is in the partially subjective business of facilitating human understanding of how the world works.

That is why I find Nina’s notion of the minimal divergence norm useful: we have to allow the scientific image to diverge from the manifest one, or we give up on science altogether. But we also want such divergence to be kept at a minimum, because otherwise we have no criteria to reject non- or even anti-scientific hypotheses, such as the radical metaphysical ones mentioned in Nina’s talk (and a number of others, I would add, like Max Tegmark’s mathematical universe). To give up on the norm of minimal divergence would basically give free rein to metaphysical speculation in science, which I’m pretty positive would not be a good idea.

Edited with BlogPad Pro