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The universe is not a wave function

Brian Leiter

Philosopher Eddy Keming Chen (UC San Diego) comments.

UPDATE:  Philosopher David Wallace (Pittsburgh) writes:

I saw you flagged Eddy Chen’s recent paper on the blog. A quick observation in case you’re interested: the article is engaging and provocative but risks encouraging a regrettably-common confusion, in that it mostly conflates 'the wave-function is representational' with 'the wave-function is real'. Consider: there are c.10,000 students at Pitt, and they take four courses per semester, so the academic results of the undergraduate body each semester are represented by a single point in 40,000-dimensional 'grade space'. Is the grade-space point representational? Does it represent objective mind-independent features of the world? Yes, obviously; indeed, we know what those features are – I'm supposed to be determining some of them now instead of writing this note. Is it real? That depends on your philosophy of math, but at most it's real in the sense that numbers are real. Is there an *object* it represents? No. Do Pitt undergraduates, collectively, live in 40,000-dimensional space? Obviously not.

It probably is the majority view in physics that the wave-function is representational, indeed that it represents inter alia the ordinary macroscopic features of the world. But that doesn't entail that the wave-function is real, or that the universe is a wavefunction. You can motivate that as a further move – it's not silly in the way that reifying grade space is silly – but it doesn't in any way follow automatically. It's a very substantive (and in my view incorrect) additional metaphysical move, by no means a consensus view in philosophy of physics and very heterodox in physics proper, even among those who agree that the wave-function is representational. Many physicists of a cosmological bent might assent to 'the wave-function represents all the dynamical properties of the Universe'; few indeed would assent to 'the universe is a wave-function'.

Chen himself appreciates the distinction, I'm sure, and the article occasionally acknowledges it ("One dominant interpretation of the wave function is that it in fact represents physical reality – some even argue that the universe as a whole is just a quantum wave function") but they're often conflated in the text and even more so in the headings and provocative title, though I appreciate Chen might not have written these himself.

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10 responses to “The universe is not a wave function”

  1. Eddy Keming Chen

    Hi David, I appreciate your comments, and I understand your worry. As you know, it can be difficult to strike a balance when writing for a popular audience – how to make it engaging while not oversimplifying too much. While I was mostly arguing against the general view that the wave function is representational, I was also arguing against the more specific view that the universe is (or emerges from) a wave function. The editors chose to focus on the latter view in the titles and the headings, and suggested changes in the text. The difference between the two views, which should be obvious to the experts, wasn’t highlighted in this popular article. So I understand your worry. I was hoping that, despite its limitations, it may be sufficiently engaging and provocative such that the readers will go on to read the relevant academic articles and books (such as those by yourself), where the issues are presented more carefully.

    I’ve written a survey article for Philosophy Compass that discusses these issues in more detail. Perhaps I should highlight a terminological difference between us. In the article, I characterize realism about the wave function as the view that the wave function represents something objective and mind-independent. That is similar to your idea that “the wave-function is representational / represents objective mind-independent features of the world.” As I explain in the article, realism about the wave function is compatible with a variety of interpretations and does not automatically entail that the wave function represents a field on a high-dimensional yet fundamental space. For example, I classify your view (‘spacetime state realism’ as discussed in Wallace and Timpson 2010) as a version of realism about the wave function. So I’ve been using the label “wave function realism” in a broader sense than some other philosophers.
    Chen, E. K. (2019). "Realism about the wave function." Philosophy Compass, 14(7): e12611. https://arxiv.org/pdf/1810.07010.pdf

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  2. Eddy Keming Chen

    Perhaps I should add that in the popular article I'm arguing for an alternative view called Density Matrix Realism, according to which the quantum state of the universe is objective (representational) but impure (represented by a mixed-state density matrix). And in particular it's an argument for the nomological interpretation of the universal mixed state. That's what the "zooming out" metaphor is about. Interested readers are welcome to check out Chen, E. K. (2021). "Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State." The British Journal for the Philosophy of Science. https://www.journals.uchicago.edu/doi/10.1093/bjps/axy068

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  3. David Wallace

    Hi Eddy – yes, I quite appreciate the difficulties and compromises involved in popular articles. Thanks for the clarifications and links.

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  4. mahmood

    Very informative comments by both David and Eddy!

    Among other thing, I think Eddy makes it clear that there're lots of variations on how one can understand the representationality of the wave function. Now, on this understanding, is it fair to say that it'd be very 'odd' to argue that the wave function is NOT representational in any sense and to any degree? I mean, denying its representationality WRT the unobservable aspects of the world is understandable, but doesn't its predictive success (along with the Schrodinger equation) secure some sense of representationality WRT the observable phenomena?

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  5. Eddy Keming Chen

    Hi Mahmood, thanks for your comments and questions!
    As a scientific realist, I agree that the predictive successes of our best theories often give us good reasons for believing in the reality (or representationality) of their theoretical entities. But things become subtle when we have empirical equivalence. What if two theories are equally successful in their predictions and explanations of the observable phenomena? They may postulate different objects that seem to differ in what they represent. That is the case, I believe, in quantum theory. We can describe many observable phenomena using a wave-function theory (such as the quantum Mentaculus) and also using a (mixed-state) density-matrix theory (such as the Wentaculus). Which is real / representational, the wave function or the density matrix? The answer to that question might come down to super-empirical virtues. On my view, the Wentaculus has many advantages over the Mentaculus. But that is controversial.
    Here are some papers where I discuss the advantages of the Wentaculus in more detail:
    Chen, E. K. (2022). Fundamental Nomic Vagueness, The Philosophical Review, 131(1):1-49. https://arxiv.org/pdf/2006.05298.pdf
    Chen, E. K. (2022). From Time Asymmetry to Quantum Entanglement: The Humean Unification, Noûs, 56(1). https://arxiv.org/pdf/2006.05029.pdf
    Chen, E. K. (preprint). Strong Determinism. https://arxiv.org/pdf/2203.02886.pdf
    Chen, E. K. (2020). ​Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical Probabilities. in Valia Allori (ed.), Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature, World Scientific. https://arxiv.org/pdf/1902.04564.pdf

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  6. David Wallace

    It's helpful to consider the contrast class. Alternative views of the wavefunction include
    – that it's epistemic: it describes an agent's beliefs about something else not represented by the wavefunction
    – that it's, more generally, probabilistic: it describes some (underspecified) sense of a probability distribution over something else not represented by the wavefunction
    – that it's nomic: it defines laws by which the actual physical stuff in the world (not represented by the wavefunction) acts
    – that it's pragmatic: it constitutes advice to agents as to how to act vis-a-vis goings on in the world not represented by the wavefunction.

    The devil in the details of all these alternatives is of course: what's the 'something else'? For some advocates of the Copenhagen interpretation, arguably it was the classical world: classical descriptions are representational, quantum ones aren't, or not directly. (Bohr didn't use the 'representation' terminology, though, and interpreting Bohr is always a delicate business.) But the sharp classical/quantum divide that implies is a bad fit to modern physics. For some modern quantum information theorists, it's directly, primitively, experimental results – but of course, it's then not clear how we are to describe the experimental results, given that we're giving up on quantum mechanics as a descriptive framework. For some modern advocates of modifications to quantum theory, it's a 'primitive ontology' of localized particles – but (although this is a longer story) I think they underestimate how impoverished that descriptive framework is for actually doing justice to experimental phenomenology. (Commonplace descriptions like 'the atom de-excites by emitting a photon' become problematic, for instance.)

    You can make the case that a common theme here is: alternatives to taking the wavefunction as representational end up committing to something that plays a similar role to the positivists' theory language/observation language divide. I don't think that's viable and so I agree with you that we can't get away from having the wavefunction play a representational role. But lots of thoughtful well-informed people disagree.

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  7. mahmood

    Eddy, many thanks for your thoughtful reply and the links to your papers at the end (I'll definitely look them up).

    I think my wording was terrible! TBH, I'm usually much closer to the antirealist end of the spectrum on most issues.

    Here, my point was that even a constructive empiricist (for example) cannot do w/o recognizing at least some sense of representationality of the WF, i.e. the sense in which the WF (possibly along w/ the Born rule or its equivalents) 'represents' measurement results (of course, only in a probabilistic sense). Now, I understand that this might be just a confusion (of terminology) on my part; this (minimal) relation between the WF and measurement results might not be considered representational.

    Thank you so much, again, for your very interesting response!

    Reply
  8. mahmood

    Dear David, what an extremely helpful categorization of the logical space (simplified to suit this brief exchange, of course)!

    I think I can relate to at least two aspects of your response:

    First, especially considering the existing variety of positions, proving the representational role of the WF even in the most minimal of senses is far from a trivial task; I found the last, pragmatic alternative (advocated by Richard Healey?) the hardest to deal with for a defender of representationality.

    Second, by depriving the WF of any representational role, it will be hard (if not impossible) to explain how we are able to describe experimental results. This, if I haven't misunderstood you, is very much in line with my own unpolished intuition.

    Your reply was highly enjoyable to read and think about; thanks very much!

    Reply
  9. Justin Fisher

    As someone who spends more time wearing my "philosopher of mind" hat than my "philosopher of science" hat, I have a hard time parsing this talk of the wave function being "representational". I would have thought that the question of whether A is "representational" was largely a question about whoever it is that is using A, and what exactly they were using A to do, rather than a question about what things exist in the world, which is what I take to be at issue in these debates about quantum mechanics. E.g. my fingers usually aren't "representational"; they start to be "representational" when I start using them to count things; and the fact that they've become "representational" in this way doesn't tell us anything about whether the things I'm counting are real. I think I'm probably just using this term differently from what you mean, so perhaps someone can clarify?

    My, perhaps-mistaken, way of understanding Eddy's view was as saying that the wave function contains more detail than actually exists in reality: that his coarse-grained density matrix assigns numbers to the only (relevant) things that actually exist, whereas the more fine-grained wave function contains further numbers that don't correspond to anything that actually exists. Using David's grade-space analogy, I took the situation to be one in which some folks view the grade-space as involving real-numbered grades, whereas people like Eddy instead view the reality as being just a 13-point grading scale (letter-grades with optional plusses or minusses) and view any attribution of further detail to the grade-space as being an embellishment beyond what actually exists in the world.

    If that's the right way of viewing the issue, then it seems like talk of "representational" misses the point. Sure, a grade-space with decimal precision could be used to *represent* a 13-point grading scale — I often do so in my spreadsheet! — but that doesn't say anything about whether all the possible gradations within this representation actually match up to real details in the world. (In the grading analogy, I think that, for some courses, digits after the decimal point do represent something real, e.g. an average score of a student's graded work through the semester, but this finer-grained structure needn't be uniform across all courses, and may not be present at all in some. I expect that quantum mechanics is probably more uniform than this, with there being more fine-grained wave-function detail than just densities present in the world either in all cases or in none.)

    Reply
  10. Eddy Keming Chen

    Hi Justin, many thanks for your comments and questions. I like your analogy using the 13-point grading scale. In the case of grading scales, there are circumstances where we need the decimal precision. Since the Wentaculus theory (with a universal density matrix) is empirically equivalent to the quantum Mentaculus (with a universal wave function), no empirical observation can distinguish between the coarse-grained reality (represented by a density matrix) and the fine-grained reality (represented by a wave function).

    As you can tell from my earlier comments, I like talking in terms of “real” instead of “representational,” but perhaps the difference is small. Regarding the “representational” talk, I’m not sure if this is how David and others would prefer to clarify it, but perhaps one has the option to say that a mathematical object can represent the world (or some of its aspect) in better or worse ways, for the purpose of accurately depicting reality. While a perfect representation would be ismorphic, preserving all the structure and containing no redundancies, an imperfect one fails to represent some structure or attribute too much structure. Suppose we want to represent a 3-dimensional Euclidean space. A particular Cartesian coordinate system R^3, with an absolute origin, absolute orientations of the axes, and absolute lengths between points, would attribute more structure than there is in reality, while an equivalence class of Cartesian coordiate systems would be just enough. Taking an equivalence class is one way of doing coarse-graining. That can lead to a better match between the representation and “the real details of the world.”

    Talking in terms of “representation,” one can summarize what I say in the article as follows: the wave function is not a perfect representation — in some respect it attributes too much structure to the world, and in others it attributes the wrong structure. We can then have a debate about how much and what kind of structure one needs to recover the empirical predictions of quantum mechanics and secure an adequate explanation of the phenomena. Now, we already use equivalence classes of wave functions to get rid of global phase, which seems like surplus structure. The Wentaculus goes beyond excising surplus structure. It replaces the wave function of the universe with a different kind of mathematical object (a density matrix), which is strictly speaking not an equivalence class of wave functions but still carries less information than an individual wave function does. I suggest that the specially chosen density matrix is sufficiently simple so that we can move it from the category of physical objects to the category of physical laws. It represents not physical objects but part of the rules according to which physical objects must move.

    Although I like talking in terms of “real” instead of “representational,” I suspect in the end no English word is perfect.

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