Meaning of the Wave Function

Why ever the wave function, of all things?

This topic contains 11 replies, has 3 voices, and was last updated by  Ulrich Mohrhoff 4 years, 5 months ago.

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  • #638

    Ulrich Mohrhoff
    Participant

    Abstract: There are strong reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the existence of their correlata (which ought to be self-evident) is demonstrated. The demonstration makes use of the fact (which is implied by the indeterminacy principle) that physical space is not partitioned “all the way down,” and it requires that the eigenvalue-eigenstate link be replaced by a different interpretive principle, whose implications are explored.

    #879

    Ulrich Mohrhoff
    Participant

    I suggest all participants write a few posts under his or her topic, which gives a clear summary of his or her ideas, before the workshop starts. This will be helpful for discussions during the workshop.

    OK, here goes. The question I am asking here is this: why focus on the wave function? After all, there are (by a recent count) at least nine different formulations of quantum theory. The wave-function formulation presents us with two mysteries: why is the unitary evolution disrupted by the occasional collapse, which results in the assignment of probability 1 to a particular outcome, and why is probability 1 sufficient for the factuality of that outcome? The only way the latter mystery can be solved is by adopting the so-called eigenvalue-eigenstate link, which postulates that probability 1 is sufficient for the factuality of that outcome. But doing so makes the quantum-mechanical correlation laws, which presuppose the existence of correlata (measurement outcomes), inconsistent with the existence of the correlata, which is absurd.

    The consistency of the quantum-mechanical correlations with the existence of their correlata can be demonstrated if one gives up the eigenvalue-eigenstate link. The demonstration takes place in two steps. First I show (here in outline, in greater detail in some of the referenced papers) that the world is not spatially differentiated (or partitioned) “all the way down”: its spatial (and hence spatiotemporal) differentiation is incomplete. From this I deduce the existence of a non-empty class of objects whose positions are “smeared out” only relative to an imaginary spatiotemporal background that is more differentiated spacewise than the actual world. If anything truly deserves the label “macroscopic”, it is these objects. The testable correlations between the outcomes of measurements of their positions are consistent with both the classical and the quantum laws. This makes it possible to attribute to these positions the measurement-independent reality that is lost by giving up the eigenvalue-eigenstate link, and it enables them to define the obtainable values of observables and to indicate the outcomes of measurements.

    Trigger phrases like “measurement” and “macroscopic object” are likely to elicit accusations of instrumentalism, Copenhagenism, or some such. Common or garden instrumentalism, however, leaves the meaning of “macroscopic” up for grabs. What is accomplished here is a consistent definition of “macroscopic” in the theory’s own terms. And that’s only the beginning. (To be continued.)

    #880

    Ulrich Mohrhoff
    Participant

    The eigenvalue–eigenstate link is an interpretive principle that saves the appearances in the context of the wave-function formulation of quantum mechanics. To go beyond a metaphysically sterile instrumentalism, a different interpretive principle needs to be used, as well as as a different formulation of quantum mechanics: Feynman’s. Both the wave-function formulation and Feynman’s feature a pair of dynamical principles; in the former they are unitary evolution and collapse, in the latter they are summation over amplitudes and summation over probabilities. In the context of the wave-function formulation, unitary evolution seems “normal”; what calls for explanation is collapse. In the context of Feynman’s formulation, adding probabilities seems “normal”; what calls for explanation is why we have to add amplitudes. What is at issue, then, is not what causes the wave function to collapse but why we have to add amplitudes whenever quantum mechanics requires us to do so. To answer this question I have proposed the following interpretive principle:

    (I) Whenever quantum mechanics requires us to add amplitudes, the distinctions we make between the alternatives correspond to nothing in the physical world. They cannot be objectified (represented as real).

    Next, I apply this interpretive principle to two paradigmatic setups, one concerning distinctions between regions (of space or spacetime), the other concerning distinctions between things. Applied to a two-way interferometer experiment, (I) tells us that the distinction we make between “the particle went through the left arm” and “the particle went through the right arm” corresponds to nothing in the physical world, whence it follows that physical space cannot be an intrinsically differentiated expanse. Its so-called parts need to be physically realized by the sensitive regions of detectors (defined in terms of macroscopic positions), and the indeterminacy principle prevents them from being realized “all the way down”.

    Applied to an elastic scattering event involving two particles of the same type (two incoming particles N and S, two outgoing particles E and W), the interpretive principle (I) tells us that the distinction we make between the alternative identifications (N=E, S=W) and (N=W, S=E) corresponds to nothing in the physical world. There is no answer to the question “Which outgoing particle is identical with which incoming one?” Now why would that be so? Watch this space.

    #888

    Ulrich Mohrhoff
    Participant

    So why is there no answer to the question “Which outgoing particle is identical with which incoming one?”? Because the incoming particles (and therefore the outgoing ones as well) are one and the same entity. What’s more, there is no compelling reason to believe that this identity ceases when it ceases to have observable consequences owing to the presence of individuating properties. We are free to take the view that intrinsically each particle is numerically identical with every other particle; what presents itself here and now with these properties and what presents itself there and then with those properties is one and the same entity. For want of a better word I call it “Being” with a capital B.

    As I see it, the main reason it is so hard to make sense of the quantum theory is that it answers a question we are not in the habit of asking. Instead of asking what the ultimate constituents of matter are and how they interact and combine, we should ask: how are forms manifested? This question, too, has a straightforward answer: The shapes of things are manifested with the help of reflexive spatial relations. By entering into reflexive spatial relations, Being gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is ignored and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified.

    To my mind, the most fruitful way to understand the necessary distinction between the classical or macroscopic domain (which contains measurement-independent properties) and the non-classical or quantum domain (whose properties exist only if, when, and to the extent that they are measured) is that it is essentially a distinction between the manifested world and its manifestation.

    Quantum mechanics thus presents us with a so far unrecognized kind of causality — unrecognized within the scientific literature albeit well-known to metaphysics. This causality is associated with the atemporal process of manifestation, which effects the transition from a condition of complete indefiniteness and indistinguishability to a condition of maximal definiteness and distinguishability. It must be distinguished from its familiar spatiotemporal cousin, which links states or events across time or spacetime. The latter causality plays no role in the manifestation, which is why it is inapplicable to the subject-matter of quantum mechanics — the correlation laws that are instrumental in the process of manifestation. The atemporal causality associated with the process of manifestation thus casts new light on quantum theory’s mysterious violation of outcome-independence. The reason why local explanations do not work is the same as the reason why the manifestation of the spatiotemporal world cannot be explained by processes that connect events within the spacetime arena.

    #963
    Richard Healey
    Richard Healey
    Participant

    Ulrich,

    I’m afraid your session is scheduled for a time that is too late for me to participate. I will certainly read the posts afterwards when I have time since I find your views interesting & would like to learn more.

    Richard

    #965

    Ulrich Mohrhoff
    Participant

    Richard,

    You are welcome to ask questions any time, even now, if it’s not too late for you. (I just finished my breakfast.)

    Ulrich

    #976
    Ken Wharton
    Ken Wharton
    Member

    Dear Ulrich,

    I certainly appreciated your main points, especially your attempts to interpret the path integral, a question that has certainly not received the foundational attention that it deserves.

    But… having spent a lot of time trying to make sense of this very issue, I’m afraid I’m not yet convinced your approach is getting us closer to such an interpretation. One problem is that even if you do draw some line in the sand about what measurements are “really” macroscopic, I’m reading from your approach that we can say nothing about what happens inbetween those ultimate measurements. So it’s not just interferometer arms in which nothing can be said to happen; it’s also all the space between us and a gravitationally-lensing supercluster. This seems a bit extreme, at least for those like me who want to understand what the path integral is telling us about what’s happening when we’re not looking. Can you offer me any hope in the case of the supercluster?

    The other concern I have has to do with your use of the word “atemporal” near the end. Whenever I see this word accompany terms that normally have temporal meaning, I wonder whether the author is (accidentally or purposefully) imagining a 5th time dimension in which things can “happen” in some order without any usual-4th-time-dimension time being involved. Would you say that this new type of causality is effectively happening in some new dimension of time? If not, is there a block-universe account of these last paragraphs that might help me make sense of them in 4D? (Is it mere updating of possibilities upon learning new information, or something more than that?)

    One final note on your last footnote. It’s true that many temporal correlations have the same mathematical form as Bell-inequality violating spatial correlations, but that doesn’t make them “spooky”; there are certainly many local-interacting models that can make sense of correlations between the past and future of a single particle. So I didn’t really understand that last sentence. All that such an explanation requires is that the intermediary beables are affected by at least one of the measurement settings. The reason that the exact same correlations seem “spooky” in the case of EPR-Bell geometries is that we instinctively don’t want to allow the (past) beables to be affected by the (future) measurement settings, not because we don’t know how to explain time-like correlations in the first place.

    Best,

    Ken

    #977

    Ulrich Mohrhoff
    Participant

    Dear Ken,

    Many thanks for your challenging questions. I’ll start with this one:

    I’m reading from your approach that we can say nothing about what happens in between those ultimate measurements. So it’s not just interferometer arms in which nothing can be said to happen; it’s also all the space between us and a gravitationally-lensing supercluster. This seems a bit extreme, at least for those like me who want to understand what the path integral is telling us about what’s happening when we’re not looking. Can you offer me any hope in the case of the supercluster?

    I’m afraid I can’t, for I wouldn’t know a sufficiently fundamental difference between the lab interferometer and the gravitationally-lensing supercluster. Do you? Besides, it’s not a question of looking. It’s a question of there being an objective fact of the matter about the path taken by the photon (or whatever).

    I’ll need more time to contemplate your subsequent questions, so I’ll shoot this off right now.

    #978
    Ken Wharton
    Ken Wharton
    Member

    My 2 cents on the path integral: If there was a particle-like, one-path interpretation, waiting to be found, I’m sure Feynman would have found it right away. But he shied away from field-based interpretations, and I don’t think those have been ruled out properly. My instinct is that the intermediate field passes through *both* arms, in both lab interferometers and the supercluster, even for single photons. All you then need is a little anomalous phase shift (at *any* point in either arm) to kick the net field into something that looks like a single-photon upon measurement. The path integral mathematics is then telling us how big a kick we need, and presumably bigger kicks are less probable.

    (Getting this kick matched up with the choice of final measurement is the tricky part… 🙂 )

    #980

    Ulrich Mohrhoff
    Participant

    Ken, on to your next bundle of questions.

    The other concern I have has to do with your use of the word “atemporal” near the end. Whenever I see this word accompany terms that normally have temporal meaning, I wonder whether the author is (accidentally or purposefully) imagining a 5th time dimension in which things can “happen” in some order without any usual-4th-time-dimension time being involved. Would you say that this new type of causality is effectively happening in some new dimension of time?

    While “causality” does normally have a temporal meaning, it doesn’t necessarily have such a meaning. There may be no superluminal causal connections, but the term “superluminal causal connection” is not self-contradictory. (This is just a counterexample.)

    I certainly do not imagine another time dimension, though I’m familiar with the difficulty we have in imagining any dimension (including time) except in analogy with a spatial dimension. Whatever happens, happens in the usual time dimension. An atemporal dimension in which “things can ‘happen’ in some [temporal] order” is a contradiction in terms. So, no, this new causality is not effective across any temporal dimension. The different stages of the “transition” from undifferentiated unity to multiplicity coexist, but still there is some kind of causal arrow that makes it legitimate to speak of “stages”, in the sense that the multiplicity exists because of the spatial relations that Being entertains with itself; Being does not exist because of the multiplicity of the manifested world.

    is there a block-universe account of these last paragraphs that might help me make sense of them in 4D?

    I’m afraid there isn’t. The whole block universe concept strikes me as an illegitimate spatialization and reification of mathematical tools we use to calculate distances and durations.

    Is it mere updating of possibilities upon learning new information, or something more than that?

    It is more than that, but I’ll admit that it’s hard to get one’s mind around the idea, considering the years I have spend in disabusing myself of the habit of reifying our calculational tools, which makes it impossible to look beyond them.

    #982

    Ulrich Mohrhoff
    Participant

    Ken, here I respond to your note concerning the last footnote of my paper, which I reproduce here for the benefit of the others:

    “Actually, the diachronic correlations between events in timelike relation are as spooky as the synchronic correlations between events in spacelike relation. While we know how to calculate either kind of correlation, and therefore know how to calculate the probabilities of possible events on the basis of actual events, we know as little of a physical process by which an event here and now contributes to determine the probability of a later event here as we know of a physical process by which an event here and now contributes to determine the probability of a distant event now.”

    It’s true that many temporal correlations have the same mathematical form as Bell-inequality violating spatial correlations, but that doesn’t make them “spooky”; there are certainly many local-interacting models that can make sense of correlations between the past and future of a single particle. So I didn’t really understand that last sentence. All that such an explanation requires is that the intermediary beables are affected by at least one of the measurement settings. The reason that the exact same correlations seem “spooky” in the case of EPR-Bell geometries is that we instinctively don’t want to allow the (past) beables to be affected by the (future) measurement settings, not because we don’t know how to explain time-like correlations in the first place.

    I used “spooky” rather loosely here and need to apologize for it. My presupposition is that all that quantum mechanics gives us is correlations between measurement outcomes, and that we don’t know of any physical mechanism or natural process by which the outcome of a measurement determines the probabilities of the possible outcomes of a subsequent measurement, any more than we know any physical mechanism or natural process by which Alice’s outcome determines the probabilities of the possible outcomes of Bob’s measurement (in Alice’s mind only, QBists would insist).

    It’s my turn to admit that I’m not clear about the intent of your last sentence, but given what I believe is required of an explanation, I do not believe that we know how to explain time-like correlations.

    Thanks again for your questions,

    Best,
    Ulrich

    #983

    Ulrich Mohrhoff
    Participant

    Dear All,

    My scheduled time is now up, but I will be happy to respond to any further questions or comments later.

    Ulrich

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