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B Meaning of Wave Function Collapse

  1. Jul 13, 2018 #1
    When a layman like myself hears the term 'Wave function collapse' is brings to mind physical things. A wave of some sort physically getting smaller or shrinking. Obviously that's not what it is but it does sound like it. In reality, if I have it right it's just a fancy way of saying a measurement has been taken and whatever it was that was being measured has been found to have a value (or range of values). But it might as well be called 'measurement function resolution' or even 'monkeyguts'. And by using "loaded" terms (loaded with physical sounding meaning) confusion might accidently arise. This is similar to web programming with the awful term 'cookies'. We all know it's just a file. But you can imagine a discussion that takes the analogy too far, and wanders into things like, if I mix enough dough, and then add chocalate chips, I can create numerous cookies. And someone replies, well it depends on how you bake the cookies and the type of oven you use. Pretty soon you're talking about cooking itself, instead of file operations and data storage. And if you're not careful you come to conclusions about baking, i.e. about the analogy, and not file storage. Is there a possibility of something like that happening in discussing QM and wave function collapse? Discussions and conclusions are stated having to do with the math (the baking as it were) instead of the thing itself, the files or thing being measured.
     
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  3. Jul 13, 2018 #2

    Nugatory

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    "Collapse"isn't the only loaded term - "observation", "measurement", and "particle" are also easily misunderstood. These are used for historical reasons; they were introduced before the modern form of the theory was understood, and once a phrase makes it into common usage it generally sticks even if we later realize that it is inappropriate (consider, for example, that we still call Caribbean islands the West Indies, even though the connection to India has proven to be non-existent).
    There is, and the antidote to confusion is to learn the mathematical formalism of the theory.
     
  4. Jul 13, 2018 #3
    Seems like at some point the formalism needs to be grounded back to reality in a way that's understandable without the formalism. In my analogy, we can formalize the notions of "baking" as much as we want, but at some point it has to come back to files and data. I'm just always interested in how much discussion here sounds like we're (well you guys) are coming to conclusions about the math, instead of the things the math is supposed to describe. Or maybe that's the key. It's no longer about the things in themselves, but only about the measurements that can be made. (Meaning we can't get to the thing itself, so we've settled for getting at measurements about it so to speak. Which isn't a dig, just the way it turned out that yields more useful information.)
     
  5. Jul 13, 2018 #4

    ZapperZ

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    No. It is more of laymen getting too enamored by the "name" that has been given to an aspect of physics. Maybe for you, you should replace the word "collapse" with a phrase such as "acquire immediately a specific value". After all, you had no problems when the coin that you tossed and landed to attain a particular state of either heads or tails.

    Will this make it simpler?

    Zz.
     
  6. Jul 13, 2018 #5

    atyy

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    In some old presentations, the collapse is presented as part of the Born rule. Nowadays, we usually separate out the collapse from the Born rule. So the Born rule tells us the probability of a measurement outcome, and the collapse tells us the probability of the state that the system is in after the measurement outcome has been obtained.

    Technically, if one doesn't make a subsequent measurement, then there is no need for collapse. The collapse is about the measurement outcome that has just been obtained, and its relationship to the next measurement outcome, ie. the collapse is needed if one calculates the conditional probability.

    The Born rule itself, which is about the probability of a measurement outcome, is not exactly like classical probability. In classical probability such as flipping a coin, the outcome is unknown, but the coin has a definite trajectory while it is being flipped. Classical probability comes about from your ignorance about the complexities of the coin's trajectory, which is a deterministic hidden variable. However in quantum mechanics, although one can measure position or momentum, in many cases, the system cannot have definite position and momentum before the measurement outcome has been obtained. Thus in quantum mechanics, if hidden variables exist, they must be different from those of classical physics. Furthermore, Bell's theorem tells us that if hidden variables exist, then they must be nonlocal.
     
    Last edited: Jul 13, 2018
  7. Jul 14, 2018 #6

    Nugatory

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    I sympathize with your expectation here, but I don't think it can be met.

    "Understandable without the formalism" requires a reasonably accurate math-free description, which in turn requires both that natural language includes words for the basic concepts (easy) and that these words can be explained in non-mathematical ways (probably impossible - some very talented teachers and explainers have been trying and failing for more than a century). Consider your original example: "wave function collapse" can be used as a natural language term, but it fails on the second requirement; it is, as you say, misleading. But what's better? We could, as you suggest, say "monkeyguts" and not risk misinterpretation based on the word "collapse", but we still have to explain what we do mean by the term.
     
  8. Jul 14, 2018 #7

    bhobba

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    As Feynman explains it has been found, at least nobody has figured out how to do it, that you cant really explain physics without math:


    It just seems to be the way it is.

    Those like me into math love that its like that - others not so much. If its any consolation Feynman got the highest scores on mathematics and physics in his entrance exam for his PhD - but the lowest they had ever seen in the humanities. The methods used in the humanities simply do not seem to work and its highly doubtful they, via their methods, could ever have come up with for example the very profound Noethers Theorem:
    https://hackaday.com/2016/06/14/symmetry-for-dummies-noethers-theorem/

    Its maddening to those not into math, but believe me things like literary analysis are equally maddening to me - I simply do not get it. It just seems to be the way things are.

    Thanks
    Bill
     
    Last edited: Jul 15, 2018 at 6:26 AM
  9. Jul 14, 2018 #8
    I ignore all the words and just study the equations. Now I hear "blah blah blah EQUATION blah blah blah." All I want to know is how to solve a specific problem using the equation. I don't worry at all about the words, because our natural language is inadequate to describe things as complicated as quantum mechanics. We should stick to counting and measuring and use very simple words. When people start using big words and wave their hands excitedly, I leave the room.
     
  10. Jul 15, 2018 at 9:07 AM #9
    What this discussion brings up for me is how much of a gap is there in our understanding of the physical world as regards wave function collapse? Yes, we have math to accurately describe the probability of different outcomes, but isn't it correct to say there's no theory (and perhaps more importantly, no math) that explains why the collapse should happen?
    We observe that particles take on a definite value when observed but is that really any better than observing that the sun rises in the East and there being a few theories around (e.g., invisible chariots, rotating orbs) to explain why? (And the hard-nosed realists might just refer to those as philosophical theorizing and so "shut up and calculate"--we know it rises, that should be good enough.)
     
  11. Jul 15, 2018 at 9:14 AM #10

    ZapperZ

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    But this is equivalent to asking why the speed of light in vacuum is a constant in all reference frame, why is the value of elementary charge the way it is, why is there conservation laws and symmetries in our universe.... etc... etc.! None of those things are derivable either! Forget QM. Check your classical mechanics. There are many things that simply appear out of nowhere! Why would the Lagrangian/Hamiltonia work? Why should there be a principle of least action?

    And I'll go even a step further. The moment we find how those things come about, we will add ANOTHER level of starting points where we don't know how they come about! We have seen this throughout history of human endeavor and science progress. There will ALWAYS be something we don't know completely well.

    In other words, why is the mystery surrounding "collapse" of this wavefunction is such an issue, while all the other stuff, you guys seem to be OK with?!

    Zz.
     
  12. Jul 15, 2018 at 9:27 AM #11
    I think the other issues you mention are mysteries. Pondering them gives us an intuitive sense that there's some deeper structure to things we haven't gotten access to (so, we might guess that time and space are artifacts of some deeper physical reality, for example.)
    The unique aspect of wavefunction "collapse" is that it directly involves us and consciousness, and more fundamental questions of cause and effect.
    (I guess you could say speed of light being a constant also betrays our notions of cause and effect but since light is already weird in relation to our everyday experiences, it's easier to give it a pass.)
     
  13. Jul 15, 2018 at 9:31 AM #12

    ZapperZ

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    But I can play the same game. You seem to be rather free in using the name "consciousness", but do you really KNOW what that is?

    Again, you ignored the fact that even if we can answer all the "mysteries" that we have right now, there will be ANOTHER level of mysteries that will come up that we do not have the explanations for. You seem to not want to face up the reality that this chain of events will never end!

    Zz.
     
  14. Jul 15, 2018 at 9:35 AM #13
    "... You seem to not want to face up the reality that this chain of events will never end!"
    No, I get that. But it's more a matter of how consistent our understanding is. If we lived in today's society but still didn't have any understanding of how the sun seemed to rise in the East every morning, that would be an odd omission. Similar issue with wavefunction collapse and consciousness--it's odd that we don't really have the beginnings of a meaningful qualitative explanation in either case.
     
  15. Jul 15, 2018 at 9:41 AM #14

    ZapperZ

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    That would be true if we have given up on continuing to study this. But we haven't!

    As much as QM has become so prevalent in all our lives, and we have used it to such a successful degree, there continue to be research work done on the fundamental aspects of it! We still have search papers published examining the basic postulates and principles of QM. In fact, this can be said about other areas of physics as well! Come back next millennium and maybe these things will be so well-known, we teach them in kindergarten by then. You seem to want all the answers on demand!

    BTW, if you have a vector, and you measure a component of the vector, do you puzzle over the fact that you get this component right away? Will you be puzzled that making a measurement in QM is an analogous process as finding the component of a vector?

    I'm still waiting for you to tell me if you know what "consciousness" is.

    Zz.
     
  16. Jul 15, 2018 at 11:44 AM #15

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    It does not. The idea that a conscious observer is involved in wave function collapse was largely abandoned many decades ago, after the discovery of ways of formulating the theory without that assumption. Unfortunately, by then the idea had leaked into the popular imagination where it lives on to this day as a sort of urban legend.

    (This is not to say that there are not open foundational questions, the so-called "measurement problem" in its various forms, just that these problems are not encountered until you move beyond the lay notion of consciousness causing collapse).
     
  17. Jul 15, 2018 at 12:05 PM #16

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    Do we really have that understanding, in the sense what you're looking for?

    Sure, we all learned in high school about how there is a gravitational force between objects that is proportional to their mass and inversely proportional to the square of the distance between them, and that that force along with Newton's laws explains everything about the solar system including the progression of the heavenly bodies through the sky (the sun rising in the east being one of these).

    But why is the force proportional to the mass, instead of (for example) the square of the mass? Why is the force attractive instead of repulsive, and why is it inversely proportional to the square of the distance instead of, for example, the cube or the first power? For that matter, why should there be any force at all? We have a set of equations that work just fine, but no understanding of why they work, and that situation is no different than what we have with the mathematical formalism of quantum mechanics. The only difference is that classical mechanics is (and this is a tautology) consistent with our intuitive expectation of how the classical world ought to behave so we unquestioningly accept the math without looking deeper.
     
  18. Jul 15, 2018 at 2:29 PM #17

    anorlunda

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    Not at all. It is a personal bias to think that the math is not real, while that understandable without formalism is real. We may never find ways to explain all of science using natural language. The solution is for those who are interested to learn the math. I refuse to believe that learning math is impossible for every person willing to make the effort.
     
  19. Jul 16, 2018 at 2:50 AM #18

    bhobba

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    Well wave-function collapse is not part of the theory - just some interpretations. That after the observation it is in a different state is a consequence of the axioms QM is founded on - but collapse goes further - it is supposed to happen instantaneously - see for example page 15 - Schlosshauer - Decoherence and The Quantum To Classical Transition. In some interpretations we have collapse and others we do not:
    https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

    That's the problem with your question - QM does not contain collapse. Only some interpretations do.

    I will state the two axioms from which everything follows - although at the beginning level you are not likely to understand it (it requires linear algebra which most do not do until university - although I believe is should be at HS - but that is another issue and another thread).

    1. Associated with every observation on a system is a linear operator, O, whose eigenvalues give the possible outcomes of the observation.
    2. The average of the possible outcomes is given by the formula Trace (OS) where S is a positive operator of unit trace, by definition called the state of the system.

    Interestingly 2 can to some extent be derived from 1 using something called Gleason's theorem:
    https://en.wikipedia.org/wiki/Gleason's_theorem

    That it, that's all. A good textbook like Ballentine - QM - A Modern Development derives all of QM from just those two axioms. But unfortunately is advanced - you need to build up to it with a beginning and intermediate course in QM first, as well as courses in calculus and linear algebra.

    Now you see the single imprecise thing - observation.
    1. What is an observation.
    2. When exactly does it occcur. That's part of the concept of collapse which some interpretations have - but others do not. However I will also tell you some believe collapse is inherent - some do not (I am in that camp).

    There are probably others as well.

    Collapse isn't part of the Quantum theory - it something added on in some interpretations. So there is no issue here at all. Now why those two axioms. Well here is a paper deriving them:
    https://arxiv.org/pdf/quant-ph/0101012.pdf

    That reduces it to the above 5 reasonable axioms - of which the most relevant one as far as QM is concerned is why do we have continuous transformations between so called pure states - otherwise you get just normal probability theory. Well if we didn't, we couldn't use the methods of calculus to describe changes in pure states. Nature was very obliging. But that still doesn't answer why?

    Hopefully you will now see what others have been saying. Even QM can be explained by something that seems more fundamental - but it doesn't answer why. Doesn't matter what you do, what theory you have, you will always have this why question - its unavoidable.

    But what we can say is that collapse is not one of those - its just something some interpretations have introduced for their own reasons. No need to ask why about those - it's just what some have put in there for their own reasons.

    Thanks
    Bill
     
  20. Jul 16, 2018 at 8:47 AM #19

    atyy

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    Collapse is part of quantum theory. In that paper, it is stated in Eq 10, and in notes 3 and 4 on p6.
     
  21. Jul 16, 2018 at 2:07 PM #20
    just broken superpositions,
    modestly.

    maybe gravity breaks quantum superpositions


    .
     
  22. Jul 16, 2018 at 2:38 PM #21

    PeterDonis

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    Those don't say "collapse" in the sense @bhobba was using the term is part of QM. They say that the von Neumann projection postulate is part of QM. That's not the same thing. The projection postulate makes no claims about whether "collapse really happens"; it just says that, in the mathematical formalism, once you observe a particular measurement result you have to use the projection postulate to get the system's new quantum state that you will use to predict the probabilities of future measurement results.
     
  23. Jul 16, 2018 at 3:03 PM #22

    Grinkle

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  24. Jul 16, 2018 at 3:09 PM #23

    bhobba

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    As Peter suggested there may be different conceptions going on what collapse means. Can you detail what you mean by it, and why it is considered some interpretations have it and others do not?

    Thanks
    Bill
     
  25. Jul 17, 2018 at 8:31 AM #24

    zonde

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    I find Wikipedia useful as a source of common meanings for terms i.e. as a kind of dictionary. And wave function collapse is explained as projection with normalization:
    ##|\psi \rangle \rightarrow |\phi_i\rangle##
    So maybe @bhobba should explain what he means with "collapse"?
     
  26. Jul 17, 2018 at 9:41 AM #25

    ZapperZ

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    Wait... you think that "projection with normalization" qualifies as a "common meaning"?

    I illustrated earlier about this being analogous to taking the component of a vector, which I think is a more "common" knowledge for many people, especially those who wish to hang around in a forum like this.

    Zz.
     
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