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Does quantum mechanics partially supply its own interpretation?

  1. Apr 10, 2012 #1

    Physics Monkey

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    I will try to keep things brief. I am trying to understand what is considered interpretation.

    Imagine we have a totally isolated and complex quantum system in a fixed initial state which we can prepare with essentially perfect fidelity. Suppose that this system is macroscopic in which small subsystems are totally decoherent and classical and life exists.

    If we now make measurements on this system, then according to the usual prescription we will find a variety of outcomes. For example, if a living being inside the system measures a spin 1/2 particle in their world and we then measure them, then we would find that sometimes they found spin up and sometimes spin down. In this sense the same state describes two different experiences for the living being.

    Except for the absurd level of control and isolation being assumed here, can we all agree that this is what quantum mechanics predicts? (Quantum mechanics here including the usual measurement rule that describes so well what occurs in our laboratories.)

    My real question is this: where does interpretation come in? Is it just a matter of calling the state vector "really real" versus a "statistical description" versus ... or is there something more to it? If we are the living being and we believe our isolated world is described by a unitarily evolving state vector, then doesn't quantum mechanics (if we take it completely seriously) force us to conclude that the state of the world describes multiple possible experiences for beings similar to us? Is this trivial observation what it usually called "many-worlds"?
     
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  3. Apr 10, 2012 #2
    An interpretation is what you think those pretty numbers you get as results mean, in the real world. The main concern is, really, the wavefunction collapse problem.

    In Q.M. you have pretty numbers that say a lot of things about the system which is observed. But what they actually mean, in the real world, depends on the interpretation.

    For instance, the Copenhagen interpretation says that when the wavefunction collapses upon measurement, then all other possible outcomes of a measurement do not exist anymore. When this collapse happens, we do not know, but it does.

    The Many-Worlds interpretation says that there is no collapse, and that each possible existence given by the wavefunction is real. That is, there are different versions of you, each one having measured a different spin.

    Check my other thread, the poll about the Interpretations of Q.M. and see the list of interpretations of the poll. Read up on a few of them so you will see what we're talking about.

    Wikipedia gives a good explanation of what an interpretation is supposed to do, and the list I got was off the wiki, too.
     
  4. Apr 10, 2012 #3

    Fredrik

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    I don't know decoherence well enough to be sure that what I'm about to say is right, but I think the assumption in your first paragraph ensures that the state of this "system" will be indistinguishable from a classical superposition.

    There are many things one can mean by "interpretation". To some people, an interpretation is defined by the mathematical axioms and correspondence rules that define the theory. (The correspondence rules tell us how to interpret the mathematics as predictions about results of experiments). I would say that axioms and correspondence rules define theories, not interpretations, that QM is a theory, rather than a piece of mathematics that needs to be interpreted, and that the words "interpretation of QM" should refer to non-scientific speculation about what the theory we call "QM" really means.

    Some would say that the concept of "really real" that you mentioned is nonsense, since it's untestable. I think those people are missing the point. It's certainly unscientific, but that doesn't make it nonsense. The concept of "being real" is as fundamental as anything can get (certainly more fundamental than the set theories that we take as the foundation of mathematics), so physics (which is based on mathematics) can't really shed any light on what that concept means.

    In my opinion, yes. To say that the state vector describes the system, or to say that it represents all the properties of the system (rather than the properties of an ensemble of identically prepared systems) is to advocate an MWI. I have made this argument myself in this forum.

    Edit: However, Everett's MWI is something more (or maybe I should say less) than this. It's based on the idea that you can drop the Born rule from the list of axioms, and then derive it from the others. This is almost certainly impossible if you don't make any additional assumptions. So Everett's MWI simply hasn't been developed to the point where it can be called an interpretation of QM, in any sense of the word. It's just a failed idea. Of course, that doesn't imply that there aren't many worlds. :smile:
     
    Last edited: Apr 10, 2012
  5. Apr 10, 2012 #4
    Some people claim to have derived the Born rule, including Everett himself. I am uncertain about this, but whichever way, just because the Born rule hasn't been derived yet doesn't mean it's not derivable. One should not underestimate human ingenuity.
     
  6. Apr 10, 2012 #5
    I have one tiny little thing to point out. The system can't be closed if we observe this living thing that's measured a particle's spin.
     
  7. Apr 10, 2012 #6
    Once we observe it, no, of course it's not. But I believe he meant that the system was closed up until we observed the living thing.
     
  8. Apr 10, 2012 #7

    Physics Monkey

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    Thanks for the replies so far.

    James,
    I understand the general idea of an interpretation, but I don't understand many of the words within various interpretations. For example, when you say that Copenhagen declares that unrealized outcomes don't exist, what does that mean? Does it mean that there is no local unitary transformation (e.g. time evolution in reverse) that would formally take the state of the world after the measurement back to the state of the world before the measurement? If we accept that the state of the system before we look at it is a complicated superposition like (spin up and being sees up) + (spin down and being sees down), would we say, as textbooks often do for isolated spins, that the spin/being system is both up and down?

    Fredrik,
    Although I was using "really real" half in joking, I do agree with you that it is not nonsense and am happy to think about it. Mostly I just don't know what such a thing is supposed to mean even apart from scientific considerations.

    Whovian,
    I did have in mind that the system was isolated up until the time when we measure it.

    Regarding the Born rule, in many ways I feel that it should be obvious that it can be derived from unitary evolution. I say this because I believe a unitarily evolving state vector can describe beings like us who assign probability according to the Born rule. Thus with the proper definition of being, etc. it should be possible to show in the context of unitary evolution that such beings will use the born rule. But perhaps this argument is too meta.

    In other words, given a definition of classical beings, analyzing the unitary evolution of complex composite systems should reveal a notion of probability, etc.
     
  9. Apr 10, 2012 #8

    Fredrik

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    Sounds like what we'd find this way isn't that the Born rule must hold, or an explanation of what the probabilities mean. We would only be able to show that there are people who believe in the Born rule. :smile:
     
  10. Apr 10, 2012 #9
    I've not read much about this, but it sounds like you're arguing that you should be able to show that predictions that use the Born rule to assign probabilities will turn out most accurate in the long run. But for any finite number of trials, there's always a finite probability that the Born rule will look completely wrong, and I don't see how you can argue that this probability is small unless you first (circularly) assume the Born rule.
     
  11. Apr 10, 2012 #10
    Copenhagen assumes a non-unitary, non-local, all in all magical process called collapse that happens when something undefined that they call an observation happens. They mean that, once a measurement is made, there is no longer any superposition. Before we look, superposition alright. After observation, the superposition is gone.

    Many-Worlds states that the superposition is never gone, it just starts holding a larger number of things in it; in this case the person who measured the spin is in a superposition of states, too.

    ---

    Now, the Born rule is a problem. It has been shown, I think, that a conscious observer would derive the Born rule, but it's still a challenge to prove that the Born rule actually exists.
     
  12. Apr 11, 2012 #11

    Fredrik

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    I know that this is what "everyone" says that the Copenhagen interpretation says, but I think this is just how it was defined by people who have misunderstood it. It's like when creationists define the big bang theory as "first there was nothing, and then it exploded". I don't think this definition is logically consistent, and I don't think there's evidence that Bohr thought that this is how the world works. If there is, I haven't seen it.

    I like this quote from Asher Peres:
    There seems to be at least as many different Copenhagen interpretations as people who use that term, probably there are more. For example, in two classic articles on the foundations of quantum mechanics, Ballentine (1970) and Stapp (1972) give diametrically opposite definitions of “Copenhagen.”​
    The quote is from this article (page 6). Peres goes on to explain how he thinks the Copenhagen interpretation should be defined.

    I believe that Bohr's idea was essentially just that QM should be viewed as a way to calculate probabilities of possible results of measurements, rather than as a description of what's actually happening. This would mean that his view is an ensemble interpretation, regardless of whether he said that explicitly or not.

    This is by the way the reason I didn't answer that poll. There's no consensus about how the interpretations should be defined, or even about what an interpretation is. I don't want to put a label on my views of QM when I know that different people would interpret that label differently.
     
  13. Apr 11, 2012 #12

    Demystifier

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    The Born rule is derivable, and several derivations of it are already known. But the point is that all derivations rest on some ADDITIONAL ASSUMPTIONS. What different people disagree is whether the specific assumptions (in a given derivation) are appealing or not.
     
  14. Apr 11, 2012 #13

    Hurkyl

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    The central feature of the Copenhagen interpretation is wave-function collapse. As far as I tell, the main variations are whether you take that at face value (as I was originally taught was meant by the phrase "Copenhagen interpretation", and still often seen it defined as), or you interpret it as ignorance about an unknown hidden variable theory.

    I know I'm being a bit glib, but since no details of the hidden variable theory are supplied, there really isn't any difference between the two variations, except in the amount of leeway it gives people to rationalize away criticism.


    On an unrelated point, if Peres is really giving a fair representation of Bohr, then Bohr was being rather silly on at least one point. (i.e. the "argument" that experiments must be described in classical terminology, which consists of nothing more than an assertion that experiments must be described in classical terminology)
     
  15. Apr 11, 2012 #14

    Fredrik

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    Peres's article about the CI doesn't even contain the word "collapse" or its synonym "reduction", so I doubt that he would agree. But I suppose that if almost everyone in physics believes that collapse as a physical process is a part of the CI, then maybe we should define it that way. This is like reluctantly admitting that "nucular" (nuke-you-lurr) is now an acceptable way to pronounce the word "nuclear", just because the mistake is so common.

    If this collapse is assumed to be exact rather than approximate, it would probably make the CI logically inconsistent (it seems to contradict the unitary time evolution), so this would make the CI a nonsense interpretation. If it's approximate, then we're just talking about decoherence, which is already a part of the theory. So if the CI is defined by an assumption of "collapse", it's either nonsense or a bunch of words that don't actually say anything.

    I don't understand this objection. Science requires us to test the predictions of our theories, so we obviously have to do experiments that have (classical) results. How else would we know if the theory has passed the test or failed it?
     
  16. Apr 11, 2012 #15

    martinbn

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    Fredrik, I don't agree. I don't think that the collapse is viewed as a physical process in CI, and I don't think that's what Hurkyl meant. Also, I don't see any inconsistency in having two different ways in which the evolution is described, one the unitary and the other the non-unitary projection.
     
  17. Apr 11, 2012 #16

    Fredrik

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    It's pretty common to claim that collapse as a physical process is an essential part of the CI. See post #10 for example. I think almost all the attempts to explain what the CI says that I've seen have said something similar.

    It's true that there's no obvious contradiction between unitary and non-unitary time evolution. Isolated systems evolve unitarily, and non-unitary time evolution is something that happens to systems that interact with their environments. However, if collapse is supposed to be something different from decoherence, then I think a contradiction is unavoidable, but it's of course impossible to prove that without a definition of "collapse".

    So what is a collapse? Isn't it supposed to be the process that allows us to think of QM as a description of what actually happens, without having to accept that there are many worlds? If it is, then collapse is not decoherence, because decoherence doesn't eliminate unwanted worlds. It just puts quantum systems into states that are indistinguishable from classical superpositions.

    The stuff I said in the quote below is also relevant. I have changed my mind about one thing since I wrote it. I wouldn't say that the CI is defined as in this quote, because now I understand that everyone means something different by that term.
     
  18. Apr 11, 2012 #17
    I like Ballentine's interpretation, personally. We note that quantum mechanics doesn't let us make predictions for single experiments, only for ensembles of experiments. So the obvious thing to do is to take the wavefunction as predicting probability distributions. Taking on experiment is taking one sample from the distribution.

    No collapse, no extra worlds. Its a very minimal interpretation.
     
  19. Apr 11, 2012 #18

    Fredrik

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    In his 1970 article that defines the interpretation, Ballentine is assuming that every particle has a well-defined position at all times* (in particular, each particle in a double-slit experiment goes through one of the slits, we just don't know which one). I prefer to not make that assumption. If we don't, what we have left is just the idea that QM is a way to calculate probabilities of possible results of experiments, and not a description of what's actually happening. This is an "ensemble interpretation", but I don't know if I really want to call it an "interpretation", since it tells us nothing at all about what's actually happening to the particle between state preparation and measurement.

    *) I used to think that this contradicts QM, but it doesn't, if we can tolerate that particles behave in a very strange way. There's some discussion about this in this thread.
     
  20. Apr 11, 2012 #19
    QM is an approximation tool but strong in the same time, the philosophical implications to QM is much harder to be described to us by our life experience, we have two explanations to QM, one is CI and second is Many Worlds interpretation, I suggested the following title
    http://arxiv.org/abs/quant-ph/0101077, 100 Years of the Quantum Theory By Wheeler, Tegmark
    as start point ,
    Bos-einstein Condensation is an overlap Wave-Functions at the same state, which make us very close to Real World.
    I think we can not be able to understand all the quantum world and its behaves without have theory unified all the forces in the nature.
     
  21. Apr 11, 2012 #20
    mwalmasri, there are far more than just those two interpretations. Look at this chart:

    http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
     
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