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A Measurement problem in the Ensemble interpretation

  1. May 15, 2016 #1

    ShayanJ

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    The ensemble interpretation asserts that QM is only applicable to an ensemble of similarly prepared systems and has nothing to say about an individual system and in this way, it seems, it can prevent the need for introducing the concept of wave-function collapse and so it may seem that there is nothing called measurement problem in this interpretation. But is it really correct to say that ensemble interpretation prevents the measurement problem? If not, how would you describe the measurement problem in ensemble interpretation?
    I think there is still a measurement problem in ensemble interpretation because I can't even see how can I start to think about quantum to classical transition in ensemble interpretation. It seems that ensemble interpretations just obscures the measurement problem.
    Thanks
     
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  3. May 15, 2016 #2

    bhobba

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    There is no collapse - in the usual sense anyway, being replaced with the concept of preparation. All a filtering type observation does is prepare the system differently and states are the equivalence class of preparation procedures leading to the same state.

    The measurement problem however has a number of parts as explained by Schlosshauer:
    https://www.amazon.com/Decoherence-Classical-Transition-Frontiers-Collection/dp/3540357734

    1. Why we generally do not observe interference.
    2. The preferred basis problem ie why we get particular stable eigenstates in certain observations.
    3. Why do we get any outcomes at all. Technically its how a improper mixed state becomes a proper one.

    The formalism of QM (ie in any interpretation including ensemble), with some what I consider minor caveats no need to go into here, explains 1 and 2 via decoherence. However it stands powerless before 3. Some interpretations like BM and MW explain 3 with ease, but minimalist interpretations like Ensemble and most versions of Copenhagen do not - they simply assume it. There are some modern interpretations like Decoherent Histories that skirt it entirely - in that interpretation QM is the stochastic theory of histories.

    So Ensemble does not solve the measurement problem, but with our modern understanding of decoherence has morphed it somewhat. There is also the issue of if its a problem at all - nature may simply be like that ie improper mixed states are the same as proper ones. That's the view of my interpretation ignorance ensemble - you simply accept its the same.

    Thanks
    Bill
     
    Last edited by a moderator: May 7, 2017
  4. May 16, 2016 #3

    ShayanJ

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    Thanks Bill. One more question:
    An example of a filtering type observation that comes to my mind, is the Stern-Gerlach experiment. You can do this experiment with very dim beams, so you can't think of the beam as an ensemble of particles. What does ensemble interpretation has to say about such experiment?
    What concerns me here, is the quantum to classical transition. Because ensemble interpretation surely is good in usual measurements on ensembles where you want to check whether you've calculated the correct wave-function by comparing the theoretical and experimental probability distributions for different measured quantities. But when talking about the quantum to classical transition, we usually think about how just one system behaves quantum mechanically on some level and then behaves classically on another. It seems to me if ensemble interpretation only cares about ensembles, then its simply unable to address such issues, not that it hasn't yet, but that its impossible for it to do!
     
  5. May 16, 2016 #4

    vanhees71

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    In the case of the SG experiment you can have 1 particle in the apparatus at any time you do the experiment. You just have to repeat the experiment with this one particle, always prepared in the same way, in the apparatus many times, and you get an ensemble.

    With the appropriate setup the motion of the particle in the SG experiment is very close to the classical approximation. For a fully quantum theoretical treatment, see

    Potel, G., Barranco, F., Cruz-Barrios, S., Gómez-Camacho, J.: Quantum mechanical description of Stern-Gerlach experiments, Phys. Rev. A 71, 2005
     
  6. May 16, 2016 #5

    Demystifier

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    I absolutely agree with every word you say above.

    The measurement problem is a problem about outcomes of single measurements. What exactly happens when we perform one measurement? That is the measurement problem. As long as ensemble interpretation refuses to talk about single measurements, it cannot say anything about the measurement problem. An inability to say anything about the problem is a problem itself.
     
  7. May 16, 2016 #6

    kith

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    If you take the ensemble view in QM serious, it carries over to classical mechanics.

    For example in a single particle interpretation, you may have a particle with a narrow probability distribution of both position and momentum where you can approximate the dynamics with Newton's laws. In the ensemble view, you end up with a (conceptual) ensemble of particles which behave classically. The single particle ontology seems to be natural in classical mechanics but it is an assumption nevertheless. You cannot check predictions with single particles.

    So if the ensemble interpretation "solves" the measurement problem, it does so by weakening the explanatory power of physics in general.
     
  8. May 16, 2016 #7

    A. Neumaier

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    The real problem here is to clarify what it means to perform a measurement. This is a very complex task in general, and has even classically no clear definition. Thus it is no surprise that interpretations that assume that there is a unique, perfect meaning to it have problems.
     
  9. May 16, 2016 #8

    Demystifier

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    True, but it is even less surprising that interpretations that do not assume anything specific about measurements have problems too, simply by being unable to say anything specific about that important and interesting issue.
     
  10. May 16, 2016 #9

    A. Neumaier

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    They don't have problems since they exclude the question from their domain of discourse.

    Not making statements about single particles is practically equivalent with treating the latter as nonexistent and assigning properties (hence existence) only to the beams containing them. Though the ensemble interpretation replaces the term ''beams'' by ''preparation procedure'', there is little difference in practice.

    The beam is obviously existent and has clear and objective properties while the particles are unobservable entities (thought of being inside them) with mysterious properties that reveal a glimpse of their existence only through their macroscopic traces or impacts.
     
  11. May 16, 2016 #10

    Demystifier

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    This is like saying that non-relativistic mechanics applied to low velocities has no problems because high velocities are excluded from its domain of discourse. OK, you may say that it is not a problem, but it is definitely a deficiency.
     
  12. May 16, 2016 #11

    ShayanJ

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    Just to clarify what I meant (which I think is also what Demystifier means):
    The measurement problem is usually stated as "what is wave-function collapse?". So its no surprise that when people encounter with an interpretation of QM that discards wave-function collapse entirely, they may think "amazing, problem vanished!". This seems to be true about the de Broglie-Bohm and the Many worlds interpretations but its not true about the ensemble interpretation. Because actually there are two problems here, the nature of wave-function collapse and the quantum to classical transition. In the interpretations that embrace collapse, these two problems are the same and if you explain collapse, you've explained quantum to classical transition. But this shouldn't lead one to think that if you prevent the question of the nature of wave-function collapse, you've also prevented the problem of quantum to classical transition, it just means that you've decoupled the questions and eliminated one of them, still retaining the other. So the situation is you either have two synonymous questions (collapse interpretations) or only one question (no-collapse interpretations).

    Now the measurement problem in collapse interpretations is the nature of collapse(which is synonymous to quantum to classical transition) which with the help of decoherence(as Bill mentioned), is partly solved. In non-collapse interpretations, the measurement problem is only the quantum to classical transition which the dBB and the MW interpretations seem to completely solve but it seems they have other theoretical problems.

    But the situation about the ensemble interpretation is different from other non-collapse interpretations. It discards collapse and makes it impossible to state the problem of quantum to classical transition at least clearly. So ensemble interpretation, although prefect for physicists who only care to use QM efficiently(which is of course fine), is inadequate for addressing foundational questions about QM. It seems to me an advocate of the ensemble interpretation who also cares about the foundational questions, is inevitably an advocate of hidden variables.
     
  13. May 16, 2016 #12

    A. Neumaier

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    I agree. But every theory except a Theory Of Everything has such a deficiency. And the latter also has one since it can never be detailed enough to predict everything.
     
  14. May 16, 2016 #13

    Demystifier

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    I agree. But you cannot blame me for preferring theories with less deficiencies. So if one theory can say something about single measurements and the other can't, I think it's a good reason for having more interest in the former theory.
     
  15. May 16, 2016 #14

    Demystifier

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    Exactly!
     
  16. May 16, 2016 #15

    A. Neumaier

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    The ensemble interpretation is there precisely to avoid the foundational problems; so this deficiency is its virtue, as it makes the success of quantum mechanics understandable without any need to resolve these problems.

    I understand both merits and limits of the Copenhagen interpretation and the ensemble interpretation although I adhere to neither. My own thermal interpretation is a golden way in-between that solves the foundational questions, at least to my own satisfaction. It makes meaningful statements about the individual case that become more and more crisp as the observables studied become more and more macroscopic. Thus it displays the quantum to classical transition in an easily comprehensible way.
     
    Last edited: May 16, 2016
  17. May 16, 2016 #16

    Demystifier

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    The best defend of ensemble interpretation I have ever seen!
     
  18. May 16, 2016 #17

    bhobba

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    I think adherents (and I am one) would rather use the word minimalist than avoid :smile::smile::smile::smile::smile::smile::smile:

    But discussions of interpretations leads to long threads that don't really resolve anything and can get rather heated. Still understanding them can be quite illuminating.

    Thanks
    Bill
     
  19. May 16, 2016 #18

    bhobba

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    That's what Ballentine pretty much did in his original 1970 article. But since then has changed his conception a bit to skirt the issue.

    There is zero doubt the ensemble interpretation leaves a number of questions unanswered, the most fundamental being exactly how does a improper state become a proper one. Its purely a matter of scientific tact, taste etc etc if that is a problem or a virtue. Its even debatable if its a problem at all. Being philosophy its not likely to have an answer without some way to decide it experimentally.

    My view as you might have guessed is its not a problem, nature is just like that. But as I often stress, and an ex boss of mine stressed this to me when I was working as a programmer, opinions are like bums, everyone has one - it doesn't make it right - but its important to have one.

    Thanks
    Bill
     
  20. May 17, 2016 #19

    Demystifier

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    Why is it important to have bums? :wideeyed:
     
  21. May 17, 2016 #20

    ShayanJ

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    To avoid a naked singularity!
     
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