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Ballentine's Ensemble Interpretation Of QM

  1. Oct 24, 2011 #1

    bhobba

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    Hi Guys

    I have recently been reacquainting myself with Ballantines - Quantum Mechanics - A Modern Development.

    He is pretty big on the Ensemble interpretation, and I must admit I am rather attracted to it as well - none of this collapse of a wave function stuff, many worlds etc.

    He also makes an argument that sometimes, by promoting a correct intuition, it has advantages in solving problems and detailed a little story about it when participants at a 1955 conference had to calculate the interference pattern of an electron beam:
    'Apparently many of the participants had neglected to perform the actual calculation and instead relied on their intuition about wave functions. Hence they expended considerable time debating the size and coherence length of supposed wave packets of individual electrons. Someone espoused the view that a spread in the energy of the beam leaving the cathode was essential for the occurrence of interference, whereas in fact energy spread tends to wash out the interference pattern. None of the confusion would have occurred were it not for the habit of associating a wave function with an individual electron instead of an ensemble. It goes to show that questions of interpretation in QM are not devoid of practical utility.'

    What you you guys think - does Ballantine have a point? Or is it just metaphysical mumbo jumbo?

    Thanks
    Bill
     
    Last edited: Oct 24, 2011
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  3. Oct 29, 2011 #2
    Re: Ballantines Ensemble Interpretation Of QM

    Ballentine (Ballantine is the guy of the whiskey :biggrin:)

    Criticism of his interpretation at http://www.mat.univie.ac.at/~neum/physfaq/topics/mostConsistent
     
  4. Oct 29, 2011 #3

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    First thanks for the link. That paper Classical And Quantum Sytems Via Lie Algebras looks interesting.

    Can't say I understand:

    The statistical interpretation explains almost everything, and only
    has the disatvantage that it explicitly excludes the applicability
    of QM to single systems or very small ensembles (such as the few solar
    neutrinos or top quarks actually detected so far), and does not bridge
    the gulf between the classical domain (for the description of detectors)
    and the quantum domain (for the description of the microscopic system).

    I will think about it a bit more but can't see how it excludes single systems - you can consider a conceptual ensemble of single systems as easy as any other system.

    Thanks
    Bill
     
  5. Oct 30, 2011 #4
    Re: Ballantines Ensemble Interpretation Of QM

    He refers to the traditional 'foundations' of ensemble theory. This must be of some help:

    http://www.mat.univie.ac.at/~neum/physfaq/topics/QMSingle

    I would add to his discussion that many of the usual statistical 'reasonings' involve taking the limit N--> infinite, so that automatically the fluctuations go to zero and the averages <A> are equivalent to the values A_i for single systems.
     
  6. Oct 30, 2011 #5

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    Hi Juaringa

    Yes it does help thanks.

    I still think it is by far the best interpretation though and really helps in developing the theory.

    Interesting new paper by Smolin where he thinks the Ensembles could actually be real:
    http://arxiv.org/PS_cache/arxiv/pdf/1104/1104.2822v1.pdf

    Thanks
    Bill
     
  7. Oct 30, 2011 #6

    Ken G

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    Re: Ballantines Ensemble Interpretation Of QM

    In my view, the ensemble interaction is like no interpretation at all. It is basically the "shut up and calculate" approach-- the wave function is just a recipe for making statistical predictions that can only be tested by ensembles (this is demonstrably true if we strike "just"). So yes, this is correct, but what does it mean? We always want to know about our physics means, it's never really enough for us to "shut up and calculate." If it were, there would not even be a need to argue in favor of the ensemble interpretation-- we just wouldn't care about any interpretation (the claim that the ensemble interpretation is more likely to get the calculation right seems very weakly supported to me). When all we do is shut up and calculate, we don't even bother to say "shut up and calculate"-- we just calculate, and shut up.
     
  8. Oct 30, 2011 #7

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    I actually think its telling us something and is why Einstein subscribed to it. It is wrong to say Einstein thought QM was incorrect - he thought it incomplete - not incorrect. In fact he was very enamoured with Diracs book on QM thinking it was a gem and always referred to it when he need to know something about QM.

    What I think it is telling us is in statistical theories like say those used by Actuaries etc or even statistical mechanics, we know full well the cause of the randomness eg in statistical mechanics it is because its true underlying theory is mechanics. The statistical interpretation is, strictly speaking, silent on that but, for me at least, and at would seem for Einstein as well, it shouts - what causes the randomness. Strictly speaking it does not force you to consider it - you can simply say nature is like that. But for me it strongly suggests some deeper theory is really at work.

    The trouble though is the Kochen–Specker theorem and Bells Theorem (especially the version proved by Stapp) suggests that realm is non local and if it exactly leads to QM then it denies naive reality. For me non locality is fine but denying the existence of stuff out there independent of us and how we choose to measure it is just too big a pill to swallow and I believe the theory QM depends on has QM as its limiting case. Smolins theory looks an interesting step in that direction. I have only gone thorough it once and will need to go through it a few times to really get the gist of it.

    Oh - yes you are correct - of course we always want to know what the physics means. Interestingly however over on the philosophy forums where I had a bit of a discussion about this interpretation one guys view was it was irrelevant. I suspect there is a gulf between those that actually do physics and those who think about it at a philosophical level. He even asserted theories carry their own interpretation and none extra need to be supplied.

    Thanks
    Bill
     
    Last edited: Oct 30, 2011
  9. Oct 31, 2011 #8

    Fredrik

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    Re: Ballantines Ensemble Interpretation Of QM

    He's essentially just saying that we know that QM is a very good assignment of probabilities to possible results of experiments, but we don't know if it's anything more than that. All he has done is to remove the metaphysical mumbo jumbo and focus on what the theory actually says.
     
  10. Oct 31, 2011 #9

    Demystifier

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    Re: Ballantines Ensemble Interpretation Of QM

    The clearest explanation of the ensemble interpretation I ever seen. :approve:
     
  11. Oct 31, 2011 #10

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    IMHO it certainly removes metaphysical mumbo jumbo but it does leave open different questions than say consistent histories does.

    Thanks
    Bill
     
  12. Oct 31, 2011 #11

    Ken G

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    Re: Ballantines Ensemble Interpretation Of QM

    I think the history of physics is pretty clear that seeking an interpretation to a theory can be quite valuable in finding a new more fundamental theory. Often, it is only in hindsight that we "get the message" that the shortcomings of some interpretation could have told us, and that message could have motivated the new theory decades or even centuries in advance of when it was actually found. Maybe it's just a question of "20-20 hindsight", but I think that if we paid even more attention to interpretations, and less to shutting up and calculating, we would actually advance in physics even more quickly. On the other hand, many times we just need the higher technology observations, and we're just spinning our wheels until we get them. But to give one example of what I mean, Copernicus' model of the solar system was not based on any new data, it was based purely at the "interpretation" level. Copernicus felt that Ptolemy's theory lacked a satisfactory interpretation, and that was his main reason for rejecting it-- which in turn advanced astronomy and set the stage for when the telescope did become available. Mach rejected the interpretation that underlaid Newtonian mechanics, and that helped inspire Einstein to finding a better model of gravity. Perhaps Einstein will one day be right about quantum mechanics-- the absence of a satisfactory interpretation may indeed mean that someday a better theory will be found. On the other hand, quantum mechanics has many stunningly parsimonious elements, coupled with spectacular accuracy, so maybe there are limits to what we can get from the demand for satisfactory interpretations.
     
  13. Oct 31, 2011 #12
    Re: Ballantines Ensemble Interpretation Of QM


    This thread has been moved from the philosophy board to the skepticism and debunking board and now to the quantum mechanics board. Which is it? Is it now the task of quantum physicists to assess philosophical issues like metaphysics?
     
  14. Oct 31, 2011 #13

    Ken G

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    Re: Ballantines Ensemble Interpretation Of QM

    I'd say that depends on whether or not quantum physicists are interested in whatever theories come after quantum mechanics. Insofar as they are only interested in the predictions that quantum mechanics makes, there is little need for discussion about interpretations-- everyone is free to use whatever interpretation they like best, or none at all, since the mathematics is not any different in any of them. Now, show me a quantum physicist that is not interested in whatever theory might come after quantum mechanics, or who is not interested in anything quantum mechanics has to say about "how the world works", which is an issue of interpretation. I believe the difficulty in actually producing such a person is the reason we find this thread under "quantum physics", but I should let the mentors speak for themselves on that point.
     
  15. Oct 31, 2011 #14

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    Indeed. I have found myself in the lets calculate stuff brigade and really interested in details like just how does renormalisation work and at other times wondering why is QM like that. I have reached a tentative conclusion it is related to invarience. I have posted the following agrument elsewhere but I would like to repeat here.

    Consider a system with N possible outcomes each with probability Pi. Write them as a row vector and expand in bra-ket notation. u = P1 |b1> + .... + Pn |bn>. This is all vectors with positive entries that add up to one. A perfectly good norm but in physics you generally use the inner product norm so map it to sqrt(Pi) instead and you end up with all vectors in this basis with a representation that is not negative, of unit norm and with Pi = |<u|bi>|^2/<u|u>. First problem is that in physics no basis is special so if we shift to another basis legitimate vectors will have a different representation and we can tell what basis we are using. To get around that we need to map it to the entire vector space which is easily done since in the formula Pi can be calculated for any vector. Secondly notice it is invariant to the transformation cu where c is any complex number suggesting it should be a complex vector space. And lastly since no basis is special we have to assume any orthonormal basis is a possible list of outcomes of some observation which immediately leads to the superposition principle and for any vectors a and b with b of unit norm |<a|b>|^2/<a|a> gives the probability of observing a system in state a to see if state b is the result. Suppose values ai are assigned to the outcomes and define a linear transformation A by A|bi> = ai|bi>, and we have <A> = sum (aiPi) = sum (ai <u|bi> <bi|u>) = sum (<u|ai|bi><bi|u>) = sum (<u|A|bi><bi|u>) = <u|A|u> = sum (<bi|A|u><u|bi>) = Tr (PA) where P = |u><u|.

    This immediately leads to the two axioms Ballentine uses which are:

    To each dynamical variable there corresponds an Hermitian operator A whose eigenvalues are the possible values of the dynamical variable

    To each quantum state there corresponds a unique state operator P that must be Hermitian, non-negative, and of unit trace such that the average value of a dynamical variable A is <A> = Tr (PA).

    In some treatments you will find another axiom along the lines of if you observe a system in state A to determine if it is state B then if that happens immediately after the observation it will be in state B. This is the collapse of the wave-function issue as detailed at great length in Von Neumanns Mathematical Foundations Of QM and is a problematical issue because it begs the question - what caused it collapse. There is also the problem of two ways a state can evolve - by the time operator and this collapse via a observation. Many attempts have been made to avoid it such as quantum decoherence but my understanding is none are entirely successful and problems remain. However if you adhere to the ensemble interpretation it is not required and no problems of that nature arise.

    As Ballentine examines in Chapter 9 the collapse view leads to all sorts of problems and is best avoided. Of course it does not mean nature may not be like that but from the viewpoint of simplicity and avoiding inherent problems its best to not go down that path.

    Thanks
    Bill


    Exactly why nature respects this syymetr
     
    Last edited: Nov 1, 2011
  16. Nov 1, 2011 #15
    Re: Ballantines Ensemble Interpretation Of QM

    An interpretation of a theory does not have to involve metaphysics and there is yet again another message board for discussing anything beyond the standard theory. I hear no arguments presented that this theory does not involve metaphysics, just opinions, and not the slightest reason why it should be posted here. Personal satisfaction may be important, but is this really the place to discuss such things?
     
  17. Nov 1, 2011 #16

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    I am not sure what you mean by the standard theory. As Griffiths says in the preface of his standard undergraduate level textbook, Introduction To Quantum Mechanics, 'There is no general consensus to what its fundamental principles are, how it should be taught, or what it really means. Every competent physicist can do Quantum Mechanics, but the stories we tell ourselves about what we are doing are as varied as the tales of Scheherazade and just about as plausible'

    Thanks
    Bill
     
    Last edited: Nov 1, 2011
  18. Nov 1, 2011 #17
    Re: Ballantines Ensemble Interpretation Of QM

    Why tell a story at all and is this really the place to be telling stories or talking about the best way to teach?
     
  19. Nov 1, 2011 #18

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    That's not the key part of the quote - that there is no general consensus is the key part - ie there is no standard interpretation. It varies from textbook to textbook.

    If you think there is a standard interpretation feel free to post its axioms.

    In the past probably the two most influential textbooks were Dirac's Principles Of Quantum Mechanics and Von Neumann's Mathematical Foundations.

    Dirac's book advocated the calculate and shut up position which is basically the ensemble interpretation as others in this thread have correctly pointed out. Its the minimum you need to do the physics.

    Von Neumann formally analysed the collapse of the wave-function issue and concluded that the entire physical universe could be made subject to the Schrodinger equation. Since something outside this was needed to collapse the wave function, Von Neumann concluded that the collapse was caused by the consciousness of the experimenter. This is so weird it never really caught on but Von Neumann was a mathematician par excellence and it took a brave sole to go up against him - he thought he had iron clad mathematical reasoning to back it up but Bell and others eventually found cracks - he had made hidden assumptions. The modern version is probably Penrose's theory:
    http://www.quantumconsciousness.org/penrose-hameroff/quantumcomputation.html [Broken]

    Other books I have read, such as Griffiths, give lip service to the Copenhagen interpretation and present a watered down version but I suspect it is probably the most common one in practice.

    So I would say take your pick. I back the ensemble interpretation presented by Ballentine:
    http://www.kevinaylward.co.uk/qm/ballentine_ensemble_interpretation_1970.pdf

    Thanks
    Bill
     
    Last edited by a moderator: May 5, 2017
  20. Nov 1, 2011 #19

    Fredrik

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    Re: Ballantines Ensemble Interpretation Of QM

    The interpretation defined by Ballentine's 1970 article claims that particles actually have well-defined positions at all times, even when their wavefunctions are spread out. I don't think his textbook makes that assumption.
     
  21. Nov 1, 2011 #20

    bhobba

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    Re: Ballantines Ensemble Interpretation Of QM

    Yes. I think he may have evolved it slightly in light of developments like the Kochen-Specker Theorem - although that was published in 1967 before the article. I actually hold to the original version and get around Kochen-Specker by assuming an underlying theory like Primary State Diffusion that reduces to QM as a limiting case. Of course no need to do what I do - you can simply leave it as is.

    Thanks
    Bill
     
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