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Definiteness and Interference

  1. Apr 3, 2013 #1
    Usually the only indication that a system (maybe particle) is in a superposition of different eigenstates of a particular observable is the finding of interference.
    I wonder if there is any interpretation that would consider the possibility of having a system (maybe particle) in a situation in which different eigenstates coexist (or at least we can say that the system does not have a definite value) even though some process of decoherence (not necessarily environment induced) has randomized the phase relationship between different eigensatates. Formally this would correspond to the situation after the density matrix has been diagonalized but no eigenvalue has been identified as being the "real" value.
    I don't think this situation would be considered within the Copenhagen, Many Worlds, Relational or Transactional interpretations, but I may be wrong.
     
    Last edited: Apr 3, 2013
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  3. Apr 3, 2013 #2

    strangerep

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    Try to learn more about statistical interpretations of QM, e.g., from Ballentine's textbook "QM -- A Modern Development".
     
  4. Apr 3, 2013 #3
    Thanks strangerep, I found this link:
    http://en.wikipedia.org/wiki/Ensemble_interpretation
    At first sight it looks more like a realist interpretation. I'll read more about it tomorrow.
    I am sure I had heard about this interpretation before but I had forgotten.
     
  5. Apr 3, 2013 #4

    strangerep

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    I have a few problems with that Wiki page, so read it with a grain of salt and try not to form your "final" impression from that source alone.

    BTW, if you're a serious student of QM, investing in a copy of Ballentine's textbook definitely won't be a waste of money...
     
  6. Apr 3, 2013 #5

    bhobba

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    Its basically shut up and calculate also called the Minimal Statistical Interpretation (MSI). The slight variation of the Ensemble Interpretation is the statistical part is given pictorial vividness by means of the concept of an ensemble. Its the interpretation I hold to with a slight twist - I include decoherence so that observations are of improper mixed states which means I can assume it has the property being observed prior to observation - its more reasonable in terms of everyday conceptualisations that way.

    Thanks
    Bill
     
  7. Apr 3, 2013 #6

    bhobba

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    I have read a few and it IMHO is far and away the best. But it is a graduate level textbook which means its probably not the best to start with - I recommend Quantum Mechanics Demystified by David McMahon for that:
    https://www.amazon.com/Quantum-Mechanics-Demystified-Edition-ebook/dp/B00BPO7APS

    I also have Griffith's text but am not as enamoured to it as some - its OK - but I think Davids book is just as good and a LOT cheaper. Either way - you should move onto Ballentine once you feel confident.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  8. Apr 4, 2013 #7
    Thanks strangerep and bhobba for your recomendations. Some time in the future I may get a hold of one of those books and take a look. One problem I see in reading a particular book completely is that this book usually presents a single interpretation. If I were already sold on that interpretation, I might get the motivation to devote a lot of time to read the whole book. With respect to textbooks, I have read many, but they usually avoid the subject of interpretation or stick to the Copenhagen version. But my opinion is that none of the current interpretations gives a satisfying picture of what is going on. In order to compare different interpretations, I think it should be sufficient to use a small set of postulates or statements made by each interpretation.
    When I have some time I will read a little more about the ensemble interpretation, but I am skeptical about it.
    With respect to my original question, I should clarify that I was not trying to discuss the merits of a particular interpretation which would make it worth adopting. I was just trying to see if there was a particular interpretation which considered the "coexistence or at least indefiniteness" of eigenstates, after decoherence has taken place at the local level and interference is not observable anymore.
    From the little I have read about the ensemble interpretation, it does not seem like it does consider that situation. Please let me know if you think I am wrong about this (about what the ensemble interpretation implies, not about the merits of considering the coexistence of decohered states)
     
    Last edited: Apr 4, 2013
  9. Apr 5, 2013 #8

    strangerep

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    Umm, you do realize that interpretations make no difference to the actual experimentally-confirmed predictions of QM, right? (Otherwise, they'd be different theories, not different interpretations.)

    In that sense, interpretations are mostly a waste of time (imho). Hence I adopt only the minimal extra baggage that allows the maths of QM to be related to concrete experimental situations. Some call this the "shut up and calculate" interpretation. I think that's not quite accurate, and prefer to call it the "stop w*nking and calculate" interpretation. :biggrin:

    So... you're "skeptical" about it without knowing what it is, and without studying a book like Ballentine's properly? Hmmm. :rolleyes:

    The question doesn't really make sense in that form. For such cases, a mixed state operator is more appropriate tool for calculating experimental predictions. If you're not already proficient in working with general state operators, that's probably a good thing to study.
     
  10. Apr 5, 2013 #9
    I know that up until now, this has been correct. Plaga has proposed an experiment that he thinks could show different results depending on which interpretation is correct. (many worlds vs. Copenhagen) but having read the paper, I think there may be a mistake. I haven't taken the time to analyze it. I think there was another proposal by David Deutsch. I understand your reasoning, which assumes that the theory in it's current form would be able to make correct predictions about any experiment. However, we dont't know if some time in the near future someone may not come up with some experiment where how to apply the formalism of QM could depend on interpretation.

    I think there are many investigators who would dissagree with this. The list would be long. But there are many people who think that tehere is still "something missing" (not necessarily hidden variables)

    Have you read the Bible? If you have, then my argument does not apply. But if you haven't then I would wonder if you are not skeptical about it. Would you have to read it from the beguinning to the end in order to decide that it is not worth reading?. Nowadays we are swamped by information, and usually we have to do some filtering and read only part of what is available.
    I don't think "I don't know what it is" (the ensemble interpretation). I think I now have a rough idea, and I don't think it contributes anything new.

    What makes you think I am not proficient? My question was not on how to use it but on how to interpret it. If you read about the process of environment induced decoherence (M. Schlosshauer has made a very exhaustive analysis of it) you'll see that there are some issues that are not clear yet.
     
    Last edited: Apr 5, 2013
  11. Apr 5, 2013 #10

    strangerep

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    I have no problem with actual experiments that reveal a deeper understanding -- if any such experiments are ever actualized.

    Sure. But if others want to carry around extra baggage, that's their business.

    I also wonder about that -- but it's all rather speculative, istm. If a better theory can be constructed, or new experiments shown to differentiate between interpretations, then... good.

    That's not what I said. I said "if". There was not enough detail in your posts for me to be sure one way or the other. I don't know your background.
     
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