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B QM interpretations defined as eigenvalues?

  1. Jan 26, 2016 #1
    And back again with a strange/odd layman question:

    Actually, this remark of Jilang is a perfect illustration of what I am wondering about:
    It seems as if realism and locality are behaving like two eigenstates in a space of interpretations of QM. Most people seem to suggest that you must have either one or the other. However, does that make sense if both are possible? Could there be a space in which, depending on the set of measurements and/or experimental setup, there is a mixture of degrees to which two or more interpretations form an explanation of the experimental outcome? Most scientifically educated forum members seem to suggest interpretations are not the field of QM. If that is the case, please let me know. I am not asking this odd question because I suggest I have any anwer to anything. I have just been wondering about exactly this for a long time! It is an insight in my strange world of thought! o0) I hope someone can pinpoint where I am mistaking (probably everyone :wink: ). Thanks! :smile:

    UPDATE: In fact, forget the notion of eigenvalues. Is it possible that certain experiments can be interpreted by a mixture of degrees of mutually exclusive interpretations? (I imagine aspects of the experimental setup determine the values of the degrees - so the experimental setup is part of the definition of the interpretation of the experiment and its outcomes. In other words: the experimental setup is the definition of the interpretation of it; that we can have different interpretations doesn't necessarily have to mean that interpretations can't be combined. I could rephrase this in: of which is realism or locality the property? :smile::nb) ).
    Last edited: Jan 26, 2016
  2. jcsd
  3. Jan 26, 2016 #2
    Of the interpretation.

    No, setups are independent of interpretation.

    The interpretation isn't a physical entity, so it doesn't make sense.

    Also realist interpretations avoid superpositions of states, that's the point.
  4. Jan 26, 2016 #3


    Staff: Mentor

    As far as I can see, mixture of mutually exclusive interpretations is a non-sense statement like immovable object meets irresistible force. Mutually exclusive means they each exclude the other so you cant have a mixture. In QM, and physics in general you need to put some thought into what you say and not just put forth whatever word salid pops into your head which is what you seem to do.

    As to how eigenvalues come into it, it comes from the very foundations of QM - see post 137:

    Last edited: Jan 27, 2016
  5. Jan 26, 2016 #4
    I don't intend to take this discussion out of topic but I have a real quick question.
    In order for a system to be in a superposition, does one have to drop counterfactual definiteness?
  6. Jan 27, 2016 #5


    Staff: Mentor

    All superposition is is pure states form a vector space. It has nothing to do with CFD.

  7. Jan 27, 2016 #6


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    Staff: Mentor

    Quantum mechanics is a theory about the results of measurements. It says that the result of a measurement on a system will be one of the eigenvalues of the corresponding operator, with probabilities given by the rules of QM and the way the system was prepared. This is very much a black-box picture: You have a prepared state and an operator, you do some abstract math involving Hilbert spaces and inner products, and out pops a bunch of eigenvalues with probabilities attached to each one. But that's all that quantum mechanics does for you, which is why "shut up and calculate" is so often sound advice.

    However, we humans generally hate black boxes. We cannot resist the temptation to make up stories form mental models about hypothetical machinery that might be operating inside the black box to make it produce the results that it does. Those stories mental models are called interpretations... and no, they are not formally part of quantum mechanics.

    The analogy that "realism and locality are behaving like two eigenstates in a space of interpretations of QM" is quite unhelpful. The mathematical formalism is precise and rigorous; sloppy vague language about how it "behaves" loses the precision and rigor and gives us in return only misconceptions and incomplete understanding.

    This thread is closed, as there is little point in carrying on a discussion based on this bogus analogy.
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