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Is Quantum theory complete?

  1. Jun 22, 2010 #1
    I am sorry if this issue has been already addressed previously in this forums, but I have been looking for old threads on the subject and I haven't found any specific to the matter. If anyone knows about any, please let me know and sorry again.

    Otherwise, this is my question: "Is Quantum theory complete?"

    If I am not wrong, this was Einstein's point in the famous letter to Bohr in 1920. According to Bohr quantum theory is complete because what is to supposed to be left in the theory (hidden variables) is also left in the very reality. Ok. I understand it, and I already know and accept that there are important reasons to debunk hidden variables.

    Nevertheless, I still have a doubt. When a measurement takes place an unpredictable value is obtained (under certain circumstances of uncertainty). How can we say that quantum theory is complete and at the same time that quantum theory cannot predict accurately the outcomes of a measurement? This is the very point I don't understand. Reality is given us the accurate outcome, whilst quantum theory is not, so reality is in fact "more complete" than quantum theory!

    Call me "retro" and "stubborn" but I sincerely still think Einstein was right about this point, but at the same time I am ready to open my mind to reasonable statements about the completeness of Quantum Theory.

    Thanks in advance.
  2. jcsd
  3. Jun 22, 2010 #2
    Define what you mean by "complete".
  4. Jun 22, 2010 #3
    We have to know what reality is and how reality is, then we will be able to say if qm is a complete description of reality. If there is no underlying reality, qm is complete. But such questions should be relegated to God(Nostradamus comes as a second option).
  5. Jun 22, 2010 #4
    I am going to try it: a complete theory means to me that every outcome of a given experiment (*) could be accurately calculated using that theory.

    * under the scope of application of that theory.

    I assume that the position of a free electron, for example is inside the scope of quantum theory.
  6. Jun 22, 2010 #5

    This is not enough. You need to elaborate if "accurately calculated" includes probabilities or not.
  7. Jun 22, 2010 #6
    First of all, thanks for the answer, GeorgCantor, I am kind of a fan of your posts, by the way.

    I still don't understand how can we see QM as complete, even in the case that there is no underlying reality. My concern is that a simple quantum experiment outcome is showing certain information that the theory is unable to render, as for example the exact location of an electron.

    So, if the theory is unable to render the outcome of an experiment, would be correct to say the theory to be complete?

  8. Jun 22, 2010 #7
    Then it is complete. QM predicts that the outcomes of a measurement of an observable are the eigenvalues of the operator associated with that observable.
  9. Jun 22, 2010 #8
    No probabilities. The outcome of an experiment is not a probability, but a value. The outcome of a complete theory should also be a value, not a probability. Sorry if I am too naive.

    The same way that thermodynamics is not a complete theory of the microstates, could we say the same about QM?

  10. Jun 22, 2010 #9

    You can't know the location of the electron simultaneously with the momentum of the electron.

    The theory would be complete even if there exists a deterministic underlying reality(to which we wouldn't have access).
  11. Jun 22, 2010 #10

    Then this universe isn't for you :smile:. The probability "thing" comes as a result of the wave nature of matter. Waves aren't well localized in space.

    If you push it that far, there isn't ever going to be a complete theory of anything.
  12. Jun 22, 2010 #11
    Hmmm. It seems you have objections to the probabilistic interpretation of the wavefunction. I will refer you to Sakurai's introductory section.

    Let's look at polarization of light. An unpolarized light beam passes through a polarizer. As a result, the light becomes linearly polarized in the direction of the polarizer's optical axis. Then we put another polarizer at an angle different from 90o to the first one. Some light still passes, but it is now polarized in the direction of the second polarizer's axis.

    But, then, we use yet a third analyzer. Its axis is parallel to the first one's. The question is: Will some light still pass through?
    Last edited: Jun 22, 2010
  13. Jun 22, 2010 #12


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    It's definitely not complete in the sense that it's a unified theory of everything.

    But of course, no theory is complete like this, or we'd have a unified theory of everything and science would be dead and applied science would be the new thing.

    I don't personally think a TOE is even possible, because:

    You're trying to model reality. Reality consists of a lot of stuff (virtually infinite bits of matter and interactions between that mater). Anytime you want to model that reality, you have to use stuff to do it (whether it's your neurons, pencil and paper, computers, or actual 3d models) and those models aren't going to have anywhere near the infinite resources that reality have, so they're always going to be missing information.

    All you can do is scale your model from general to specific, taking on the flaws of one, or compromising for a little of the flaws of both for a more balanced model.
  14. Jun 22, 2010 #13
    I think I haven't, honestly. The theory says that there could be several eigenvalues with given probabilities and I accept (even believe) that it is due to the very nature of the world and not a flaw of QM.

    Nevertheless, my concern is the information that an experiment give us (a single, accurate and certain value) but the theory does not (theory gives us values and probabilities). How can QM explain that information?

    QM cannot tell us which one of the eigenvalues is going to be detected. QM cannot predict completely the event happening when doing the measurement. The event is that certain eigenvalue is the outcome, but not that a set of eigenvalues with certain probabilities are the outcome.

    The fact is that we measure a value, whilst QM only renders sets of values and probabilities.

    Facts don't match completely with QM predictions. Is that correct?

  15. Jun 22, 2010 #14
    Yes, eigenvalues, plural. But the experiment outcome is not a set of eigenvalues, but only one single eigenvalue. Nature in someway has chosen that one and not any other of the set. The process by which nature makes that choice is not addressed by QM. Right?

  16. Jun 22, 2010 #15


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    By your definitions, if nature happens to be nondeterministic, then I think every scientific theory must be incomplete by your definition.

    Have you tried your hand at understanding some of the non-collapse interpretations, like MWI or Bohm?
  17. Jun 22, 2010 #16
    So, you object that the position or momentum can have any possible value?
  18. Jun 22, 2010 #17
    When a theory predicts an experiment outcome under its scope, we should say it is complete, as for example, Newtonian Mechanics. Of course, NM gets out of its scope when relativistic corrections are needed. So, at least we have a complete theory of something here.

    In contrast, my point is that QM seems to me to be a theory that cannot predict an experiment outcome under its own scope, as for example the position of a free electron (after measuring its momentum).

    Do you agree?

  19. Jun 22, 2010 #18
    Not exactly. If you consider the proper scope/range of a given theory, NM would be complete but QM wouldn't be.

    Do you think that a non-collapse interpretation could "fix" the QM incompleteness?

  20. Jun 22, 2010 #19
    What principle of Nature requires that we should simultaneously know the position and momentum of a particle?

    QM says that the state of a system is described by a wave function. It also provides an equation that gives the time-evolution of the wave function. It is true that we cannot solve this equation for all but the simplest cases, but that does not mean that the theory is incomplete. A similar situation arises in classical mechanics, where the three-body problem is unsolvable, but that does not mean the theory is incomplete.
  21. Jun 22, 2010 #20
    I am not sure if I understand what you are asking me ... but according to the experiment of measuring the position of a free electron you get one and only one eigenvalue. Do you agree with it?

    Of course, according to QM, you get a set of eigenvalues, not just one. So, I must conclude that QM cannot predict a fact, an event, a measurement (under proper QM scope/range).

    Einstein called it an incomplete theory. I just would like to know whether he was wrong or not, and where is the flaw in this way of reasoning.

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