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I am getting into a mess with the HUP

  1. Feb 21, 2013 #1
    Now, I am lost, I am stuck with the Heisenberg principle..

    Seriously, the more I read papers, standard textbooks, or any books on it, I find I am more lost, nearly all seem to contradict all.

    In page 365,
    This asserts that what we know as the HUP relation (which, in the context, is called dispersion principle) is not even closely related to a single measurement of position and momentum. ( I understand what it means about the standard deviation )

    *A book called "Philosophy of Quantum Mechanics" claims that Heisenberg meant, by his principle, the measurement of one observable that ruins the measurement of the other.

    *Wikipedia, then, says that HUP shouldn't be confused with observer effect, so it's different from what we said.

    *Others say that position and momentum are meaningless terms unless the measurement defines them, so it's the HUP...

    Another problem is that I'm being unable to trust the standard textbooks this while, because of the many writings that contradict them.

    I hope you get me out of this..
    Are Physicists actually not agreeing on this, or is it me who can't get the point?
    I am interested in last view, it is the most meaningful for me, if you clear it up, I will appreciate it.

    I ask you too to clarify the other ideas that some people think are the HUP, but they really are not, and whether their content is true or not.

    Best Wishes
    Last edited: Feb 21, 2013
  2. jcsd
  3. Feb 21, 2013 #2


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    That is true. The HUP describes a fundamental physical relationship that is independent of any measurements we can make. It DOES mean that there are limits on simultaneous measurements, but the fundamental effect is not due to any limitation in our ability to make measurements to some degree of accuracy.
  4. Feb 21, 2013 #3


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    From the referenced paper by Ballentine:
    This does seem to contradict the statement of the HUP that is usually given.
  5. Feb 21, 2013 #4

    Jano L.

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    I think so, it is quite messy subject. My advice: read Heisenberg first:-) and then others...
    What HUP proposes is that at one instant a particle cannot have both position and momentum determined with arbitrary precision, and their simultaneous existence is purely hypothetical (not rejected).

    Which of the pair is better determined will depend on the manner of measurement (experiment on the particle).

    No, this is not how it happened. In fact Heisenberg got the absence of simultaneous x and p from his theory of matrices, and then invented arguments why it should be so also in the measurements, so that his theory would fit measurements.

    In my opinion, it is hard to show that every possible measurement will fail to measure x and p, so I do not think that HUP is rock solid. What can be said for sure is that uncertainty relations (not the principle!) can be derived for normalized wave functions. Then they say that statistical dispersion of x and p cannot be simultaneously zero for any such wave function. Similar relations hold also for the probability distribution of a Brownian particle, so I do not think they are exclusive characteristic of the quantum theory.

    Hypothetically, if there existed state of particle with definite x and p, it couldn't be described by the wave function, and would require some extension of the quantum theory (one such extension already exists: the Bohmian mechanics).
  6. Feb 21, 2013 #5


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    I've the contrary advice. Don't read Heisenberg first but Bohr or at least a later Heisenberg than the very first publication about the principle, because Heisenberg's first interpretation of the uncertainty relation as a noise-disturbance relation due to measurement is definitely wrong. This has been proven experimentally only recently, but it has been clear from quantum theory all the time. I don't understand, why the wrong interpretation stuck. It's a miracle that the English Wikipedia got it right, although even many textbooks describe it wrong (the German Wikipedia is not as good).

    Have a look at the following, I wrote to summarize this here in the forum some time ago. Perhaps, this is another chance to get some discussion on the different interpretations of the uncertainty relation, which indeed refers to the preparation of a system in a (pure or mixed) state (i.e., a projective or ideal von Neumann measurement as this is put more precisely nowadays) but not necessarily on the influence of the measurement of one variable on another non-compatible one. So here's the link to this posting, I wrote a while ago:

  7. Feb 21, 2013 #6


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    It's better to read his more recent textbook "QM -- A Modern Development" than that rather old paper.

    I like Ballentine's emphasis (in his textbook) on what vanhees71 already mentioned, i.e.,
    (my emboldening).
  8. Feb 22, 2013 #7


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    I just want to point out that there is no dispute among physicists about the mathematics of quantum mechanics, or how to apply it to make (probabilistic) predictions for results of experiments, once the experimental setup has been described with sufficient precision.
  9. Feb 22, 2013 #8


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    Good point. Maybe there's even a useful principle lurking in the words I've underlined.

    Something like:
    "All disputes involving QM interpretations are resolved by describing the experimental setup with greater precision, and expressing the predicted results probabilistically".

  10. Feb 24, 2013 #9
    In a previous discussion in these forums here

    what is it about position and momentum that forbids knowing both quantities at once?
    There are some 300 posts..and I, at least, reached some definite conclusions based on the comments of experts here reflected in my notes below.

    the answer was determined to be : nothing prevents an arbitrarily accurate single reading. The better your scientific apparatus, the better your readings. But there are interesting details [below].

    My notes regarding your referenced paper:


    This was the concsensus, I believe, of several experts from these forums [advisors,mentors,etc].

    My synopsis notes from the discussion:

  11. Feb 24, 2013 #10


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    Naty, I have clearly been mistaken about this (the above is incorrect about simultaneous measurements) forever and I appreciate the excellent discussion you have provided. I will stop misleading people in the future if/when I contribute to answers to similar questions.
  12. Feb 24, 2013 #11
    Here are a few other insights, some from that same very long discussion, some not....

    you may want to read that discussion and pick out descriptions that make sense to you....
    these gave me some insights I found helpful....

    There was a mathematical reference but I don't recall seeing a word interpretation:
    Heisenberg's Uncertainty from Dirac's Brackets

    John Baez

    Somewhere in the physicsforums discussion I posted above is a reference to Zapper's blog explanation....I'll post it here if I can find it...it is consistent with my prior posts, I think above, and very well done.

    Note carefully ......That seems to be the source of single measurement issues.

    [I did not record this source, but it sound like Messiah's QUANTUM MECHANICS:]

    edit: one more,possibly from Fredrik:

    [Whoever wrote this, it's about the clearest and most concise explanation I can find.]

    It is possible to measure position and momentum simultaneously…a single measurement of a particle...... What we can't do is to prepare an identical set of states…. such that we would be able to make an accurate prediction about what the result of a position measurement would be and an accurate prediction about what the result of a momentum measurement would be….for an ensemble of measurements.

    edit: that last one is my abbreviated interpretation of a longer post.
    Last edited: Feb 24, 2013
  13. Feb 24, 2013 #12
    welcome to the club!![LOL].....
  14. Feb 24, 2013 #13
    Not to beat this to death, but when trying to decipher all this myself, I found different [but consistent] perspectives really helpful.

    I read Vanhees link [posted earlier in which he discusses Heisenberg-Robertson uncertainty.....

    I especially liked this part: [his post happens to be about neutron spins but that's incidental here]

    which serves as a great introduction to this one [which I finally found in my notes]

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