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I Uncertainty Principle... Intent Behind It?

  1. Jul 6, 2016 #1
    I've been pre-occupied with Heisenberg's uncertainty principle for around four years now, and I've come to fabricate a lot of questions.

    The most pressing one, however, is as follows:
    To me, the uncertainty principle seems to reference our (relatively) poorly controlled methods to measure a particle's momentum and position rather than being some special quantum phenomenon. Is this how it was intended?

    If I measure a coffee mug's position using a crowbar, I change the coffee mug's momentum by measuring it. I do not, however, change its momentum simply by having knowledge of the coffee mug's position. This is how I think of the uncertainty principle, but was it meant this way? If it was, then doesn't that screw up multiple other concepts such as entanglement and electron configuration around nuclei?

    Or did Heisenberg believe in some phenomenon that changed one of the particle's traits merely because we observed it?
     
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  3. Jul 6, 2016 #2

    phinds

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    Absolutely not. The POINT of the HUP is that it is not at all a measurement problem but rather a fundamental fact of nature.
     
  4. Jul 6, 2016 #3

    fresh_42

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  5. Jul 6, 2016 #4

    Nugatory

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    You have been misled by superficial treatments of the subject. The uncertainty principle is not a consequence of the way that we measure position and momentum, nor does it only apply to those two properties; that's a misconception dating back to the early days of quantum mechanics, before we had developed a complete understanding of the theory.

    Instead, it is an inescapable mathematical consequence of the laws of QM: If the operators corresponding to two observables have a particular mathematical relationship (they "do not commute" in the lingo) then any quantum state in which one of them has a definite value is necessarily also a state in which the other one does not. Position and momentum are everbody's favorite example of such a pair of incompatible operators, but there are many more.

    There are many more threads here, both on what the uncertainty principle is and the history behind it.
     
  6. Jul 6, 2016 #5
    Just for curiosity sake... could you list a few other such pairs of operators?
     
  7. Jul 6, 2016 #6

    Nugatory

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    The x, y, and z components of angular momentum. I cannot prepare a quantum system in a state such that more than one of the three is definitely known. (Although I can prepare a system in which the magnitude of the angular momentum vector and any one of its three components is are both definite).
     
    Last edited: Jul 6, 2016
  8. Jul 6, 2016 #7

    bhobba

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    To understand the uncertainty principle you really need to see a proper statement of it.

    The correct statement is the following. Suppose you have a large number of similarly prepared systems ie all are in the same quantum state. Divide them into two equal lots. In the first lot measure position to a high degree of accuracy. QM places no limit on that accuracy - its a misunderstanding of the uncertainty principle thinking it does. The result you get will have a statistical spread. In the second lot measure momentum to a high degree of accuracy - again QM places no limit on that. It will also have a statistical spread. The variances of those spreads will be as per the Heisenberg Uncertainty principle.

    Note:
    1. You can measure momentum and position to any accuracy you like. QM places no limit on that.
    2. Its simply a statistical statement about a fundamental property of QM - if you observe a system in a quantum state the result can only be predicted statistically.

    If you want to read up on it a very careful and correct analysis can be found in Ballentine:
    https://www.amazon.com/Quantum-Mechanics-Development-Leslie-Ballentine/dp/9810241054

    Unfortunately in physics generally, and its particularly true in QM, correct understanding is not always given in beginning texts or popularizations. Its a big problem - Feynman for example, being the great educator he was, worried about it a lot but saw no way around it. Its simply not possible to give the full detail to start with - you must build up to it which means you need to unlearn and relearn things as you progress.

    That's why you will usually only find correct treatments of the uncertainty principle in advanced books like Ballentine.

    Thanks
    Bill
     
    Last edited by a moderator: May 8, 2017
  9. Jul 7, 2016 #8
    Well, this is frustrating, but I'd rather be displeased and know the truth than live with an incorrect understanding. Thank you. :)

    Why is it that humans are so certain of this, though? Was it purely because of the double slit experiment and the calculations following it? The double slit experiment is less controlled than I would like to take that as our fundamental proof... Given what you said, however, electron configurations do make more sense to me now that I'm not viewing this as a classical situation. Don't get me wrong, I take no pleasure in trying to argue with what physicists have discovered thus far, but my view is that it should try to be explained with classical physics, and if it can, it isn't unique nor is it quantum mechanics at work.
     
  10. Jul 7, 2016 #9
    So theoretically, if I had all three axis components of a particle's angular momentum, I would know/be able to calculate its position at any given time and "break", for lack of a better term, the uncertainty principle. Correct?
     
  11. Jul 7, 2016 #10

    phinds

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    The single slit experiment is more persuasive regarding the HUP. The double slit experiment is more about showing how light can have the characteristics of both particles and waves.
     
  12. Jul 7, 2016 #11
    But was the double slit experiment really the only reason this was theorized? Or was there something else that made physicists think particles could also behave as waves?
     
  13. Jul 7, 2016 #12

    DrChinese

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    You can't know the non-commuting components simultaneously. Position and momentum are non-commuting as well, so you can't know those either. You can't cheat the uncertainty principle, many have tried! EPR being a great example of that.
     
  14. Jul 7, 2016 #13

    phinds

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    When you start talking about two entirely different phenomenon in the same thread, it gets confusing. If you want to know about the double slit experiment and the fact that light can act like both a wave and a particle, please read some of the thousands of threads on that subject and if you still have questions, start a new thread.
     
  15. Jul 7, 2016 #14
    No haha that's not what I'm saying. I know it can't be done, but what I was trying to clarify was that if I had all 3 axis components at the same time, I would in turn be able to calculate its position. Now that I retype it, it becomes clear to me that this is the case.
     
  16. Jul 7, 2016 #15
    That's not necessarily what I'm referring to. I'm just wondering what the first thing was that made physicists think "huh, these particles are behaving as if they're in two positions at once". I need to verify that the double slit experiment, or something of a very similar nature, isn't the reason Heisenberg even came up with the uncertainty principle.
     
  17. Jul 7, 2016 #16

    DrChinese

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    If you knew the momentum, you could not calculate the ending position unless you knew the starting position. But any previous position information would be invalidated by learning the momentum. So you still could not calculate the ending position.
     
  18. Jul 7, 2016 #17
    So then why are we incapable of measuring all three parts of the momentum? It's not possible to measure it multiple times and account for the variations in those measurements to gather an x, y, and z vector?
     
  19. Jul 7, 2016 #18

    DrChinese

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    If you measure any fundamental observable very precisely - say position - any non-commuting partner observable moves into a superposition of states (momentum, for example). When you later measure that, you will find that the new outcome (for momentum) is random and uncorrelated to any prior measurement of that observable.

    Keep in mind that for all practical purposes, particles do not have simultaneous (well-defined) values for both position and momentum. Experiments on entangled particle pairs demonstrate this very convincingly.
     
  20. Jul 7, 2016 #19
    Forgot about relativity... Looks like I'll be doing a lot more reading and contemplation. Thank you!
     
  21. Jul 7, 2016 #20

    phinds

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    Relativity has nothing to do with what we have been discussing, so if you think it does then that's some more reading you need to take on.
     
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