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Uncertainty Principle

  1. Jul 30, 2004 #1
    In my eng. phys II class my prof. today was telling us about how in a bb experiment if you shoot it through a small slit (very small) and shoot lets say 20 bb's in a row and then look at where they embedd themselves past the slit if you have lets say piece of cardboard they bbs even if all shot exact same position would land not at the dead center but arranged chaotically in a gausian distribution lol no clue on that one but he said that was because of uncertanity principle but i ask him about the limits of uncertainty to my knowledge I thought it only held for small light wavelength sizes and below he said it applied to everything. Is it not just a statement that when you deal with ultra small particles you can never know both the vel and position and onces you know one it alters it?
     
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  3. Jul 30, 2004 #2

    selfAdjoint

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    The gaussian would be...ummm... VERY peaky. In fact I doubt even the best experimenter could detect it given other inevitable uncertainties (classical ones) in the experiment. Variation in size of BBs, finite properties of cardboard, stuff like that. But in theory he's right.
     
  4. Jul 30, 2004 #3
    Id say your prof is right and wrong. It does apply to everything, but when you apply it to things that are larger than particles, then the effect will be soo small, it will be non noticable.
     
  5. Jul 30, 2004 #4
    confused

    so does the uncertainty principle hold for all objects no matter what size, but you can't detect it but for things smaller than the wavelenth of light. So he's right about it but he's wrong saying that all the bb's go everywhere because bb's are too large to detect uncertainty.???

    Cheers Woody
     
  6. Jul 30, 2004 #5

    turin

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    Yes. If the uncertainty in position is even like only 10% of the size of the BB (barely noticeable), then the uncertainty in momentum would be absolutely miniscule (like 10-alot). BB's tend to fly around with an uncertainty in momentum and position that are both extremely small (compared to it's classical properties), since the product is on the order of 10-34 J-s (and it's classical properties are on the order of 10-4 m and 10-4 kg).
     
  7. Jul 31, 2004 #6
    Turin i'm sorry for not fully understanding that, do you mean that as large as a bb is you would not notice any uncertainty effects. aka the bb's would all go as planned straight where I aim the bb gun to send them?

    Cheers
    Woody
     
  8. Jul 31, 2004 #7

    Doc Al

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    Turin is explaining that the inherent quantum uncertainty of a bb is miniscule--way below detection. But there are plenty of other sources of non-quantum "uncertainty" and "random" variation. These "classical" sources of "noise" can be reduced to the limit of our ability to build the "perfect" bb gun--but it will cost you. (Just compare a crappy bb gun to a sharpshooter's precision competition rifle.) Quantum uncertainty, however, cannot be reduced.
     
  9. Jul 31, 2004 #8
    so you are saying don't take a bad make and model with bad precision to be uncertainty. I like that my prof still says that the bb's go everywhere and thats because of uncertainity is he crazy or is he right somewhere.
     
  10. Jul 31, 2004 #9

    Chronos

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    The uncertainty principle is the hard limit to predictability of quantities in any system. Classical sources of variance [bb size/mass, air currents, ejection force] would dominate in this example. The prof is technically correct, but, you would not be able to derive Planck's constant using this approach.
     
  11. Aug 1, 2004 #10
    so what can be used or said when he states that quantum uncertanties can be seen! on large objects.

    I am not trying to be mean to my prof whatever i say will be humble but when he and i have these conversations i learn tons its the only way i can get him to talk about this stuff.

    so anything for my arsenal will help.
     
  12. Aug 1, 2004 #11

    selfAdjoint

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    I believe the largest object ever seen that was in a pure quantum state was a supercooled droplet abour 2mm across. Scanning tunneling electron microscopes can see individual atoms, but their methods are too crude (it think) to detect uncertainty.

    Uncertainty is built into all quantum theories. It is the cornerstone, as it were, of quantum electrodynamics, via the "equal time commutation relations'. And QED makes predictions that match experiment to six decimal places. So that's an indirect confirmation of the uncertainty principle.
     
  13. Aug 1, 2004 #12
    thanx self adjoint, you don't by chance have a link or anything to the 2mm supercooled stuff do you.
     
  14. Aug 2, 2004 #13
    I have another question about uncertainty principle:

    suppose the spatial wavefunction of a particle extends outside the lab (there is a chance that the particle is found outside the lab).
    Experiments are carried out in the lab, measuring the momentum of the particle.

    Is the minimum experimental uncertainty larger than the quantum uncertainty of the momentum?
     
  15. Aug 2, 2004 #14

    turin

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    I would imagine so. The primary source of uncertainty would probably be in the device that was used to cool the particle and make it's deBroglie wavelength extend outside the lab. Furthermore, once the particle extended beyond the cooling chamber, there would be entangling effects and decoherence.
     
  16. Aug 5, 2004 #15
    I think you misunderstood my question.

    "Is the minimum experimental uncertainty larger than the quantum uncertainty of the momentum?"

    I was trying to ask whether the dimension of the lab (or cooling chamber) in which measurement is performed, itself causes an uncertainty that cannot be minimized.

    Assume the cooling device causes no uncertainty in the results, (either assume the particle is already cool, or the cooling device is Perfect). Let the environment of the lab (inside and outside) be vacuum so there's no entangling effect and decoherence.
     
  17. Aug 5, 2004 #16

    turin

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    If I understand you correctly, then the uncertainties are the same; not just the same value, but the same thing. The fundamental quantum uncertainty is a feature of the experimental setup, and it cannot really be separated. The uncertainty due to the lab is the quantum uncertainty.
     
  18. Aug 5, 2004 #17
    Is Uncertainty Principle meaningless ?

    In theory a single photon can measure either the position or the (angular) momentum of an electron in an orbit precisely, but not both, right?

    If we send in two photons at the exact same time along the exact same vector and in phase, then they would both hit the electron at the same time, right? Can we then measure one photon to determine the position of the electron, and at the same time, measure the other photon to determine the (angular) momentum of that same electron?

    So, the next question is: Are there any laser techniques or other techniques that can bunch two photons together?
     
  19. Aug 5, 2004 #18

    turin

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    I'm not so sure about that. A single photon is either entirely absorbed by the electron or it passes the electron completely obliviously. The best you can intentionally do with a single photon is hope that the electron absorbs it, and subsequently emits a photon that you can detect. Then, when you detect the emitted photon, you can determine from which direction it came. Perhaps the distance between the emission and detector can be inferred from this process, but, off the top of my head, I don't see how. The procedure to determine a momentum state using a single photon is a bit more indirect. Basically, if the sent photon resonnates with the electron, then there is an energy difference. That together with the direction can then lead to a determination of some aspects of the momentum. But, again, off the top of my head, I don't see how the momentum could be completely specified.




    The process of generating such a well defined photon-pair aside, you still have no control over whether either photon will interact with the electron.




    Hmm. I don't know of any.
     
  20. Aug 6, 2004 #19
    continue exploring the 2nd question:

    Assume measurements (of multiple same 1-particle systems) are done inside the lab, the experimental position uncertainy you get will not be larger than the range of the lab. WHY? because the data you get is always in the range, so the standard deviation is always less than or equal to the range.

    Implication is:
    If the particle is close to a momentum eigenstate, the uncertainty principle is violated, since the position uncertainty never blows up.


    ???
     
  21. Aug 6, 2004 #20

    ZapperZ

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    Eh??? <notice the same number of question marks>

    The "physical" range of your measurement has nothing to do with the uncertainty of the measurement.

    Let's say the system has a plane-wave description such as exp(ikx), which is certainly a momentum eigenstate, as you require. Let's also say that the lab you are measuring this has a width of L, and your setup that emits this plane-wave particle (not an oxymoron) is at x=0. So the physical range of your detection of the position of this particle is from x=0 to x=L.

    You start emitting the particle one at a time and try to measure it's position. If you do this enough number of times, the statistics of the position measurement will look like a flat line extending from 0 to L. However, is THIS the uncertainty of your measurement? It isn't! If you try to fit a gaussian or a lorentzian to this set of data points, it'll blow up, or at least give you some arbitrary answer depending on your fitting routine. The profile of the spread (a flat line or a square wave with abrupt boundary at 0 and L) will give you an uncertainy in position that is certainly extremely large even when you can only physically measure a finite range of position.

    There are no violations of the uncertainty principle here....

    Zz.
     
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