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Uncertain about uncertainty!

  1. Sep 27, 2010 #1
    Hi people. I am a bit confused about the uncertainty principle. According to Heisenberg, we cannot exactly determine the position and momentum of an electron at the same time because the minimum energy we have to give out (say light energy) is absorbed by the electron and one of the quantities will change. Am i right?

    Theoretically, then, it should be possible to "ping" an electron with a particle of almost no energy (very low energy compared to an electron). This way, the electron cannot gain any energy from it and thus we should be able to get both momentum and position right?

    If the above is true, then can we consider uncertainty principle as a limitation of current technology? (Assuming a very low energy particle is found in future/such a method is possible)
     
  2. jcsd
  3. Sep 27, 2010 #2
    Hi,

    As I see it - uncertainty is a fundamental concept, simply caused by the fact that in QM we're dealing with waves with all their inherent properties including diffraction.
    And with waves you can go only as small as their wavelength.

    So for your specific example, sending a low energy particle is equivalent to sending a long-wavelength wave (for photons E~p~1/wavelength). And you won't be able to locate the tested particle very accurately - uncertainty holds.
     
  4. Sep 27, 2010 #3
    As far as conservation of energy or a transfer of energy exists as a property of particles then the Uncertaintity pricnciple still takes place.
     
  5. Sep 28, 2010 #4

    Demystifier

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    Yes, but the wave function of such a particle will be very wide in the position space, so the position of the particle will be very uncertain.
     
  6. Sep 28, 2010 #5
    Yeah, but then you have to measure this very particle by some other instrument. How would you do this? Use even less energy? The point is to amplify various properties to macroscopic scale.
     
  7. Sep 28, 2010 #6
    Has it ever been considered that the particle/wave may in fact be the very same entity and the reason we can only detect a small point is because it is the point of impact and the rest of the object cannot be discerned correctly? Just curious.

    Thanks.
     
  8. Sep 28, 2010 #7
    You need not "ping" an electron with anything to see how the Heisenberg Uncertainty Principle works. You only have to localize it, somehow. For example, consider diffraction of the electron from a slit. In order to pass through the slit, the particle has a position somewhere in the slit. In fact slits are used as position measuring devices in some experiments. So, passing through a slit gives us [tex]\Delta x[/tex], which results in an uncertainty in momentum according to the Heisenberg Uncertainty Principle
    [tex]\Delta p \ge \hbar /2\Delta x[/tex]. The electron can now be deflected in many different possible directions, which is what happens in a real diffraction experiment. As far as we know, there is no energy exchange and no interaction between the electron and the slit. There is no photon involved in this experiment. The uncertainty in momentum, and resulting electron deflection take place simply because we have localized the electron.
    So, in a way, the experiment you want to do already exists. But, you still do not know position and momentum with certainty. They are both still uncertain. Heisenberg lives!
    IMHO we are wasting our time trying to find a way to violate the Heisenberg uncertainty principle.
     
  9. Sep 28, 2010 #8

    diazona

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    Let me issue a correction there: what you've stated is just a physical justification that somebody made up for the uncertainty principle. A lot of people try to make up these sorts of justifications, e.g. saying that in order to measure a particle's position you have to bounce something off it thus changing its momentum, but I think they're rather misleading.

    The real reason for the uncertainty principle is that particles are really represented by wavefunctions. Given any particular wavefunction, there is a way to compute the probability of finding the corresponding particle at each possible position, and a way to compute the probability of finding the particle to have each possible momentum. Now what Heisenberg's uncertainty principle says is that if you take the standard deviation of all those possible positions (weighted by their probabilities, of course), and the standard deviation of all those possible momenta (again, weighted by probability), and multiply them together, the result you get has to be at least a certain value, namely [itex]\hbar/2[/itex]. This means that both the position and the momentum have to have some "spread" - that is, if you measure them multiple times, you can't get exactly the same result every time, but there has to be some variation, just because that's the nature of the wavefunction. So the HUP is solidly grounded in math. It's not because of some limitation of our measurement process; it's due to a "limitation" in the very nature of reality.

    Of course, depending on what measurement process you actually do use, you may have an even larger uncertainty than that. If your measuring device is not very precise, it can introduce additional uncertainties, beyond the "fundamental" uncertainty required by the HUP. That's why there's a ≥ sign (instead of an = sign) in the equation.
     
  10. Sep 29, 2010 #9
    There are still (respected) suggestions that the uncertainty principle can be beaten:

    http://arstechnica.com/science/news...-topple-heisenbergs-uncertainty-principle.ars

    This suggestion involves entangling a particle with a quantum 'memory' that encodes all its states, then measuring its position and then checking what its momentum was in the 'memory'.

    It looks a bit speculative, and cannot be experimentally implemented yet, so can't be taken too seriously.

    btw, can anyone explain how to measure a particle's momentum without doing two position measurements?
     
  11. Sep 29, 2010 #10

    DrChinese

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    I absolutely dispute the idea of the article. This is nothing more than the EPR paradox revisited. You can indeed store Bob's entangled state in something, but that will in turn be entangled with Alice. Once either is observed, the entanglement ceases. As you know, the process is the same as occurs with entanglement swapping schemes.

    Ergo, you can't beat the HUP.
     
  12. Sep 29, 2010 #11
    I'm not convinced that the particle (point) is the full extent of the particle phenomenon. In other words, The particle/wave duality description never has satisfied me. Inherent uncertainty of physical attributes isn't logical. I feel something is missing, as in the physical description of the object. There seems to be more here that we're not aware of.
     
  13. Sep 29, 2010 #12

    DrChinese

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    No, this is not correct at all. Two reasons (among others) should suffice:

    1. You can create particles that are essentially clones of each other, and then measure the position of one and the momentum of the other. The HUP is still respected.

    2. You can measure commuting attributes of the same particle to unlimited precision, and the HUP does not apply. But you cannot do the same for non-commuting observables.

    So clearly, technology is not an issue. Instead, it is a consequence of theory.
     
  14. Sep 29, 2010 #13

    Demystifier

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    Maybe the Bohmian interpretation would be more satisfying for you. Are you familiar with it?
     
  15. Sep 29, 2010 #14
    Hi again..... Thanks a lot guys! I should say that i am highly impressed by the responses i got. And i understood my mistake. Thanks a lot people. This forum is just great!
     
  16. Sep 29, 2010 #15
    I am not familiar with the Bohmian interpretation. Can you explain it?
     
  17. Sep 29, 2010 #16
    http://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

    This should help.

    Thank you Demystifier. I was thinking more of the topographical description of the "particle/wave" phenomenon as being incorrect. It could be we lack the ability to uncover the true nature of the "sub-atomic particle". If for example (as Einstein mused) that the particle could be a singularity, to what degree can we envision or measure the extents of the object.

    If our knowledge of "black-holes" is not quite correct, as in there's something we don't understand yet; the subatomic "black-hole" as being fundamental and "flexible" so to speak, could be altogether different than we perceive. It could possibly take on shapes we don't foresee being plausible. This could be the key to understanding some uncertainties.
     
  18. Sep 29, 2010 #17
    ok, in answer to the question "how to measure momentum without doing position measurements" you can use some other property of the particle such as em charge and measure deflections:
    http://www.particleadventure.org/measure.html

    (In general, for any type of particle (including em uncharged), I guess you could (in theory) measure gravitational deflections)


    On a simpler level, here's a nice overview of the uncertainty principle with some experimental details to clarify things:
    http://galileo.phys.virginia.edu/classes/252/uncertainty_principle.html
     
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