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My biggest issue with QM

  1. Nov 30, 2009 #1
    Hi all,

    My understanding of the Heisenberg uncertainty principle is this:
    1) in order to measure something, we have to hit it with something smaller.
    2) in order to know the exact position of something we have to know the exact position of the thing we hit it with.
    3) therefore, we cannot know the exact position of anything, because we don't and can't know the exact position of any smaller particle/wave we could measure it with.

    My first question is: is this an okay explanation?

    My second question is more general, and is my biggest issue with QM (so far).

    Many people suggest the following leap in logic, but I can't follow it.
    They say, since the HUP states that we cannot know the exact position/velocity of a particle, that a particle doesn't have one exact position/velocity.

    This leap between position/velocity being "unknowable" by us and being actually "indeterminate" is lost on me. Just because you don't know how many fingers I'm holding up doesn't mean I'm not holding up a particular number of fingers. Sure, for your purposes, you might create a probability curve to represent the number, but, again, that doesn't mean I actually have a finger "cloud".

    Help me get on track here.
    Thanks.
     
  2. jcsd
  3. Nov 30, 2009 #2

    DaveC426913

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    "They say, since the HUP states that we cannot know the exact position/velocity of a particle, that a particle doesn't have one exact position/velocity."

    That's not the reason its position is not knowable.

    HUP does state that the position/velocity of a particle is not simply a measurement problem, it is a real property.

    Here's how I rationalize it. Whether it's a valid analogy or not, I'll leave to others:

    I envision a particle as the sum-total of a wave packet smeared over a distance.

    How do you define the exact location of a wave smeared over a distance? Pick the middle point? The narrower you try to pin down an exact location, the more of the wave you have to ignore.

    Conversely, if you try to determine its total momentum, you must include the entire wave. If you count the entire wave, smeared over a distance, it becomes meaningless to talk about its exact location.
     
  4. Nov 30, 2009 #3
    No it's not.

    A better explanation is this......

    Imagine a waves hitting seashore. Those waves have a well defined frequency, but not a well defined position.

    Now imagine one giant wave hitting the shore. That one wave has a well defined position, but not a well defined frequency.

    It so happens that when you do QM, the momentum of a particle corresponds to its frequency. So if you localize the particle in one place, it no longer has a well defined frequency and hence no well defined position.

    Replace that ocean wave with a light wave, and you see the problem.

    That's because you are using a wrong mental model. It turns out that particles have properties that are indeterminate rather than merely unknowable. It gets worse, since you can do a thought experiment to show that if particles actually had unknowable information, that all the particles in the universe would have to exchange information to keep the bookkeeping right.
     
  5. Nov 30, 2009 #4
    The Heisenberg Uncertainty Principle is a mathematical property of QM.

    You've got it backwards: "They say, since the HUP states that we cannot know the exact position/velocity of a particle, that a particle doesn't have one exact position/velocity."

    The particle doesn't have one exact position/velocity therefore we cannot know the exact position/velocity of the particle. This is how you should look at the uncertainty principle.
     
  6. Nov 30, 2009 #5

    jambaugh

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    The critical distinction between classical and quantum mechanics is that in QM we move from a language of system state to a language of observer-system interaction. This is why we go from "knowledge of system state" to "indeterminacy of system observable". It's a matter of no longer speaking in terms "what is" (ontological language) and speaking rather in terms of "what happens" (empirical action language or epistemological language).

    As Orwell points out we think with language. We find this action language of QM more general allowing us to conceive of systems where the assumption that we have acted to determine one observable necessitates the indeterminacy of another observable.

    It is more a matter of making explicit the implicit assumption that we have made measurements when we speak of the system's state. In making them explicit we must then also ask if the assumption that we've measured all variables is valid which raises the question of compatibility between different observables (such as position and momentum).

    Once we see in the theory that the order in which such pairs of measurements are made matters we can no longer say a prior measurement (of say momentum) reflects current information about what we would see if we repeat the measurement given we have since made an incompatible measurement (of say position).

    You could say measuring the position changed the momentum but that is using a language of classical states. Sticking to the language of actions in QM we should only say that measuring the position changes our ability to predict future measurements of momentum.

    Being thus careful about format you avoid asking questions which cannot be answered by empirical means e.g. "do electrons have souls?". Once you are clear on the answers to such empirical questions (and have learned to make the distinction as to type of questions) you can go back and ask if and in what way ontological statements about system states can be made which are consistent with the empirical questions and their answers. You can then ponder hidden variables, EPR experiments and Bell type inequality violation.
     
  7. Dec 1, 2009 #6

    Demystifier

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    Archosaur, you are absolutely right. If we cannot know something, it does not imply that it does not exist. Indeed, there is a formulation of quantum mechanics in which particles have both positions and momenta even when we don't measure them. This formulation is known as - the Bohmian interpretation.
     
  8. Dec 1, 2009 #7
     
  9. Dec 1, 2009 #8
    I have to admit I'm asking this question rhetorically because I have very little faith or expectation that anyone could answer it in a way that would satisfy me but in any case here it is: why don't your electrons radiate? The charge cloud doesn't radiate because it is stable, but what about your little particles being wafted about by the wave potential??
     
  10. Dec 1, 2009 #9

    Demystifier

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    I have to admit I'm answering this question rhetorically because I have very little faith or expectation that anyone could answer it in a way that would satisfy you but in any case here it is:
    When classical equations of motion (for charges and electromagnetic fields) are satisfied, then accelerated charges necessarily radiate. However, the Bohmian laws of motion are not the classical ones. The quantum potential affects not only the electrons, but photons as well. It turns out that this influence is such that it completely prevents radiation when the electron wave function is an energy eigenstate. In other words, my little particles being wafted about by the wave potential are stable too.
     
  11. Dec 1, 2009 #10

    jambaugh

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    I think the error people make is in confusing the "cloud" which represents our knowledge and uncertainty about how many fingers we would see if we look, for a representation of the realty of your fingers.

    Begin with the interpretation of the wave function as a representation of knowledge about the system in the same sense that a probability distribution is. Understand that in QM when we speak of "an electron with momentum p" this is not a direct statement about the electron's state but a statement that we have made a momentum measurement of the electron, or more precisely that we know what the value of an immediate momentum measurement will be.

    It is in this sense that we speak of indeterminacy of values of observables. This again is not a statement about the state of the system (that it's fuzzy) nor do we assume the system state has achieved some fuzzy cloud state. One is explicitly avoiding any reference to the system's state and only to what we know about how the system will behave with regard to potential future measurements. That is what is cloudy. It is not a matter of unreality but of agnosticism about reality.

    It is fine to further speculate about the nature of the reality behind the predictions and descriptions in quantum theory. But you need to acknowledge that in so doing you are beginning to walk outside the actual theory which concerns itself only with what is an can be known about a physical system.

    You can compare it to an ideal court trial where one can only infer facts based on admissible evidence. (Not a perfect analogy but another example of where one limits scope for the sake of rigor.)

    Demystifier advocates a Bohmian pilot wave interpretation which reifies (treats as real) the wave-function. Others advocate Everett's many universes which assert a different universe exists for each possible combination of measurements. I see such further interpretation as futile as it is speculation about that which nothing can be empirically verified.

    It is similar to aether theories of light propagation in classical relativity. You can introduce an aether and get all the same predictions of SR but there is no need and one is introducing that about which nothing can be empirically verified. The standard theory excises the aether and speaks only about that which we can know something. Hence time is what a clock reads and distances are what measuring rods measure. In QM system variables are outcomes of system measurements. We need only concern ourselves with how such measurements behave.
     
  12. Dec 1, 2009 #11
    Do your electrons orbit the proton in little circles like the Bohr atom or do they meander randomly about?
     
  13. Dec 1, 2009 #12
    True and that works. The trouble with the Bohm interpretation is that it's a non-local theory. To get it to work you have to assert particles are secretly exchanging information instantaneously. What happens is that you can set up situations in which you have two particles whose quantum states are correlated, so if you measure one particle, somehow the information on how you measured the first particle influences the measurement you get in the second particle. (I'm wildly oversimplifying, but look up the Bell inequality for a specific situation that this happens.)

    It's one of those "choose your poison situations." Something weird is going on.
     
  14. Dec 1, 2009 #13
    One reason this is worth thinking about is that it's not immediately obvious that there isn't some sort of empirical difference between the different interpretations of quantum mechanics. One problem with the standard Copenhagen interpretation is that the interpretation doesn't very clearly define when a wave function collapse occurs
     
  15. Dec 2, 2009 #14

    Demystifier

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    The trajectory depends on the wave function and on the initial particle position, but it is certainly not random.
     
  16. Dec 2, 2009 #15

    Demystifier

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    That is all true, except that I don't see this as a trouble and I don't find it weird. But that's just me.
     
  17. Dec 2, 2009 #16

    zonde

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    I can't follow it either. If there are billiard balls they have exact position and velocity even if they are very small.
    So to me it seems that this statement can have alternate conclusion like that:
    Since the HUP states that we cannot know the exact position/velocity of a particle, that particle is not a particle at all but wave instead.
     
  18. Dec 2, 2009 #17

    Codexus

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    Except those "waves" also show particle-like behavior in some experiments. So they are something that has a particle aspect and a wave aspect. Now maybe we should have invented a new name to avoid confusion with classical particles, but when we refer to particles in a QM context we're really talking about these wave/particles. It's really just a question of semantics.

    Anyway they are weird things that we have trouble imagining since the world we experience in our everyday lives has nothing similar.
     
  19. Dec 2, 2009 #18

    zonde

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    Yes the waves are quantized. So probably the name "quanta" is the one you are looking for.
    And clearly it could help imagining those things if we would find satisfactory example of quantized waves in macro world.
     
  20. Dec 2, 2009 #19
    I so believe that part of this confusion arise from the fact many high schools teachers like to state things like "photons are waves and particles at the same time". You'll have to simply step out from this mentality. Ill quote R. Feynman

    Its a new animal. Something unlike anything you ever seen.
     
  21. Dec 2, 2009 #20
    If you can't give me an example of a typical trajectory for an electron in a hydrogen atom, then I don't know what your theory is good for.
     
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