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Is this statement about the Uncertainty Principle correct?

  1. Jul 29, 2015 #1
    I was reading the Feynman Lectures awhile back and I remember reading something he said about the Uncertainty Principle and it seemed slightly odd to me. I don't remember the exact quote and combing through some of the lectures online I can't quite find it. I've heard it more than once from different sources so I know it's something someone said. It is roughly as follows:

    A way the Uncertainty Principle manifests itself in the macroscopic world is when you are applying an increasing force on a floor, you are reducing the Δx of the atoms. This causes the Δp to increase or increasing the range that the momenta of the atoms can take. So, due to this compression in x and gradual increase in the range of p, the floor will push back more and more as the force increases.​

    Now, I understand this from a classical point of view with electromagnetic forces and the properties of solids but can this quantum phenomenon be applied as a legitmate explanation for this macroscopic phenomenon?
     
  2. jcsd
  3. Jul 29, 2015 #2
    It makes sense qualitatively, but I am not sure that one could make quantitative predictions with the idea.

    Why do different materials have a different delta x for a given delta p?
     
  4. Jul 29, 2015 #3

    bhobba

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    It wrong - the reason the floor pushes back is the Pauli Exclusion principle as was sorted out by Dyson:
    https://en.wikipedia.org/wiki/Electron_degeneracy_pressure

    The correct statement of the uncertainty principle 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.

    Thanks
    Bill
     
    Last edited: Jul 29, 2015
  5. Jul 30, 2015 #4
    I don't think it's wrong. The electron degeneracy pressure and the uncertainty principle are closely linked. Both can be formulated in reference of the phase space volume of a system. Heisenberg's uncertainty says the phase space volume of a single electron is not compressible. Pauli's exclusion says that even the combined phase space volume of many electrons is not compressible. So from a phase space geometry point of view, the two are closely related and you can ultimately reduce the idea of degeneracy pressure to the phase space volume of a single electron being incompressible (plus identical particle symmetry).

    Cheers,
    Jazz
     
  6. Jul 30, 2015 #5

    bhobba

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    Good point.

    Thanks
    Bill
     
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