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Me not falling through the ground and Pauli's Exclusion Principle

  1. May 31, 2012 #1
    I explained to myself that I don't fall through the ground due to electrons repelling. Using classical electrostatic repulsion.
    Once in a while I hear it explained through Pauli's exclusion principle (PEP).

    • Do we need PEP to explain this, or is classical electrostatics enough?
  2. jcsd
  3. May 31, 2012 #2


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    Classical electrostatics accounts for almost every feature of the interactions between macroscopic bodies. Occasionally, the interaction can be modeled with Van der Waals forces, http://en.wikipedia.org/wiki/Van_der_Waals_force#Van_der_Waals_forces_between_macroscopic_objects.

    In order for the exclusion principle to be relevant, the object must be at an huge density. One such example is the neutron star, http://en.wikipedia.org/wiki/Neutron_star. There the intense gravitational interaction is balanced by an effective repulsion between nucleons that serves to prevent further collapse of the stellar core. For larger bodies of mass, even the PEP effect cannot prevent further collapse to a black hole.
  4. May 31, 2012 #3
    Hi Swimmingly!
    It depends on how far you want to go
    electrostatic repulsion is a good answer, but eventually if you want to work out the details of how did molecules even get to setup into this kind of mesh, so as to get the full picture, then Pauli's exlusion principle would kick in.
  5. May 31, 2012 #4


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    That is not true. In typical molecules, the energetic effect of the "exchange interaction" is only one order of magnitude less, and sometimes not even that much less, than the direct Coulomb repulsion. That can be seen from Hartree-Fock or Kohn-Sham calculations, where you get a direct number for this "exchange energy". While "one order of magnitude less" might sound small, those energy scales are *astronomical* on chemical scales, easily being 10000 times as large as typical energy differences you get in molecular reactions (and let's not even talk about conformations or intermolecular, or weak interactions, which are much smaller but still account for a great deal of everyday physics).

    In short: Without taking the antisymmetry of the wave function properly into account (and thus accounting for exchange interactions), there is no way you would even get something remotely describing real matter in any sensible way.

    So to OP: It's both, electrostatics and exchange. The latter is, however, not a real force, but a kind of fake interaction which can be used to describe the effects arising from combining the regular Coulomb interaction with antisymmetry constraints of Fermionic wave functions.
  6. Jun 1, 2012 #5
    yes, in order for the electrostatic repulsion to be effective the ground must be a stable solid, and a major reason for that is the Pauli Exclusion Principle as deduced by Dyson and Lenard in 1967:

    FJ Dyson and A Lenard: Stability of Matter, Parts I and II, J. Math. Phys., 8, 423-434 (1967)

    the argument was subsequently improved, eg by Lieb in 1976, see section IV of The Stability of Matter - Lieb 1976

    and an updated paper available at Project Euclid:

    The stability of Matter: from Atoms to Stars - Elliot Lieb 1990
  7. Jun 1, 2012 #6
    Thank you all for the answer.

    Why must it be solid, I don't understand what context you're referring too?
    My question applies to for example liquids too. Water doesn't run through my hand.
  8. Jun 5, 2012 #7
    yeah, the reason water doesn't run through your hand is because it's a liquid, try running your hand through ice.
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