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Is Quantum Mechanics Scale Invariant?

  1. Apr 6, 2005 #1
    I'm wondering what happens if the scale factor of cosmological expansion increases without limit? Will you always calculate the same quantum foam and virtual particle production rates no matter what the scale is of the universe's expansion? If particles are extended objects, then of course virtual particle pair production is effected by the stretching of space. But if particles are singularities, then space may always have the same quantum foam properties no matter how much space is stretched by cosmic expansion. What do you think?
  2. jcsd
  3. Apr 6, 2005 #2

    I think that the quantum foam properties are self-regenerative.

    That is to say, as the universe expands the sub-quantal volumes are replaced by new sub-quantal volumes with the same properties as the original.

    However, it is possible that the new sub-quantal volumes so created have different properties, and such a situation would mean that the universe is constantly evolving and that over time some of it's macro-properties will become subject to change. The time frame here would relate to just how fast the universe is expanding and how many levels the new sub-quantal volumes would have to pass through before macro-properties are affected.

    Last edited: Apr 6, 2005
  4. Apr 6, 2005 #3
    Or is the quantum foam itself the mechanism by which space expands? If particles are extended objects, then perhaps space is pushed aside as a virtual particle is created. Then only those virtual particles that do not recombine would be responsible for the expansion of the universe. That would at least link the expansion rate with the cosmological constant, right? But if particles are extended objects, then the quantum foam cannot be scale invariant,right?
  5. Apr 7, 2005 #4
    what do you by scale factor of the cosmological expansion
  6. Apr 7, 2005 #5
    I think this is a question that we cannot answer yet because this involves Quantum Gravity. But speculation is always fun! :smile:
  7. Apr 7, 2005 #6
    I don't know much about the subject but we can know the scale behaviour of the Schroedinger equation for example :

    starting from space scaling:

    x->ax implies t->t*a^2, V->V*a^2

    With that scaling law, all the Schroedinger physics is invariant...but for other equations, the scaling is different....was that the question ?
  8. Apr 7, 2005 #7
    Hi Mike,

    The quantum foam itself is scale invariant since it only exists at the smallest sub-quantum levels.

    Imagine that the foam arises from an infinite potential at various symmetric points in the universe. It is only indeterminate foam until it reaches the planck level where it becomes a determinate potential.


    Last edited: Apr 7, 2005
  9. Apr 7, 2005 #8
    Let's see. If it were possible for the uncertainty principle to allow an infinite energy for the briefest of time, then the existence of infinities would seem to indicate singularities which would not vary with scale factor. But I hear that QED and such has an "ultraviolet cutoff" so that we don't consider pair production higher than a particular level. Did I get that wrong? Thanks.
  10. Apr 8, 2005 #9


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    As far as I know the rates for virtual particle production are not the same (i.e. the vacuum is not the same) viewed from different comoving times in cosmology. This is due to the fact that the vacuum state of a field is defined to be the the lowest energy eigenstate of the Hamiltonian. However, in case of an expanding space, the Hamiltonian is an explicit function of time and does not have time-independent eigenstates that could be chosen as ‘the vacuum’. One possible solution to this problem (which does not always work) is to define the lowest energy eigenstate of the instantaneous Hamiltonian. This different instantaneous vacua lead to particle production.
  11. Apr 8, 2005 #10
    Let's see, if pair production is related to ZPE which is related to the cosmological constant which is related to universal expansion, then since expansion is not constant, then ZPE and therefore pair production is not constant. It would seem that pair production is related to expansion so that a Conformal invariance, that is, scale invariance in not in effect. Does this prove that particles are extended objects which cannot be scale invariant? Thanks.
  12. Apr 12, 2005 #11
    EVERYTHING in the Universe IS EXPANDING!
    this includes YOU, the distances in atoms, molecules, and the Planck distance!
    the equations of Physics are independent of scale guage.
    for example, if all your meter sticks were marked off only in even numbers; SO WHAT?!
    love and peace,
    peace and love,
    (kirk) kirk gregory czuhai
  13. Apr 12, 2005 #12
    And this expansion of the Universe is now Accelerating!
    love and peace,
    peace and love,
    (kirk) kirk gregory czuhai
  14. Apr 12, 2005 #13
    i should add that these expansions are a lot of times "overruled" "temporaily" by other attractive forces such as gravitation or nuclear or electric charge.
    peace and love,
    love and peace,
    (kirk) kirk gregory czuhai
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