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Zero-point energy cancelled by its gravitational energy?

  1. Aug 18, 2011 #1
    Consider the uncertainty principle:

    dp * dx = hbar

    For photons we have the relation:

    E = p c

    Substituting into the above uncertainty principle:

    dE = hbar c / dx (1)

    As we look at a smaller and smaller piece of the zero-point field the (positive) energy diverges.

    But that energy has a mass equivalent which therefore has a negative gravitational potential self-energy, dP.

    dP = - G dM^2 / dx (2)

    As dx -> 0 then dP -> -infinity as fast as dE -> infinity so they cancel each other out.

    If we have:

    dE = -dP = dM c^2

    and substitute this relation into (1) and (2) we get a relation for the length scale dx:

    dx = sqrt(G hbar / c^3)

    This is the Planck length.

    I would guess that space-time quantisation is equivalent to the zero-point energy at each point being cancelled out by its negative gravitational potential energy.
  2. jcsd
  3. Aug 20, 2011 #2


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    Hrmm...I wish I knew more on this. Maybe someone else knows something about this? I didn't think that zero point energy had any gravitational field.
  4. Aug 20, 2011 #3


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    I assume you are making a case against ZPE as the source of dark energy.
  5. Aug 21, 2011 #4
    Yes - I think the zero-point energy at each point in space is exactly cancelled by its negative gravitational energy.

    I speculate that the dark energy/negative pressure is caused by advanced gravitational waves which impinge on the accelerating matter in the Universe and lead to that matter having an inertia - a possible mechanism for Mach's principle.
    Last edited: Aug 21, 2011
  6. Aug 22, 2011 #5
    This is actually a more technical question than the initial responses and question seem to assume. The appropriate framework for this question is quantum field theory in curved spacetime (or quantum theories for gravitation). There are others on the forum who are much more proficient and technically savvy than I am on this issue but an interesting paper was recently written by Maggiore which deals with this issue.


    Basic conclusion is that the ZPF contribute a subdominant 'dark' contribution leaving the nature of the dominant contribution to dark energy a problem for current research trends in theoretical physics. This is a fairly technical paper and I probably need to really sit down and read it properly, consider his derivations etc (as opposed to just reading through it somewhat briefly) - I wonder if anyone else has seen this paper or has any strong feelings on it one way or the other? I'd be glad to hear any thoughts on the paper from people.

    As for Johne1618's post above, your line of approach is along that of backreaction in cosmological models. Be aware that your model requires a mechanism that can generate such horizon scale gravitational waves whilst remaining a subdominant contribution to perturbations (e.g. tensor modes are suppressed relative to scalar perturbations) - there are constraints from the CMB, CMB Polarisation, formation of large scale structure, growth history of the Universe etc. You would need to provide more explicit technical details before I can really comment on the viability of such a proposal. Similar backreaction effects have been considered in research by the likes of Buchert, Coley, etc. See, for example,


    Hope this is of some interest and help.
    Last edited: Aug 22, 2011
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