Thursday, March 02, 2017

Yes, a violation of energy conservation can explain the cosmological constant






Upon closer inspection, the Physics World piece summarizes the paper:















  1. Thanks Dr. H. Another good read. Doesn't QFT allow for local and temporary violations of energy conservation? Perhaps as with the process resulting in black hole evaporation some of these "temporary" violations become locked in?

  2. Hi Sabine,

    many thanks, this post is interesting and very refreshing (which is so rare in physics :).

    The paper is of particular interest to me because I think it has direct relation with the one I pointed to you a few weeks ago. The point is that writing the non-conservation equation for a start (and then maybe understanding what it means), you get straight to the densities of matter, dark matter and dark energy. Plus other goodies like MOND.

    But of course it requires to start with classical GR and not a straight jump to quantum fields.


  3. Sabine,


    It seems to me that "much more work" would be welcomed by GR theoretical physicists.

  4. Baryogenesis, non-classical gravitations, dark matter, and SUSY are empirical failures. Add dark energy. If physics must be fantastical, perhaps physics should be different, Aristotle versus Galileo.
    ...Empress Eugénie's Circle is a suspension bridge with no anchorages.

  5. One thing that confuses me is that, in Einstein's seminal 1916 'Grundlage' paper, the condition [root (-g) = 1] is imposed in quite a few instances. It looks like he is using uni-modular gravity, but I presume he's just using the condition as a way of simplifying things, is that right?
    Regards, Cormac

  6. Professor,

    I'm not much of a historian, so I can't answer your question, sorry - maybe some of our readers can answer your question. What I recall is that Einstein tried various equations and ways to arrive at these equations and he was missing a constraint (the Bianchi identities), so it's quite plausible he'd have tried this.

    Having said that, note that the Schwarzschild metric in standard coordinates has deg g = r^2 sin(theta)^2, which you could set to one when you take cartesian coordinates. It's quite a natural way to fix the gauge which isn't the same as fixing the variation. Best, B.

  7. @Professor R: In section 14c, 'The Final Steps', of the superb Einstein biography 'Subtle is the Lord', Abraham Pais writes:

    "The remaining flaw was, of course, Einstein's unnecessary restriction to uni-modular transformations. The reasons which led him to introduce this constraint were not deep, I believe. He simply noted that this restricted class of transformations permits simplifications of tensor calculus."

    So your presumption seems to be correct.

  8. It's not entirely settled whether Unimodular gravity differs from GR's prediction at the quantum level. This goes back and forth endlessly in the literature.

    At the very least, its not clear what you gain when trying to solve the cosmological constant problem. There is still a finetuning problem, the difference is -they say- that there is only one number to explain, and not an entire renormalization tower of unknown physics which tends to drag you (order by order) towards a Planckian value.

  9. In 1918 Hermann Weyl derived a restriction-free form of the traceless Einstein equations by simply assuming R^2 in the Lagrangian rather than R. Since the energy-momentum tensor for the electromagnetic field is already traceless, such a straightforward method of getting traceless equations seems to be the way to go. It would thus appear that Weyl had effectively discovered unimodular gravity long before anyone else, and without assuming a fixed metric determinant.

  10. Sabine/others: Does unimodular gravity have different observational consequences in solar system and binary pulsars as compared to GR? Which of its PPN parameters differ from GR?

  11. Shantanu,

    As I said, unimodular gravity plus energy conservation reproduces GR so it has no observable consequences. And if you relax energy conservation you want to make really sure it doesn't have observable effects that spoil the fit to data. Not much is being said in the paper about this, more work is needed etc. Best,


  12. And, yes, what Haelfix says above is correct, there is a long back and forth in the literature about whether or not quantizing unimodular gravity helps with the cosmological constant problem by taming vacuum fluctuations, but the calculations in the paper above doesn't depend on the quantization. Best,


  13. Hi

    Don't know if you already commented that new article from the same authors : they now claim they can relate the value of the cosmological constant to the top mass
    arxiv 1711.05183.pdf

    Anyway i still have a problem with equation 7 and footnote 3 of the precursor article you are commenting on this page (arxiv: 1604.04183).

    In all other papers about UG, eventually rewritten as an Einstein equation the energy momentum is conserved as usual on the right side and the cosmological constant is a mere integration constant (which is interesting because it can be anything you want and you could absorb in that way the QFT vacuum energy ).

    But keeping it in the form of equation 7 with a non conserved energy momentum on the right hand side , then the cosmological constant term is not actually anymore a constant (it varies in time). What bothers me even more is i dont understand what gives you the right to consider that the equation being written in that way , the cosmological constant term on the left hand side (which depens on Q) is really what you can probe in cosmological tests : in actual cosmological tests the acceleration of the universe is the effect that appears as a departure from equations in which the energy-momentum of matter is conserved ... so it is only the departure from the equation written according footnote 3 (as usual for UG) that should be interpreted as a cosmological constant effect ... what did i miss ?!





