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Jacobson renews LQG with a roto-Reuter

  1. Jul 29, 2007 #1


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    Jacobson renovates LQG with a roto-Reuter

    I think the word for it is RENOVATION
    A roto-rooterTM is a tool for clearing clogged drains.

    I've been watching Martin Reuter papers since 2004, especially since a possible link with Loll's CDT appeared in 2005, but with reserve. I found Reuter's talk at Loops '07 very persuasive and gave me confidence in what he is doing.

    After Loops '07 a central question seemed to be how asymptotic safety, non-perturbative renormalizability, the running of newton G and Lambda---how these things will affect LQG and other non-string QG approaches.

    What Reuter has put on the table can actually bring about a revolution in LQG. Maybe resolve the quandary about the Hamiltonian constraint. In any case bring new results and energy into the field.

    In my humble view, it's time to see how Reutering will impact various features of LQG. even ones long taken for granted.

    Jacobson brought out a 7-page paper today and it looks to me as if he is going right to work on this.

    Renormalization and black hole entropy in Loop Quantum Gravity
    Ted Jacobson
    7 pages
    (Submitted on 26 Jul 2007)

    "Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds."

    Jacobson's reference [15] is a Martin Reuter paper
    [15] M. Reuter and J. M. Schwindt, “Scale-dependent metric and causal
    structures in quantum Einstein gravity,” JHEP 0701, 049 (2007)
    Last edited: Jul 30, 2007
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  3. Jul 29, 2007 #2


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    Ted Jacobson IIRC was invited to Carlo Rovelli's May 2004 workshop explicitly to fill a devil-advocate or critic role. My impression is he takes such responsibilities seriously. He also did an impressive job at the KITP Singularities workshop in January this year. He puts the spotlight on stuff others might casually sweep under the fudge. Or so it seemed to me. A kind of meticulous and dedicated tactlessness. such people are worth their weight.

    I will get some quotes. this paper is neat.
    Thus, it seems to me more reasonable to expect that, if the
    microscopic calculation of black hole entropy is really correct, then it should
    agree with SBH for all values of [the Immirzi parameter] gamma.

    On the face of it this looks impossible, however in fact the comparison
    of SLQG with A/4~G has been made prematurely. The latter refers to a
    property of a semiclassical black hole. As such, the area is measured using
    the low energy effective metric field, and the Newton constant is the low
    energy effective Newton constant.
    By contrast, the area and Newton con-
    stant in SLQG are the microscopic quantities appearing in the fundamental
    formulation of the theory. This raises the question of exactly how the “cor-
    respondence principle” between the microscopic description in LQG and the
    effective field theory (EFT) description operates.
    Anything said about the correspondence now is necessarily provisional,
    since fundamental aspects of LQG have not yet been understood. The Hamil-
    tonian constraint, which encodes all the dynamics, remains to be understood,
    much less solved. Once solved, the theory can in principle only make state-
    ments about diffeomorphism invariant observables, and only tentative first
    steps have been achieved for the identification of a suitable class of such
    observables. Nevertheless, the setting of the black hole entropy computa-
    tions is well-defined, and reasonably well-motivated, at least enough to merit
    scrutiny of its theoretical basis and self-consistency.
    We now come to the central point of this note: there is no reason to ex-
    pect the correspondence between microscopic and macroscopic quantities to
    be trivial.
    There are two different reasons for this. One is that in translating
    from a discrete spin-network to a field theoretic framework there is a pro-
    found change of objects and language. The other, independent reason is that
    even once the correspondence to an effective field theory has been made, the
    renormalization group flow of that theory from the UV to the IR
    is highly
    nontrivial. What then can be said?
    In writing these relations, and in the rest of this paper, I am simply
    assuming that a semiclassical EFT limit of LQG exists, for at least some gamma
    [as before, gamma is the Immirzi parameter.]
    The problem of understanding these renormalization relations is a crucial
    part of understanding the semiclassical limit of LQG. While this is a wide
    open problem, it can nevertheless be asked at present what properties must
    they exhibit if the existing microscopic black hole entropy calculations are
    to be valid?
    Area renormalization significantly changes the picture however. The
    renormalization of G can then be arbitrarily complicated, and dependent
    on the matter content, as long as it is universally tied to the renormalization
    of the area operator in the appropriate fashion indicated by (9). I see no
    reason why this could not be the case. If the continuum limit indeed exists,
    and the LQG black hole state counting is correct, then I would assert that it
    must be the case.

    I have indicated a scenario in which SLQG correctly counts the black hole
    entropy, without the need to select a special Immirzi parameter. It involves
    an unproven hypothesis about the correspondence between LQG and the
    semiclassical EFT of GR. Can this hypothesis be tested?
    To directly test the hypothesis requires an improved understanding of
    the EFT limit, but need not necessarily involve black holes. Although the
    numerical constant b is the one that arises in the horizon state counting,
    it does so in a way that might be more generally relevant to the relation
    between semiclassical geometry of areas and the microscopic, spin network
    variables. Thus perhaps the validity of the relation (9) can be tested in a
    simpler setting, for example even in the vacuum.

    The renormalization group flow made a big impression via Reuter's talk, it seems timely to be talking about how it may affect one's reasoning about major features of LQG. I like the forceful stylistic element of ending paragraphs with questions.

    have to go, back later
    Last edited: Jul 30, 2007
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