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Covariant loop quantum gravity and its low-energy limit (throwing the eagle)

  1. Feb 14, 2009 #1

    marcus

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    Rovelli has given his team and himself just seven months to advance LQG to a new stage. Why do I call this "throwing the eagle"? Because a Roman general would on occasion hurl his legion's eagle standard into the opposing army's midst, confident his side could rout their foes the recover it.
    http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Florus/Epitome/1B*.html#11.2

    In this case what has been undertaken is enterprising in its own way. The target date is mid-September, in time for a weeklong series of lectures at Corfu (13th thru 20th).
    http://www.maths.nottingham.ac.uk/qg/CorfuSS.html

    I've been to Corfu, a large island off the west coast of Greece, up near the border with Albania. It's beautiful.

    There will be a QG school, with a number of invited speakers giving seminars, plus 5 main speakers each giving a 'minicourse' series of lectures. The main speakers will be Ashtekar, Baez, Barrett, Rivasseau, and Rovelli. The website gives the titles and brief synopses of each minicourse. I'll quote Rovelli's:

    Covariant loop quantum gravity and its low-energy limit

    "I present a new look on Loop Quantum Gravity, aimed at giving a better grasp on its dynamics and its low-energy limit. Following the highly succesful model of QCD, general relativity is quantized by discretizing it on a finite lattice, quantizing, and then studying the continuous limit of expectation values. The quantization can be completed, and two remarkable theorems follow.

    The first gives the equivalence with the kinematics of canonical Loop Quantum Gravity. This amounts to an independent re-derivation of all well known Loop Quantum gravity kinematical results.

    The second [gives] the equivalence of the theory with the Feynman expansion of an auxiliary field theory. Observable quantities in the discretized theory can be identified with general relativity n-point functions in appropriate regimes. The continuous limit turns out to be subtly different from that of QCD, for reasons that can be traced to the general covariance of the theory.

    I discuss this limit, the scaling properties of the theory, and I pose the problem of a renormalization group analysis of its large distance behavior."

    Rovelli's course description is marked "tentative", presumably because work is still in progress to prove the theorems in every case. It will be extremely interesting to see if they can bring this project to full completion in the next few months.
     
    Last edited: Feb 14, 2009
  2. jcsd
  3. Feb 15, 2009 #2
    I do not understand much but the words covariant and low-energy limit in the context of loop quantum gravity sound very promising. :-)
     
  4. Feb 16, 2009 #3

    marcus

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    I agree with the general spirit of what you say, Micha. The announcement as a whole, and especially Rovelli's series of lectures, sounds distinctly promising. Even exciting.

    We should be clear about what he means by covariant LQG.
    This has to be one of two things.
    Starting in 2001 or 2002, Sergei Alexandrov has been developing an approach that he calls Covariant LQG. There are a half-dozen or a dozen papers on this.
    But I'm pretty sure this is not what Rovelli is talking about.

    I think when Rovelli talks about covariant LQG he is making a distinction between canonical LQG and the covariant approach that has been worked on now for over 10 years starting around 1998.
    "Covariant LQG" is just a more descriptive term for the spinfoam and GFT formalisms.
    Basically it's all one theory, there are simply alternative ways to present it: the covariant presentation and the canonical presentation.
    ===============================

    To get an up-to-date impression of what's going on in (covariant) LQG, I'd suggest watching this video.
    http://pirsa.org/09020023/
    Graviton propagator from EPRL spinfoam model
    Claudio Perini - CPT
    "We derive geometric correlation functions in the new spinfoam model with coherent states techniques, making connection with quantum Regge calculus and perturbative quantum gravity. In particular we recover the expected scaling with distance for all components of the propagator. We expect the same technique to be well-suited for other spinfoam models."
    Date: 11/02/2009 - 4:00 pm

    When he says recover expected scaling what he means is they get Newton's law of gravity in low-energy limit. It is an interesting talk partly because it is interrupted by questions from Lee Smolin and one of the experts in covariant LQG, Simone Speziale (the guy with all the curly black hair) and Florian Conrady, who co-authors with Laurent Freidel. There is a mood of excitement and tension in the room which shows itself sometimes in funny ways. Perini gives a very good talk.

    What the talk shows is that Rovelli already has the essentials of what he needs to deliver in September. But they are still doing numerical checking and extending to further cases, so there is plenty of work left. Perini is a PhD student in Rovelli's group at Marseille CPT.
     
    Last edited: Feb 17, 2009
  5. Feb 18, 2009 #4

    marcus

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    LQG has been known to be Lorentz covariant since 2007
    http://arxiv.org/abs/0711.0146
    http://arxiv.org/abs/0710.5043

    Before that one had a Lorentz covariant version of the Barrett-Crane (BC) spinfoam model, but equivalence to canonical LQG had not been shown. In 2007 a new spinfoam model was adopted. One particular version is associated with Engle, Pereira, Rovelli, and Livine, the socalled EPRL version. It does not seem to have surprised anyone when they showed Lorentz covariance.

    What got more attention, I think, was when they showed that EPRL agrees with the kinematic results of canonical LQG on spatial slices. This has been done also in 2007, which is why one now refers to EPRL spinfoam formalism as covariant LQG. Foam and loop are joined, as two parts of the same theory.

    A good summary talk on this is one Roberto Pereira gave at Perimeter December 2008
    http://pirsa.org/08120046/
    The full title is:
    LQG vertex for spin foam gravity: Lorentzian theory
    Here are the slides:
    http://pirsa.org/pdf/files/7976817d-07b5-48af-8c22-44559f23b5c5.pdf [Broken]
    If you want to watch, the way I do it is first download the MP3 audio and pause it at the beginning. Then I start the Windows presentation of the video, and as soon as it begins I start the audio. I start them in synch and they stay in synch for the whole hour. If you find a way to get both the video and audio together as a single program, please let me know.
     
    Last edited by a moderator: May 4, 2017
  6. Feb 19, 2009 #5

    MathematicalPhysicist

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    Perhaps something will turn up (most likely, not (-: ).

    Btw I remember something like a month ago there was a seminar on LQG in cambridge, dpmms, does someone have a link to this page on this seminar?

    Thanks in advance.
     
  7. Feb 19, 2009 #6

    marcus

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    You seem to think some piece of the puzzle, some significant result, is likely not to turn up. What do you think that could be?

    I ask because it seems to me that everything they need seems already in place except for dotting the I's and crossing the T's. LQG has been on a roll since 2007---seems to have a lot of momentm and to be on the right track. So what part of the program do you imagine is not likely to work?
     
  8. Feb 19, 2009 #7

    MathematicalPhysicist

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    An experiment, we need experiments to check its assertions.
     
  9. Feb 19, 2009 #8
    Sumbits, I tried to get into his "thermal time" idea with some dudes about a year ago who claimed online to be doing string theory; I got turfed. I didn't pursue Rovelli, Connes et al since, gosh darn it.

    They seemed to be convinced there was no argument: time is ontological and that's that.
     
  10. Feb 20, 2009 #9

    marcus

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    We shouldn't get Rovelli's "thermal time" idea or his recent essay on the Nature of Time entered in that contest mixed up the overall Covariant LQG program.
    I agree that they are both interesting, but they're not interdependent. He sees them as related but not everyone does.

    LQG is not just Rovelli. It is being worked on by something on the order of 100 researchers worldwide not counting those who apply LQG to cosmology. If I remember correctly the last big conference had about 200 people participating. But that included Loop Quantum Cosmology.

    Covariant LQG uses a spacetime formalism. So time exists in the theory pretty much the same way as it does for General Relativity. You can think of it as basically a path integral approach.

    As I understand it, what Rovelli is planning to present at the Quantum Gravity school in September is two things:
    1. show that Covariant LQG reproduces some of the good results of the older Canonical LQG. (Canonical treats time differently, it's based on a spatial slice, the framework of canonical quantization was worked out by Dirac.) I think Covariant LQG is an improvement but they have to show that the good stuff from Canonical carries over.

    2. show that Covariant LQG has the right low energy limit-----that whatever it does at small scale, at large scale it acts like the Newtonian gravity and General Relativity that we know and love.

    I think they may actually have proved all this if you put the pieces together. Roberto Pereira's Perimeter video talk this. But it needs a final wrap-up, which I think Rovelli's Corfu lectures will provide. If so, that will make 2009 something of a landmark years for quantum gravity, reaching some longterm goals of the program.
     
    Last edited: Feb 20, 2009
  11. Feb 20, 2009 #10
    Ok, so then time is 'available', even in LQG, for something to find a path along. Is time itself also a path something is finding?
    We have cosmic expansion which fits a Taylor approximation, e.g.
     
  12. Feb 20, 2009 #11

    marcus

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    Cosmology is simpler because there is a standard splitting. The CMB and the expansion process themselves provide a criterion of being at rest, and an idea of cosmic time.

    The general theory, whether it is GR or Covariant LQG, is a different story. No absolute time.
    Speaking of time, it's one AM here and I'm falling asleep. I'll try for more of a response tomorrow.
     
  13. Feb 21, 2009 #12

    marcus

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    The question I guess is how "available" time is even in Generivity (in seminar talks they always say it so fast :biggrin:)
    LQG is going to be more or less the same---local Lorentz invariance---covariant, like GR.

    In conventional QM you have a classical time variable because you basically deal with a subsystem---something inside a box---not the whole universe. There is a classical creature called the observer outside the box who has a classical clock on his laboratory wall.

    Relative to the quantum system being studied (the experiment to be prepared in a certain state and observed), time is outside and absolute and classical.

    I think in covariant LQG you can imitate that situation by enclosing a spacetime region and fixing the gravitational field on the boundary. This is how they compute graviton propagators in LQG. There are some recent papers on that. E.g. Rovelli's most recent (check arxiv, December 2008).

    Another thing they do, especially in LQG cosmology where there is no "box" because the universe is everything, is they put in a matter field into the picture to serve as a clock. In that situation there is no outside classical clock. The whole universe is being studied, but without the convenience of an absolute time. Instead, time is a quantum variable which is uncertain, imperfect, like everything else, and all you get to observe are correlations, or conditional expectations---amplitudes that when T says this, X says (at least approximately) that.

    I don't think we have to resort to Rovelli's thermal time idea, but the first part of his essay is still relevant. As I recall he introduces thermal time at the end, as a possible but controversial way of recovering the familiar time idea. The first part is comparatively straightforward and I think uncontroversial. What happens when you make your clock a realistic imperfect device made out of real quantum matter? What has to change when you go to quantum spacetime geometry? Time is a part of the geometry of spacetime and if that is going to be uncertain and indeterminate then time must be so too. No continuous trajectories, no continuous worldlines, only amplitudes of getting from here to there. Maybe I'm misremembering. I'll have to go back and read the first part of the essay.
     
    Last edited: Feb 21, 2009
  14. Feb 25, 2009 #13

    atyy

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    Marcus, thanks for your response on the other thread about covariant LQG! The references you've given here are also very helpful for figuring out which is what! Is Rovelli's 2008 update of his living reviews also about covariant LQG?
     
  15. Feb 25, 2009 #14
    So what is more promising: Loop Gravity or Superstrings?
     
  16. Feb 25, 2009 #15

    marcus

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    Heh heh :biggrin:
    Dmitry I stopped trying to pick winners in fundamental physics research many years ago and I suspect that theory research is like the stock market, intrinsically hard to predict.

    There are Superstring-fans who seem to me to be very touchy and protective. So that whenever I report something interesting about LQG, or mention something good about it, they feel as if String is being attacked! (Although there was no mention of String.)
    And they sometimes feel they need to come in and say things like
    "LQG is just as bad as String about having many solutions"
    "LQG isn't experimentally testable unless you made an accelerator as big as the solar system"
    "LQG isn't really background independent, the true background independence is in String."

    So you can have a thread that is intended to be only about nonstring QG and somebody will drag the topic of conversation around to String. And "who is best?" type discussion.

    I think it is interesting and legitimate to have "which is best" type discussion. It is probably instructive and valuable to compare theory lines and research programs and try to describe fundamental differences of approach. But I don't want to always be doing that.
    People should start comparative theory threads and do that, when they want.
    But I usually just like to watch what is going on in the nonstring QG research community and note progress, trends, new results etc.
     
  17. Feb 25, 2009 #16

    marcus

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    I'm delighted to hear that some of this was useful! Rovelli's 2008 review update is necessarily about both the covariant and canonical LQG formalisms.

    Before spinfoam and canonical LQG were shown to be consistent, there were two separate research lines. Spinfoam was obviously covariant, but it didn't have the Immirzi and it didn't have the same spectra. And it had problems. So around 2007 they replaced it by a new spinfoam that turned out to be compatible. So the two things merged.
    The natural name to call the new merged research line is LQG (with both covariant and canonical formulations.)

    A tidbit of possibly interesting information is that General Relativity itself has both a covariant and a canonical (space slice or "3+1") formulation.
    The canonical formulation is called ADM.
    http://en.wikipedia.org/wiki/Numerical_relativity
    "The field of numerical relativity emerged from the desire to construct and study more general solutions to the field equations by approximately solving the Einstein equations numerically. A necessary precursor to such attempts was a decomposition of spacetime back into separated space and time. This was first published by Richard Arnowitt, Stanley Deser, and Charles W. Misner in the late 1950s in what has become known as the ADM formalism.[2] "
    http://en.wikipedia.org/wiki/ADM_formalism

    In a quantum gravity context, the ADM approach uses a 3D hypersurface with constraints that ensure that the gravitational field on that hypersurface could have evolved naturally and will be able to continue evolving.
    The word "canonical" has acquired that connotation here---a timeless formulation with constraints to ensure that a time-evolving version can be recovered---a focus on a present moment containing both past and future.
     
    Last edited: Feb 25, 2009
  18. Feb 25, 2009 #17
    What, what!? Are you saying spinfoam can be used to calculate what the Immirzi parameter of the canonical method is? Does this mean blackhole entropy is finally predicted within LQG (instead of "predicted within a constant")?
     
  19. Feb 25, 2009 #18

    MTd2

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    Hi Marcus,

    Right now, do you think LQG can be a gravity pure 4D version of M-Theory?
     
  20. Feb 25, 2009 #19

    marcus

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    No, definitely not. It is simply that the Immirzi parameter gamma appears in both the EPRL spinfoam and the FK spinfoam models, and both these models turn out to agree for gamma < 1.

    And together they give the same spectra for the area and volume operators as the canonical version of LQG did, which involves gamma.

    If you did some reading about the earlier canonical version, you may recall that the eigenvalues of area were proportional to gamma. The Immirzi appears in the spectrum of area (indeed this is how it gets determined by the black hole entropy relation!)
    It was a pleasant surprise when the new spinfoam vertex formula led to a discrete area spectrum and the eigenvalues turned out to be the same, with the Immirzi appearing in them.

    The earlier spinfoam vertex formula did not accomodate an Immirzi, and did not produce discrete spectra, and of course there was no eigenvalue agreement. So the theory came a long way in 2007 when all these things were realized using the new vertex.

    The acronyms are Engle, Pereira, Rovelli, Livine for one model and Freidel Krasnov for the other. But instead of continually saying EPRL and FK it is easier now to just say covariant LQG.
     
    Last edited: Feb 25, 2009
  21. Feb 25, 2009 #20

    marcus

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    MTd2 what works for me personally is to be cautious conservative and gradual about what I expect.
    Basically I listen to gossip and side-remarks at seminar talks, but I do not make original far-reaching predictions about research programs.

    In the LQG case it now appears the covariant and canonical versions have merged and the next thing is to verify the low-energy limit, or maybe to be more exact several limits.
    This has already been done in some cases but I believe it still has to be wrapped up.
    Another milestone will have been reached if this is wrapped up by September when Rovelli is expected to report on it.

    This current effort could possibly, it seems to me, fail. I don't expect it to fail however. We will know soon enough.

    The next absolutely essential step, which I will be watching for later this year and next, is the gradual relaxation of the restrictions of homogeneity and isotropy in Loop Cosmology (LQC).
    This will make LQC closer to LQG and form a bridge.
    Work on this has already occurred. There are papers on anisotropic LQC models (Bianchi, if I remember correctly, also Nariai---I don't want to stop and look up papers, but some anisotropic LQC work has already appeared.) Rovelli also recently posted a paper about research in this direction.

    Only if that next step succeeds would I personally look further on.

    The reason it is essential to bridge and merge LQG and LQC is because this will (if it succeeds) achieve testability. It is already clear that LQC is testable in principle by observation.
     
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