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Edward Witten on LQG for lambda > 0, QG does not exist in any dimension

  1. Dec 25, 2007 #1
    Edward Witten on LQG "for lambda > 0, QG does not exist in any dimension"

    arxiv.org/abs/0706.3359 -

    page 6 "for lambda > 0, QG does not exist in any dimension" ...the reason... "cannot provide precise observables"

    As I understand Edward Witten, deSitter space is not stable but metastable, and can be explained as a part of a larger system, AdS.

    If Edward Witten is right, "it is not possible to define mathematically precise observables" then all solutions of LQG/Spinform/CDT's and BI's that describe deSitter spacetime are hopeless in any dimension (which is what astronomers believe our spacetime is). Witten proceeds to work with AdS spacetime in 2+1 dimensions.

    I have no doubt pro-stringers would agree with this, but any LQG'ers can comment? Specifically, Edward Witten believes that LQG is hopeless in describing quantum gravity with a positive cosmological constant (see Smolin and recent work on Kodama wavefunction) since it is not possible to define mathematically precise observables, in any dimension, but including 3+1.
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  3. Dec 25, 2007 #2


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    misleading quote out of context
    Witten does not say flatly that QG does not exist but that there is SOME SUSPICION that it does not exist---and all the justification offered for the suspicion is a couple of old papers 2001 And 2002.
    Back in June when this came out, I had a look at the 2001 paper and did not find it very convincing---it did not raise very much suspicion that QG does not exist in realistic (4D Lambda > 0) circumstances.

    Did not seem worth spending time on. If more convincing arguments were available one would presumably have heard more in the intervening 6 years.

    People still might like to have a look at Witten's 2001 paper that the "some suspicion" is based on because it is kind of SciFi----talks about advanced civilizations, if they can in principle (unlimited lifetimes and futuristic instruments) measure certain things in principle. Kind of fun to imagine. So I will get the link. Here it is

    Quantum Gravity In De Sitter Space
    Edward Witten
    (Submitted on 13 Jun 2001)

    "We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is embedded in a more precise theory that determines the value of the cosmological constant. We give a definition of the quantum Hilbert space using the asymptotic behavior in the past and future, without requiring detailed microscopic knowledge. We discuss the difficulties in defining any precisely calculable or measurable observables in an asymptotically de Sitter spacetime, and explore some meta-observables that appear to make mathematical sense but cannot be measured by an observer who lives in the spacetime. This article is an expanded version of a lecture at Strings 2001 in Mumbai."

    Back in June, when the paper mentioned in the original post was being discussed, i wanted to cite this, partly for the entertainment value, but I don't know if i got around to it. The basic idea as i recall is that an S-matrix or scattering matrix depends on infinitely precise measurements (at least in principle) at minus infinity and plus infinity. And in a deSitter space you cant make infinitely exact measurements infinitely far in the past or future. The paper gets very Science Fictiony at places. Maybe I or somebody will get exerpts. But I urge folks to have a look.
    Last edited: Dec 25, 2007
  4. Dec 25, 2007 #3


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    If you view de Sitter space as an approximation, this is merely an interesting side bar.
  5. Dec 25, 2007 #4


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    Exactly, Chronos! You hit the nail-head. deSitter is a highly idealized approximation: it's what you'd get with ZERO MATTER in the universe. The Minkowski space that conventional Quantum Field Theory is built on is even more unrealistic because it requires zero matter to exist AND zero expansion, zero dark energy, acceleration...
    For someone to complain that you can't do S-matrix except on Minkowski just demonstrates that S-matrix and QFT itself are approximations.

    But as a practical matter we can still do S-matrix even if the universe is expanding and accelerating.
    Quantum Field Theory can be useful as an approximation, even though constructed on an idealized spacetime.
    Last edited: Dec 26, 2007
  6. Dec 26, 2007 #5
    So does LQG/SF see DS as an approximation, and if so, to what?
  7. Dec 26, 2007 #6


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    Witten's paper is an interesting side bar for another reason as well, that I don't think you alluded to. It is called Quantum Gravity in de Sitter Space. That means it is of limited relevance to the various non-string QG approaches. At best, a tangential or approximate relevance.

    For example in Loll's triangulations approach de Sitter space does not exist.
    No global geometry is assumed. There is no smooth manifold with metric. So it is useless to complain that one cannot do S-matrix because the manifold has the wrong global geometry. There is no manifold in the first place! Loll's spacetime is a quantum spacetime that is microscopically fractal-like and nowhere smooth. Interestingly enough, as their last paper reports, at large scale, if you do not include matter, and if you average out all the quantum fluctuations, you get something that looks like de Sitter space!

    What naturally emerges is just what the universe would look like if, instead of having very sparse matter as it does, it had zero matter. I think this result is a considerable step forward, so I put it in the "Paper of the Year" poll.

    [One lesson I guess you could draw is that OK reality is not a smooth manifold with metric, the sort of thing Witten is talking about making measurements with infinite precision on, and complaining when you cant, but even though it is NOT such an ideal smooth manifold when you average all that myriad fluctuating uncertain unsmooth natural geometry together in a path integral you can still get something that imprecisely LOOKS like a smooth manifold (in the case of zero matter). I think that's beautiful. It is what i voted for in the poll.]
    Last edited: Dec 26, 2007
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