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The problems in Quantum Geometry

  1. Feb 26, 2007 #1

    marcus

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    What are the main problems in non-string QG? Who is working on them? What progress has been made in the past couple of years?
     
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  3. Feb 27, 2007 #2

    marcus

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    People are invited to contribute their notions of what the main problems are that need to be worked on in (non-string) QG.

    Several years back we were always hearing about the low-energy limit, the semi-classical limit, contact with classical gravity. Apparently in the past couple of years there has been some progress---it's an area where people are working. Some of us may have noticed the August 2006 quote from Carlo Rovelli in NewSci. I'll give the quote in context:

    ===
    For loop quantum gravity to succeed as a fundamental theory of gravity, it should at the very least predict that apples fall to Earth. In other words, Newton's law of gravity should naturally arise from it. It is a tall order for a theory that generates space and time from scratch to describe what happens in the everyday world, but Carlo Rovelli at the University of the Mediterranean in Marseille, France, and his team have succeeded in doing just that. "Essentially we have calculated Newton's law starting from a world with no space and no time," he says (www.arxiv.org/abs/gr-qc/0604044).
    ===
    http://space.newscientist.com/article/mg19125645.800

    In case someone wishes to check it out, here is the journal article to which Rovelli referred in the NewSci interview:
    http://www.arxiv.org/abs/gr-qc/0604044
    Graviton propagator in loop quantum gravity
    Eugenio Bianchi, Leonardo Modesto, Carlo Rovelli, Simone Speziale
    41 pages, 6 figures
    Class.Quant.Grav. 23 (2006) 6989-7028

    IMHO this is still an active research area despite some progress being made---undoubtably there's lots more to do.
     
    Last edited: Feb 27, 2007
  4. Feb 27, 2007 #3

    marcus

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    One reason the question interests me about what are Quantum Geometry's current problems is that JB in TWF #246 said something that I wasn't sure how to interpret.

    ...Loop quantum gravity, in particular, has problems that are just as serious as string theory.
    But, the "only game in town" argument is still flawed...


    It sounded like having problems was bad, but I don't think that having problems (if they are rapidly changing because you are solving the old ones and turning up new ones) is necessarily bad. And also this runs into the familiar conundrum "what does he mean by LQG?"
    Does he mean the static vintage 1990s version or the spinfoam approach that Rovelli was using last year, or the evolving versions that, say, Ashtekar, Thiemann, Bojowald are currently working on?

    In the latter three cases, the evolving versions seem to have been invented in 2006 or perhaps 2005. All three people (A, T, B) were at Kitp last month and what they talked about was, I guess you could call it, AQG and QC, algebraic quantum gravity and Ashtekar's latest quantum cosmology. Bojowald wrote recently that there is a convergence between how Thiemann is treating the full theory and how Ashtekar and Bojowald have independently found it useful to treat the specialization to cosmology.

    Maybe we can take the latest (vintage 2006) re-invention of Quantum Geometry to be "AQG" including both the full and the convergent application to cosmology. In that case, I'd like to know what are the serious problems with AQG.

    Probably it's inevitable that we continue to refer to all the non-string QG approaches as "Loop Quantum Gravity" because that's customary. It is important to keep in mind that we are talking about a mix of approaches that continues to re-invent itself, that addresses its old problems and outgrows its old limitations and develops new problems.

    In that spirit I'd be very interested to learn what anybody, especially John Baez but also others, thinks are the serious problems presented by the current mix of approaches called "Loop Quantum Gravity".
     
    Last edited: Feb 27, 2007
  5. Feb 27, 2007 #4
    This is misleading. The accurate statement is that despite years of trying, nothing has been accomplished that unambiguously constitutes meaningful progress on the central problem with these sorts of approaches. Further, since this is the central problem, obviously it should always be an active area of research. So when was the last serious attempt made to solve this problem? How many papers have been dedicated to this problem recently? I`ve heard that very little attention is being paid to it these days.
     
  6. Feb 27, 2007 #5

    marcus

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    Thanks for the clear statement. What you express here is a view which I think is mistaken. Perhaps as time permits i can mention some recent papers showing signs of meaningful progress on this problem, or others may.
     
    Last edited: Feb 27, 2007
  7. Feb 27, 2007 #6
    Hi Marcus,

    I think Baez meant that there are still important internal, technical problems to be dealt with in LQG, as well as the problem of how to falsify its various models (and interpretations -- as far as I could grasp, we will not be able to test DSR with GLAST if Bee is correct). So, in that overall sense, it would not be unreasonable to say that both fields (LQG and ST) have their serious problems. (But I hope Baez will elaborate on that, I could be wrong).

    But, yes, I'd add a note saying that LQG is progressing rapidly in the past few years and the contact with experiments seems more and more promissing (or not... again, it seems that one can interpret the models differently, *but* the field is changing rapidly). In that sense LQG seems more promissing, a very active field *now*. (The problems in the case of LQG are conceptually interesting and challenging and worthy of a serious investigation, in my opinion).

    ST, on the other hand, apparently has conceptual difficulties and dead-ends (like the landscape), which seems to indicate that the field is not as healthy. **I could be completely wrong here!** One thing that I am certain is that there are lots of interesting and useful mathematics to learn from ST, and who knows, some of it can end up as being useful one way or another for a consistent quantum gravity theory, yet to come. So I don't think ST should be discouraged at all, but other approaches should receive the same amount of attention and support. (Also, I think they should separate fields into "String mathematics" and "String physics" or whatever. Like there is mathematical topology and cosmological topology. Perhaps things would clean up a little).

    Christine
     
  8. Feb 27, 2007 #7

    jal

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    I agree!!
    Small step are happening regularly.
    I am seeing new papers regularly (thanks to Marcus).
    What I feel that is missing is a structured model that can handle the dynamics. (a Quantum Minimum Length Structure)
    Other people will have different ideas.
    jal
     
  9. Feb 27, 2007 #8

    marcus

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    Hi jal, I remember you from when we were discussing some of the same issues back in January. If I remember right, you referred to commentary in your PF blog. It was in this thread:
    https://www.physicsforums.com/showthread.php?p=1228523#post1228523
    which was motivated by Bojowald noting how his work, Thiemann's work, and Ashtekar's all seemed to be converging from independent directions on the same structures. I had just posted this:
    I think Kristina Giesel will also be giving a talk at the QGQG school in March-April, that Francesca told us was happening. There is listed a talk by a student of Thiemann.
     
    Last edited: Feb 27, 2007
  10. Feb 27, 2007 #9

    Kea

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    I'm sorry, but you guys sound a lot like the String bods who allegedly call String Theory The only Game in Town. All approaches to quantum gravity have serious conceptual problems.
     
  11. Feb 27, 2007 #10

    marcus

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    here is your chance, Kea. Explain to us about the conceptual problems of the latest incarnations of Loop :-)
    I am ASKING for people to try to identify and describe problems, in this thread.
    I certainly don't deny problems exist---that's what makes the game fun---and I didn't think Christine did either.

    What JAL mentioned about the step-by-step doesn't contradict that either. An example is
    1. LQC made good contact with semi/classical GR physics a long time ago as I guess we all know. But it was a simplified symmetry reduced model.
    2. So the game has been to gradually reduce the restrictions and work out the problems little by little.

    This is what Ashtekar and Bojowald and friends have been doing. there has been constant progress and they are now removing the homogeneity restriction.

    I never would deny there could be a fundamental problem with the approach. What I like is the constant change and regular progress.

    I think people who declare they know in advance that something is the RIGHT path suffer from hubris (a special kind of vanity). The proof of the pudding and time will tell :-)
    Likewise people who pretend to know in advance that someone else's program has a fatal conceptual flaw that only they can see and so they know ahead of time that it is the WRONG path.

    So what do you think are problems with the Quantum Cosmology that, say, Ashtekar is doing?
    If you can identify any problems that will be more stuff for LQG researchers to work on.
     
  12. Feb 27, 2007 #11

    Kea

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    Hah! I'm not going to spend any time at all working through a paper such as

    An Introduction to Loop Quantum Gravity Through Cosmology
    Abhay Ashtekar
    http://www.arxiv.org/abs/gr-qc/0702030

    because I see no reason to believe that I will find it particularly enlightening. Especially with phrases like 'Loop Quantum cosmology of FRW models' in the abstract. Once this theory is matched to experiment as well as existing alternatives, I might change my mind. Or if I see some conceptual clarity in their description of quantum geometry, then I might change my mind. Or if they derive the lepton masses from this framework, I might change my mind. So maybe I'm just stupid and I don't get it - but I don't believe so.
     
  13. Feb 27, 2007 #12

    marcus

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    OK, that's fine Kea. I will go over it. it is basically a pedagogical/overview paper so it could be useful to us.
     
  14. Feb 27, 2007 #13

    jal

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    Hi!
    I don't think that Baez is refering to people like me. Rather, I interpret, that he is saying, "Look at what there is on the other mountains".
    For instance CarlB is working on, (I think) a dynamic approach.
    Also, there are people working "Casual Set" which could give some answers.
    Together, .... the answer will show up.
    If I see it, I will have it in my blog.
    jal
     
  15. Feb 27, 2007 #14
    Right! :approve:

    I've just written a long post, and suddenly it went to nirwana, as Bee uses to say. Argh! :grumpy: Well, I'll not attempt to write it again. And perhaps it was for a good reason! :wink:

    BTW, perhaps I could use this opportunity to announce my new blog? :surprised I've been setting it up for a few couple of months. It's somewhat different from my previous one. And I will probably not have the time to post there regularly. You'll find there just random ideas. It's a quiet place, actually (an anti-blog???) :bugeye: And I like it that way. So don't hope to find long polemic debates!

    http://egregium.wordpress.com/

    The general subjects are: physics, mathematics and philosophy. I'll specially focus on some ideas relating quantum gravity and quantum computation, specially, quantum gravity as an inherently concurrent quantum system. The ideas are very preliminary and open for exploration... Note: some posts are not self-contained and some others are quite obscure. Details will hopefully come in small steps. The core of the main idea can be found in this post:

    Nature abhors deadlocks

    Thanks,
    Christine
     
    Last edited: Feb 27, 2007
  16. Feb 27, 2007 #15

    marcus

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    Yay!
    lovely looking blog
    I was just now reading your post about Gauss' Theorema Egregium
     
  17. Feb 27, 2007 #16

    Kea

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  18. Feb 28, 2007 #17
    Well, that's the way you see it... Or perhaps it's a sympathetic way to see it. :smile: But evidently I'm quite far off from calling myself a category theorist. I understand that cateory theory rebuilds mathematics from the concept of processes. I would like to see the idea of Nature as an inherently (quantum mechanically) concurrent system worked out in detail.

    I have a feeling this may be a missing ingredient in non-pertubative quantum gravity dynamics. Also, quantum gravity and quantum computation may have lots of common interconnections, specially in concurrent aspects of quantum information. I don't know whether I'll be able to work this out, not even the first steps. I'm trying to think further on this of course. But the idea is set for those who are interested to do this.

    I don't know whether this could be attempted from the cateory theory point of view. It would be interesting to see this idea further developed. It is often wise to work from different perspectives.

    But I don't want to further divert from the main thread, so let's get back to it! :biggrin:

    Thanks
    Christine
     
  19. Feb 28, 2007 #18

    marcus

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    Since we're on feelings I'll put in my feeling too, or my hunch (for what it's worth). My hunch is that the main caterpillar-tread tractor here is "applied" Quantum Geometry and that by slowly advancing it will SHOW us what the missing math ingredients are.

    What I mean by "applied" is Quantum Geometry applied to understanding the black hole singularity and the cosmological singularity. It is what Ashtekar has turned his attention to for the past three or four years (and not only he, others as well.)
    This is where QG makes a good solid contact with reality (it has the correct semiclassical limit, it recovers conventional cosmology) and where it has an important TASK to perform: replace the Gen Rel singularities with something else.

    So what I expect is that, like a tractor, it will keep plowing ahead and it will show us what math it needs.

    If it needs the Poincaré two-group (as I suppose Laurent Freidel thinks it might, since he is studying the reprepresentations) then the tractor will point this out to us. If it needs the deSitter group and Cartan geometry (as Derek Wise suggests it might), then it will by gradual advances point this out to us as well.

    Just now it has turned out that two "applied" people (Ashtekar and Bojowald) plus one more theoretical QG person (Thiemann) all discovered about the same time that they should use unembedded regular-grid states. it is a drastic change from embedded spin-nets----there is no manifold! The chances are, I suspect, that none of us would have predicted this. Not I anyway.

    Who would have predicted that David Gross would decide he wanted Bojowald to come to Kitp---that is, aside from Ashtekar, the world top "applied" QG person. It must mean that he sees the challenge of getting rid of all Gen Rel singularities as an important---a kind of seminal---program. So that is why I think of it as a tractor.

    and in a more general way, cosmology and high energy astrophysics as a tractor.

    Well that's just personal viewpoint. As Christine suggests, let's get back to saying what are the serious problems with Quantum Geometry.:biggrin:
     
    Last edited: Feb 28, 2007
  20. Feb 28, 2007 #19
    What is the geometry of time?

    My impression from the end of the concluding seminar at the singularities miniprogram at KITP UCSB in January 2007 conducted by Gary Horowitz was that the key issue is the Problem of Time. He seemed to think that a new view of time is essential to any real progress.

    Why does time seem to flow in only one direction? (The Arrow of Time, Roger Highfield, 1992, and, from Wikipedia:
    Halliwell, J.J. et.al. (1994). Physical Origins of Time Asymmetry. Cambridge. ISBN 0-521-56837-4. (technical).
    Boltzmann, Ludwig (1964). Lectures On Gas Theory. University Of California Press. Translated from the original German by Stephen G. Brush. Originally published 1896/1898.
    Peierls, R (1979). Surprises in Theoretical Physics. Princeton. Section 3.8.
    Feynman, Richard (1965). The Character of Physical Law. BBC Publications. Chapter 5.
    Penrose, Roger (1989). The Emperor's New Mind. Oxford University Press. ISBN 0-19-851973-7. Chapter 7.
    Penrose, Roger (2004). The Road to Reality. Jonathan Cape. ISBN 0-224-04447-8. Chapter 27.
    Price, Huw (1996). Time's Arrow and Archimedes' Point. ISBN 0-19-510095-6. Website
    Wehrli, Hans (2006). Metaphysik - Chiralität als Grundprinzip der Physik. ISBN 3-033-00791-0.
    Zeh, H. D (2001). The Physical Basis of The Direction of Time. ISBN 3-540-42081-9.
    )

    Nothing really new except for Wehrli, 2006, evidently not available in English translation.

    I'll go look at ArXiv for recent research.


    3 for time AND (quantum geometry) at
    http://arxiv.org/find/hep-th,grp_math/1/abs:+AND+time+EXACT+quantum_geometry/0/1/0/past/0/1

    here they are.

    1. gr-qc/0607130 [abs, ps, pdf, other] :
    Title: Quantum Geometry and its Implications for Black Holes
    Authors: Martin Bojowald
    Comments: 16 pages, Plenary talk at ``Einstein's Legacy in the New Millenium,'' Puri, India, December 2005
    Journal-ref: Int.J.Mod.Phys. D15 (2006) 1545-1559

    Abstract:
    “General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essential close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another.




    2. hep-th/0604120 [abs, ps, pdf, other] :
    Title: Towards Gravity from the Quantum
    Authors: Fotini Markopoulou
    Comments: Expanded version of the contribution to "Towards Quantum Gravity", edited by D.Oriti, to be published by C.U.P.

    Abstract:

    "We review quantum causal histories starting with their interpretations as a quantum field theory on a causal set and a quantum geometry. We discuss the difficulties that background independent theories based on quantum geometry encounter in deriving general relativity as the low energy limit. We then suggest that general relativity should be viewed as a strictly effective theory coming from a fundamental theory with no geometric degrees of freedom. The basic idea is that an effective theory is characterized by effective coherent degrees of freedom and their interactions. Having formulated the pre-geometric background independent theory as a quantum information theoretic processor, we are able to use the method of noiseless subsystems to extract such coherent (protected) excitations. We follow the consequences, in particular, the implications of effective locality and time. "


    3. gr-qc/0604013 [abs, ps, pdf, other] :
    Title: Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
    Authors: Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh
    Comments: Revised version to appear in Physical Review D. References added and typos corrected
    Journal-ref: Phys.Rev. D73 (2006) 124038

    Abstract:

    "Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors and significantly extend the known results on the resolution of the big bang singularity. Specifically, the following results are established for the homogeneous isotropic model with a massless scalar field: i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac observables and semi-classical states are constructed rigorously; iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the non-perturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime. Our constructions also provide a conceptual framework and technical tools which can be used in more general models. In this sense, they provide foundations for analyzing physical issues associated with the Planck regime of loop quantum cosmology as a whole. "

    Hope this is helpful to the discussion.

    R
     
    Last edited: Feb 28, 2007
  21. Feb 28, 2007 #20

    jal

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