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Time in LQG

  1. May 20, 2004 #1
    I am a student just beginning a study of LQG and I would appreciate some comment on a few questions and intuitions that I have as I enter the subject.

    My background is more in mathematics than in physics, and my perspective on space has been guided more by topology than by the concerns of HEP, and perhaps this bias affects how I view the discussions here concerning string theory and LQG. But here goes...

    My first issue deals with time. My tendency is to view the universe as a single space, which appears 4-dimensional, and I think of time primarily as an aspect of our perspective on the manifold. That is, I feel very uncomfortable accepting probability as an intrinsic aspect of the space and prefer to think of it in terms of information. GR seems compatible with this perspective. Does LQG invariably treat space as a 3-dimensional set of nodes whose connections vary with time in lock step? Is the choice of a 3-D slice an arbitrary convention or do we have to bring back the idea that the universe actually has well defined instants?

    I come to this discussion with the idea that quantizing space by discrete nodes is one thing, and saying that different possible states all exist at the 'same time' is another. Am I wrong to seperate the issues?

    Also, I am somewhat familiar with the process of triangulation of a topological space to represent it with a polyhedron. In this process every node in the sapce will have the same number of vertices stemming from it, and the number is fininte for finite dimensional polyhedra. Is this is in any way related to LQG? Do the nodes in LQG have a given number of vertices, or perhaps every node is connected to every other node?

    Finally, one of the things I find fascinating about GR is the possbility of a gravitational geon, that is, a particle that is nothing but curved space attracting itself. Does LQG limit us to saying that particles are actors playing out in the stage of space, or does it allow for the concept that particles and space are actually two manifestations of the same stuff?

  2. jcsd
  3. May 21, 2004 #2
    The biggest revelation for me is Time, and if this is married to the understanding of dimension, as differences in the strength of the gravity field, then how would you choose what model to build with such constructives, that are mathematically suitable?

    Some time ago this link in superstringtheory forum was written, as I looked into the subject of geons and the Wheeler reference.

    Geons, Blackholes & Quantum Foam, by John Archibald Wheeler, with Kenneth Ford, page 236, para 2.

    "This hypothetical entity, a gravitating body made up entirely of electromagnetic fields. I call geon(g for the gravity, e for electromagnetism," and on as the word root for"particle"). There is no evidence for geons in nature and later was able to show that they are unstable-they would quickly self-destruct if they were ever to form. Nevertheless it is tempting to think that nature has a way of exercising all the possibilties open to it. Perhaps geons had a transitory exitance early in history of the universe. Perhaps(as some students and I speculate much more recently), they provide an intermediate stage in the creation of the blackholes."

    Posted by sol on May 03, 2003 at 19:21:41:

    Osher ,

    Wheeler had much to contribute to the understanding of the blackhole. His Geon was a interesting prelude to what a string might have been? A string curves,and his geon contained similar ideas?

    His thinking was on the right track I surmized, from the implication of what he tried to imply(his understanding of the need to identify gravity) as the graviton({a comparison I see now}?) might well have been the geon.


    Without going into the issues of the Monte Carlo Effect, there is artistic impresssionism that sort of captures mind on surface, building gravitational constructs, to help explain the world of curvature, or in the case of the Monte Carlo effect, such triangulations.

    Linking the energy plot in this demonstration, one wonders how perception might have expressed itself once it was caught in such constructive attempts around the issue of gravity. This had to be born out of mind?:)

    This gives some some consideration in moving towards this pursuate whether it be string/brane or LQG or Wheelers Geon :smile:

    Might I also say, that given the opportunity now, that we also find this Introduction to Geometrodynamics as another expression of this understanding of gravity field explained.

    By the inference of uniting gravity and electromagnetism by Kaluza and Klein, there is this visionist capability called into view ofa very dynamical universe in hyperspace.
    Last edited: May 21, 2004
  4. May 21, 2004 #3


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    Although General relativity presents spacetime as a four dimensional (pseudo-)manifold, as you say, working with the dynamics people often "foliate" the four dimensions to get a local 3-space X time representation. Then they can define boundary conditions on spacelike 3-surfaces and solve the field equations (or numericallly approximate them where solution is impossible). In this context you might want to look at This paper by Arnowitt, Deser, and Milnor (ADM) describing their classic method of doing this. This is a reprint of a chapter they published in an out-of-print book, posted on the arxiv because it is a historic document.

    Now LQG as it has developed up to now, has limited itself, in the 4-dimensional Lorenzian case, to a spacelike submanifold to spacetime. The time direction is represented by a normal vector to the submanifold. I think that this is going to change as a result of the new Ambjorn, Jurkiewicz, and Loll paper, http://arxiv.org/abs/hep-th/0404156. These authors find a way to develop time and causality in their network of simplices and I think the New Variables crowd will soon find ways to exploit this advance.
  5. May 21, 2004 #4
    Thanks Self adjoint for keeping to the current realizations and thanks to Marcus as well. My post was a "generalization," in the attempts of a human nature, that I am trying to understand, and this seemed a most appropriate format because of the issues of Time in these topics, as you have shown.

    Thanks, for being the anchor of reality :smile:
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