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Matter as twists in geometry (propagation and interaction of chiral states in QG)

  1. Oct 9, 2007 #1

    marcus

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    http://arxiv.org/abs/0710.1548
    Propagation and interaction of chiral states in quantum gravity
    Lee Smolin, Yidun Wan
    34 pages, 30 figures
    (Submitted on 5 Oct 2007)

    "We study the stability, propagation and interactions of braid states in models of quantum gravity in which the states are four-valent spin networks embedded in a topological three manifold and the evolution moves are given by the dual Pachner moves. There are results for both the framed and unframed case. We study simple braids made up of two nodes which share three edges, which are possibly braided and twisted. We find three classes of such braids, those which both interact and propagate, those that only propagate, and the majority that do neither."


    http://arxiv.org/abs/0710.1312
    On Braid Excitations in Quantum Gravity
    Yidun Wan
    24 pages, 16 figures, 5 tables
    (Submitted on 5 Oct 2007)

    "We propose a new notation for the states in some models of quantum gravity, namely 4-valent spin networks embedded in a topological three manifold. With the help of this notation, equivalence moves, namely translations and rotations, can be defined, which relate the projections of diffeomorphic embeddings of a spin network. Certain types of topological structures, viz 3-strand braids as local excitations of embedded spin networks, are defined and classified by means of the equivalence moves. This paper formulates a mathematical approach to the further research of particle-like excitations in quantum gravity."
     
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  3. Oct 9, 2007 #2

    marcus

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    Sample quote from introduction:
    There is an old dream that matter is topological excitations of the geometry of spacetime. Recently it was discovered that this is realized in the context of models of quantum geometry based on spin networks, such as those used in loop quantum gravity and spin foam models[1, 2, 3]. Although the rough idea that topological features of spacetime qeometry might be interpreted as particles is very old, two questions delayed implementation of the idea till recently. First, how do we identify an independent excitation or degree of freedom in a background independent quantum theory, where the semiclassical approximation is expected to be unreliable? Second, why should such excitations be chiral, as any excitations that give rise to the low mass observed fermions must be?

    The approach here is very new (started 2005, only the preliminary work has been done so far) and remarkable for its simplicity.

    a four-valent graph represents a quantum state of GEOMETRY (four-valent just means that exactly four edges meet at every node in the graph)

    and certain tangles in the graph are found to behave like particles of MATTER---namely tangles can move around thru the graph as it evolves by simple re-connection moves called Pachner moves.

    and the same simple set of moves by which the graph evolves also allows two tangles to meet up and interact, so that a different tangle or tangles might result

    the tangles are of a simple kind called braids, or braid states---a carefully limited vocabulary of twists.
    ================

    Here is a way of describing a 100-year-old dream: in some sense, SPACE itself is nothing else than its geometry----space is essentially nothing but spatial relationships---and the gravitational field is nothing but geometry and GR is about the dynamics of how this geometry evolves. So the dream is that you could have one simple geometric way to describe both space and matter---------matter as simply the KINKS in the geometry that is space.
    ================

    It seens interesting to me that Wan and Smolin restrict to FOUR-VALENT graphs, because that has some kinship with Renate Loll and others SIMPLICIAL gravity. A 3-manifold which is triangulated with tetrahedra is dual to a 4-valent graph.

    ==quote TOC==
    1 Introduction 3

    2 Previous results 5
    2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
    2.2 Representation of twists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
    2.3 Framed and unframed graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
    2.4 Braids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
    2.5 Crossings and chirality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
    2.6 Equivalence moves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
    2.7 Classification of Braids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    3 Dynamics and evolution moves 10
    3.1 The 2 --> 3 move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
    3.2 The 3 --> 2 move. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
    3.3 The 1 --> 4 move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
    3.4 The 4 --> 1 move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
    3.5 The unframed case and the role of internal twist . . . . . . . . . . . . . . . . 16
    3.6 A conserved quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    4 Stability of braids under the evolution moves 17

    5 Braid Propagation 17
    5.1 Examples of chiral propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 20
    5.2 Which braids can propagate? . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    6 Interactions 22
    6.1 Examples of interacting braids . . . . . . . . . . . . . . . . . . . . . . . . . . 27
    6.2 General results on interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    7 Conclusions 31
    ==endquote==
     
    Last edited: Oct 9, 2007
  4. Oct 9, 2007 #3

    jal

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    How to build a universe

    In order to try to understand where Lee Smolin, Yidun Wan is coming from I went back to one of their citation.
    http://arxiv.org/abs/gr-qc/0510052
    Geometry from quantum particles
    Authors: David W. Kribs, Fotini Markopoulou
    (Submitted on 11 Oct 2005)

    p. 3
    A secondary goal of this paper is to address the low energy problem in background independent approaches to quantum gravity, namely the problem of extracting a semiclassical low energy geometry from a dynamical microscopic quantum geometry. That is, our results may also be useful to quantum theories of gravity with microscopic quantum geometry: the definition of a coherent degree of freedom we use can be applied, for example, to spin foams with a boundary to extract its effective particles (and, in fact, that is why it was originally considered in [8]). Our setup thus provides a new way to get to the much sought-after semiclassical limit. In future work, we hope to give an algorithmic construction of the class of microscopic dynamics that contains Poincar´e-invariant particles.
    p. 5
    The aim will be to find global symmetries of a classical geometry at the level of particles, without starting with a quantum geometry.
    p. 8-9
    A microscopic model of spacetime is successful if it has a good low-energy limit in which it reproduces the known theories, namely general relativity with quantum matter coupled to it. In the case of causal dynamical triangulations, impressive results show strong indications that this model has the desired features [5].
    … one can first look for long-range propagating degrees of freedom (particles) and reconstruct the geometry from these (if they exist). The specific method we adopt is promising because it deals directly with quantum systems and coarsegrains a quantum system to its effective particles. Our discussion applies to such models with a boundary.
    p. 13
    Finally, it is very important that the existence and properties of the noiseless subsystems depends entirely on the properties of the dynamics. As can be seen in the quantum information literature [26, 27, 28, 29, 30, 31, 32, 23, 24, 25] and in the application of this method to quantum black holes [33], as well as the example in the Appendix, in concrete examples of noiseless subsystems their existence depends on having symmetries in the dynamics.
    --------------
    I hope that this was helpfull.
    jal
     
  5. Oct 10, 2007 #4

    marcus

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    I was reading this "Propagation and Interaction" paper today.
    It is pretty clear to me now that it is an important paper.
    I wonder whether we will discuss it here at PF now, or only later when more people recognize what is happening.
     
  6. Oct 10, 2007 #5

    marcus

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    maybe I will ask a question of lqg who sometimes comes around to PF

    At the bottom of page 32 of this paper, it says

    "It is very interesting to note that the braids required in the three-valent case to realize
    Bilson-Thompson’s preon mode[4] also are classified by three integers representing twists
    on an unbraid[8]. This suggests that it may be possible to incorporate a preon model with
    interactions within the dynamics of four-valent braids studied here.
    "

    How might that work out? How might the Sundance preon model fit into this 4-valent picture?
     
    Last edited: Oct 10, 2007
  7. Oct 10, 2007 #6

    jal

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    I'd like to know more too.
    Here is what I found...
    http://en.wikipedia.org/wiki/Preon
    The Sundance Approach
    Sundance preon model may avoid this by denying that preons are pointlike particles confined in a box less than 10−18 m, and instead positing that preons are extended 2-dimensional ribbon-like structures, not necessarily smaller than the elementary particles they compose, not necessarily confined in a small box as point particles preon models propose, and not necessarily "particle-like", but more like glitches and topological folds of spacetime that exist in three-fold bound states that interact as though they were point particles when braided in groups of three as a bound state with other particle properties such as mass and pointlike interaction arising as an emergent property so that their momentum uncertainty would be on the same order as the elementary particles themselves.
    http://arxiv.org/find/hep-th/1/au:+Bilson_Thompson_S/0/1/0/all/0/1
    Sundance O. Bilson-Thompson two papers
    arXiv:hep-th/0603022 [ps, pdf]
    Title: Quantum gravity and the standard model
    arXiv:hep-ph/0503213 [ps, pdf, other]
    Title: A topological model of composite preons
    -------
    jal
     
  8. Oct 11, 2007 #7

    lqg

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    Hey Marcus,

    Thanks for openning a thread on our work! My answer to your question is as follows.

    In the 3-valent case, all the braids, as sub-structures of embedded spinets, are not truely nontrivial braids, rather, they are the so-called cap braids, which are equivalent to unbraids, because they can always be undone by trading the crossings for twists by means of a method introduced by Louis Kauffman. Therefore, any braid in the 3-valent case is an unbraid with certain twists on its three strands, the twists are now called Louis numbers. I am not able to say more in words without drawing anything. All the details will be seen in the forthcoming paper by Sundance, Jonathan, and Louis, in which preons might be interpreted as these unbraids labeled by louis numbers.

    In the 4-valent case, it seems that all the braids that can interact actively are those equivalent to unbraids with twists on its three strands. Note that the mechanism of undoing the braids in this case is different from that in the 3-valent case and that most braids in the 4-valent case cannot be undone.

    Therefore, there looks like to be a similarity between the braids in the 3-valent case and the actively interacting braids in the 4-valent case.


     
  9. Oct 11, 2007 #8

    marcus

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    Thanks lqg!
    That gives me a good general picture of what to expect. I am looking forward to seeing your and Smolin's next paper and also the one in preparation by B-T, H, and K.
    I like the term "Louis numbers"----using the first name is nice.

    there is something I am not getting that worries me.

    You talk about a twist of pi/3 which is radians for 60 degrees----one sixth of a full turn.
    I can't picture the effect of this on a node.
    It does not seem like enough of a rotation to make any important difference.

    I realize that you can't draw pictures here at PF, and this is a serious limitation. So perhaps you could suggest a link to somewhere there is a fuller explanation.
    Would it be the video of your Perimeter talk?
    Or Lee Smolin's ILQGS talk slides?
    Or the slides from a Loops '05 presentation?
     
  10. Oct 13, 2007 #9

    marcus

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    Fortunately I found some clarification in Lqg's paper!

    http://arxiv.org/abs/0710.1312
    On Braid Excitations in Quantum Gravity
    Yidun Wan
    24 pages, 16 figures, 5 tables
    (Submitted on 5 Oct 2007)

    This paper can be seen as the first in a series by Wan and Smolin. So it can be helpful to read "On Braid Excitations..." (or at least look at parts of it) before trying "Propagation and Interaction..."

    To grossly oversimplify, here's where it looks to me the approach is at present. Basically we are waiting for a paper by
    Sundance Bilson-Thompson, Jonathan Hackett, and Louis Kauffman
    which will introduce some quantum numbers called "Louis numbers"
    which describe matter---they subsume or capture the gist of Sundance preon model.
    This paper (what to call it? the Sundance-Jonathan-Louis paper?) will show how the Louis numbers are represented in the context of FOUR-VALENT ball and tube diagrams.
    So then we will have matter in the context of four-valent ball-and-tube.

    The work that Wan and Smolin have been posting does not say how to represent the standard basket of particles in the context of these diagrams. I think what it does is work out the MECHANICAL DETAILS of how certain braids can propagate thru the diagrams and interact with each other. And it CLASSIFIES braids into certain types that determine how they propagate and interact.

    So they are working out a model which seems like a perfectly good model of how geometry and matter could be--IF it turns out to have the right basket of particles.
    And we won't know if it has the right particles in it until we hear from Sun-Jon-Louis.
     
  11. Oct 13, 2007 #10
    keep us posted
     
  12. Oct 13, 2007 #11

    marcus

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    thanks for the encouragement, I will

    ===================
    EDIT TO REPLY TO NEXT POST by Jim Kata.

    Yes! That is a wonderful talk. I watched it back in November 2005 and have re-watched it several times since,
    including the first 2/3 of it just this morning. I find it as or more exciting and illuminating
    now than at first. Strongly recommended!

    Gives an idea of what matter really could be made of.
     
    Last edited: Oct 14, 2007
  13. Oct 14, 2007 #12
  14. Oct 15, 2007 #13

    lqg

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    You are welcome! As you've read the paper which explains the pi/3, there is no more I can say. But to visualize that you may imagine to represent a piece of cylindrical surface by three elastic lines, two but never all of which can be in the same plane, and then look at the projections of them. Hope this helps.

    Thank you!

     
  15. Oct 31, 2007 #14

    marcus

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    Here's a related Jonathan Hackett paper that I didn't pick up on at first.

    Locality and translations in braided ribbon networks
    Jonathan Hackett
    Provisionally scheduled for November 2007 in CQG (Classical and Quantum Gravity)
    http://www.iop.org/EJ/journal/CQG

    The preprint appeared February 2007
    http://arxiv.org/abs/hep-th/0702198

    The arxiv preprint page does not indicate this, but it
    evidently has passed peer-review and been accepted for publication.
    =========================
    The theorists themselves often use the term "braided ribbon network"
    I may have to give up calling it "ball and tube". But that is how I've been thinking of these structures. the balls each have four holes----so four tubes connect to each of them. And the tubes can twist, on the way from one ball to the next.
    Maybe that's an inadequate picture.
    Anyway the conjecture seems to be that there is something that underlies both geometry and matter, and that the quantum states of the thing behave like these (ballandtube or braidedribbon) structures.
    =========================

    the paper I am waiting to see is by Sundance BT, Jonathan H, Louis K-------if the paper succeeds it will put Sundance matter model into the 4-valent (call it something) network.

    If it succeeds, then (someone who knows better please correct me) we automatically get two LHC-testable predictions.

    Prediction 1: no evidence of extra dimension will be seen by LHC

    because in higher dimension the braids would unravel----knotting topology depends on spatial 3D

    Prediction 2: no evidence of SUSY will be seen by LHC

    because it is a bîtch just to get Sundance non-SUSY bunch of particles to incorporate into these 4-valent nets.
    Very hard simply to get the standard bag of particles to materialize as topology complications in the state of geometry---as twists in the geometry. No way could they add on a supersymmetry layer. They'd have to let the approach go.

    that's just my humble kibbitzer opinion of course. I think that ball-and-tube is perilously falsifiable from just the LHC machine---making clear predictions. what other theory can you think of that is predictive in such a straightforward clear way?

    Just for contrast, I gather that string theorists do not predict SUSY or extraD will be seen at LHC energy
    and they do not predict that SUSY or extraD will NOT be seen at LHC energy
    they take no risk and they predict NIX-NUTTIN-ZILCH at LHC. No theory is betting its life on some definite LHC outcome. If that is not true, please tell me about it.

    thing about this ball and tube stuff is IT DIES IF YOU SEE A CERTAIN KIND OF LHC RESULT which prior accepted theory does not rule out as impossible. So there is some kind of possible LHC result which it dispredicts.

    I think that means it's science.
     
    Last edited: Oct 31, 2007
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