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Long-awaited braid-matter paper (Bilson-Thompson, Hackett, Kauffman, Smolin)

  1. Apr 1, 2008 #1


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    Particle Identifications from Symmetries of Braided Ribbon Network Invariants
    Sundance Bilson-Thompson, Jonathan Hackett, Lou Kauffman, Lee Smolin
    9 pages, 7 figures
    (Submitted on 1 Apr 2008)

    "We develop the idea that the particles of the standard model may arise from excitations of quantum geometry. A previously proposed topological model of preons is developed so that it incorporates an unbounded number of generations. A condition is also found on quantum gravity dynamics necessary for the interactions of the standard model to emerge."

    Here is a quote from the Conclusions, section 5 on page 8:

    We have presented an embedding of the fermion and weak vector boson states of the standard model in a class of loop quantum gravity models. These are models in which the states are based on embeddings of framed trivalent spin networks, with possibly arbitrary labellings, whose dynamics is given by the standard dual Pachner trivalent moves, plus additional moves consistent with the conservation of the topological invariants (a; b; c).

    There are a number of interrelated questions that remain open before the promise of this development can be fully understood...
  2. jcsd
  3. Apr 1, 2008 #2


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    So in a sense LQG contains the Standard Model particles as crisscross complications in the network that describes the quantum state of geometry.

    There has been some progress: braid-matter contains all three observed generations of particles. Indeed, the LQG particle model actually predicts an infinite series of generations (by increasingly complicated twisting and braiding.) Thus it would be favorable to LQG if the Large Hadron Collider were to detect evidence that the number of generations is not limited to three.

    the basic idea is that (the quantum state of) space is like a WEB----a fine network of geometric relationships. And in the fabric of that web there can be little snaggies. And these little snaggly tanglets can propagate and interact with each other and make other snaggles. The way two knots can interweave with each other and make a third knot.

    The whole web evolves by local MOVES which reconnect neighbor nodes in different ways. The passage of time is realized by the constant progress of these local moves going on everywhere in the network.

    These local reconnection-moves take care of the motion and interaction of particles, as well as the evolution of geometry as required by General Relativity.

    That's the idea. It is an ongoing program. You can read the paper and see how far they have come and what the next issues are that they want to investigate.
    Last edited: Apr 1, 2008
  4. Apr 1, 2008 #3


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    Are these the first signs of unification of String Theory and LQG? Recently, a fashion started as a kind of tri-algebra was invented and was used to compute finaly compute a lagrangian for one of the kind of the multiple branes, M2, that shows up in 11 dimensions, and it is the fundamental example of a hint for M-Theory. It is a fashion because, besides this, it gives a kind of 2+1 gravity, and because of some dualities, related to 3+1 gravity, but I am not sure.

    Any way, this issue is explained here, in Jacques Distler's blog: http://golem.ph.utexas.edu/~distler/blog/archives/001642.html#more

    Compare the equation (4)-(6) in the above blog post with the equations (8)-(10) of this new Smolin article. I didn't cosistently check yet, but they seem to be essentialy equivalent.

    So, what I ask is:

    If you find a lagrangian for this Loop model, will it be dual to that string model?

    It is kind of interesting that Smolin came with that conjecture and this article in about the same time these M Theory articles surfaced.
  5. Apr 1, 2008 #4


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    You may be able to see more in this than I can. I don't know the string things you are relating it to.
    So I can't help answer, maybe someone else can. For me this paper continues the development of an interesting idea for including matter in LQG. But it doesn't nail anything down. Things are still up in the air, for me, and quite uncertain.
    They say however, that they have a followup paper in preparation. See reference [9].
  6. Apr 2, 2008 #5
    Dear Marcus,

    how does preon braiding compare with Conne's NCG as a way to get SM into LQG

    also, should LQG still be called LQG, if it can incorporate SM either through NCG or preon braiding. perhaps loop theory is sufficient.

    Both Ashketar and Ginstrup talk about SM in LQG through NC. If this union is successful, will there be a need for LQG-preon?
    Last edited: Apr 2, 2008
  7. Apr 2, 2008 #6
    I'm particularly interested in how they'll incorporate the other SM gauge groups (SU(3)XU(1)). I have to think there's some connection with Witten's '89 paper linking representations of gauge groups with link invariants.
  8. Apr 2, 2008 #7


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    to repeat a familir point, several different approaches to unifying Quantum Gravity with the Standard Model need to be developed.

    my impression is 90 percent of good ideas in science fail. I mean 90 percent of promising ideas. I see no redundancy between Ashtekar or Aastrup and Grimstrup on one hand thinking about different ways of joining Connes NCG with LQG, and on the other hand the Perimeter group trying this braid-matter approach. There might even be a deep connection.

    Saltlick, I don't know enough to conjecture how SU(3)xU(1) symmetry might emerge. Any ideas you might have about this, or anything more you can say, would be welcome. I am assuming you have read the paper and noticed the reference on page 8, the Conclusions section, to the idea that this symmetry might emerge from this setup with dynamics determined by local reconnection moves. This is left as an open problem. Maybe we will hear more about it in their next paper---the reference [9] they say is in preparation.
    Last edited: Apr 2, 2008
  9. Apr 2, 2008 #8
    Very interesting, I will try to read this in more detail later. I did want to ask a question: In some earlier descriptions of what I believe was the braid matter program, the analogy was made that particles in lqg are like "tiny wormholes". I see no attempt to make this analogy in this paper. What was that "tiny wormholes" thing about? Am I confusing braid matter with a different research program here?

    I am actually kind of excited about this paper because LQG spin network evolution has for a long time reminded me of "cellular automata". Cellular automata are a CS concept in which you have a series of interlinked cells, and the cells change their state over time according to some simple predefined rule. The interactions that arise from the state changes under this simple rule can be extremely complex, so much so that you can build little machines or even complete models of computation out of patterns of cells within the cellular automata. The LQG spin networks, with their simple evolution rules, seemed to me a lot like CAs with the difference that instead of the rules modifying states on a fixed lattice of cells, the cells are connected in a graph and it is the graph structure which the rules modify. Something I had been wondering is whether it was possible to "build little machines" out of graph configurations in LQG spin networks [or something like them], the same way one builds things out of cell-state configurations in CAs. And it kind of looks like the authors of this paper, with their braided ribbon networks, have done something very much like that!

    (Although I may not understand exactly what they're doing here-- they seem to provide a scheme for creating braid configurations that act like particles, but don't seem to specify the rules that determine the behavior of those braids? It is not clear to me whether you're supposed to apply the graph evolution rules from previous LQG work, whether [as their "There are no labels and no explicit evolution amplitudes in this paper" comment at the end of the introduction may indicate] they are withholding decision on evolution rules until a future paper, or whether I'm missing the point altogether.)

    I am a little worried about this part:

    Uh oh! Well I guess two months before the LHC turns the beam on is a good time to be making unusual predictions of new particles, but aren't there already strong constraints on the existence of n>3 generations?!
  10. Apr 2, 2008 #9


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    That is interesting. If n>3 generations can already be ruled out, then braid-matter is automatically shot down. I would like to hear more about that!
  11. Apr 2, 2008 #10


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    Marcus, I think he refers to the experimental constrain on light neutrinos. Any other generation would have a massive neutrino with a mass higher than 45 GeV.
  12. Apr 2, 2008 #11


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    I hope my question is not completely naive. Can this be shown to be impossible? Is a neutrino with that high mass too absurd to contemplate? In what sense can one exclude the possibility of n>3 generations?
  13. Apr 3, 2008 #12

    I have a feeling that LQG spin network evolution could be modelled using concurrency theory, like e.g., directed topology (topology with a further structure: local partial order). Actually, my feeling goes a little further on that issue in the sense that quantum mechanics could be recasted into some concurrency theory, entanglement being a nice example, if you see the state space as a huge concurrent system. Nature would be fundamentally concurrent. I've written a bit about these ideas in older posts of my blog, but I really never developed these ideas formally, nor intend to. I'm going into other directions.
  14. Apr 3, 2008 #13


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    The problem I personally have with an ordinary "cellular automata" picture in physics is that I can't see the physical basis for any predefined universal rules. I think the rules must be encoded or supported somewhere - or emergent (somehow). That would be pleasing. So that at the "creation of the universe" whatever that means, the laws were reconstructed. How do you picture that the laws are predefined? Predefined where? What kind of observers where around?

    Maybe you have some thinking that I haven't thought of... I'm curious to learn if there are other views on this.

    Because any given observer, must collect information about the cellular structure and the evolutionary rules - suggesting to me that the evolutionary rules itself is evolving, from the point where the rule is indistinguishable from random fluctuations.

    I think the "state-space" and the "rule-space" should be seen as one entity, where the apparent separation is indeterministically emergent and observer dependent.

    I was hoping to see something like that in the loop thinking when I started reading rovelli's book but it wasn't obvious, so I temporarily put it aside and will read up on some others. I thought a basic combinatorical approach would provide a way for unification, by means of permutation symmetries. And then the complexity of the network should but an upper bound on the size of the rule-space, and that particles would be self-stabilised communicating system of substructures. And by increasing the complety one might find probably stability optima corresponding to various particles. This is far ahead of my own progress though but I was hoping that rovelli's book would answer to my prays. But I'm not sure yet. I will get back to rovellis book later.

  15. Apr 3, 2008 #14

    you can just look at existing pdg limits :
    m_nu < 2 eV
    If there is a neutral heavy leptons
    m > 90.3 GeV if Dirac
    m > 80.5 GeV if Majorana
    So if there is a standard 4th generation neutrino, there is a big mass gap between 3rd and 4th generation.

    Then, that could be sterile neutrinos but then it is no more standard 4th generation...
  16. Apr 3, 2008 #15


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    n>3 generations is strongly disfavored, both theoretically and experimentally (and is aesthetically ugly). It spoils grand unification, clashes with all sorts of astrophysics bounds, is constrained by precision EW measurements and so on and so on.
  17. Apr 3, 2008 #16
    Haelfix---I agree with you on most of your points, however a technical detail. Four generations does NOT spoil unification. The general assumption is that generations come in GUT multiplets. You can work out the contributions to the beta function coefficients and see that the new generation contributes equally to all of the beta functions, given that you normalize hypercharge in the normal way.

    I do agree that four generations is ugly, though. And the new neutrino would have to be cleverly hidden.
  18. Apr 3, 2008 #17
    If the Euler characteristic of the compact manifold is >3, then this is possible.
  19. Apr 3, 2008 #18
    Marcus -

    I did read the paper, and have just gone back to read the two earlier papers they reference to make sure I'm not missing something obvious. My initial reaction was, and still is, that while I really like the direction they're taking, the specific choices they're making for topogical invariants seem fairly arbitrary. I don't pretend to have anywhere near the same grasp of the LCQ subject matter and history as Smolin et al, but I've been wondering for a while whether investigations might move in this direction. My impetus has been the following:

    1. Fundamental particles (as we understand them today) seem to come in groups, and these groups obey certain symmetries and respond to similar forces. We've recognized that these symmetries correspond to certain mathematical symmetry groups - SU(3)xSU(S)xU(1), also known as gauge groups. Individual particles in the SM can be associated to specific representations of these groups.

    2. Witten showed in '89 that using Chern-Simons theory you could identify a link invariant for every representation of a gauge group.

    3. LCQ and related theories consider spacetime to emerge in some way from linked graphs.

    4. People are now theorizing about "fundamental" particles as being formed from braids and links from these graphs, and invariant quantities for these braids and links represent quantum numbers that distinguish one particle from another.

    It would seem to me that there could be another direction to approach this topic. The approach shown in the paper seems to me to start with a relatively arbitrary choice of braid type and topological invariant, and then show that this matchs the SM with certain assumptions. I'm in no way criticizing their approach here, but I think an alternative approach would be to start with the symmetry groups we already know exist in nature, to deduce the link invariants that correspond to each of the representations of these groups, and to see what kind of braids, and braiding rules, these might imply.

    I have no idea whether this approach would be practical - I imagine it could get very complicated very quickly - but it would have an immediate connection with existing mathematical physics. Perhaps this has already been tried and found to be impractical or illogical, but the concept is intriguing to me.
  20. Apr 3, 2008 #19
    How is this different from string model building?
  21. Apr 3, 2008 #20
    So, I know nothing about this except what I've heard from other people, but my understanding is

    1) It is possible, but
    2) It would be very problematic.

    The thing is that the existence of the extra generations would interfere with all kinds of other processes in strange and not-immediately-obvious ways. Unless the fourth generation is contrived in certain ways (really heavy, I guess?) one would expect it to have impact on various lower-energy processes that we see normally. We don't see these impacts. I can't remember exact examples of such problems a fourth gen creates but a couple have been mentioned by other people in the thread.

    As coincidence would have it (I ran across this digging up a dorigo url for another thread) Dorigo Tomasso actually wrote a post last week (before the braid matter paper hit arxiv) about this. He gives some vague and technical arguments about why a fourth generation is considered unlikely, then goes on to talk about CDF's ongoing searches for a fourth generation. If I'm reading this right the weight of the lightest 4th gen quark, if it exists, must be at least 284 GeV. (Also apparently the search saw a bump at 400 GeV but it's basically smaller than the margin of error.)

    Interestingly he does say a couple of unusual things in the comments which make it sound like he thinks infinite generations (as smolin&co predict) are more plausible than just four if only on aesthetic grounds...

    I made a post asking if he had any opinion about the braid matter people's prediction, but it seems to have been eaten by his spam filter...
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