C, P, and T of Braid Excitations in Quantum Gravity (Song He, Yidun Wan)

  1. marcus

    marcus 24,730
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    http://arxiv.org/abs/0805.1265
    C, P, and T of Braid Excitations in Quantum Gravity
    Song He, Yidun Wan
    28 pages, 5 figures
    (Submitted on 9 May 2008)

    "We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T."

    I think this is an important paper. It is the companion of another He-Wan paper that I nominated last week for this quarter's MVP (most valuable non-string QG research) prediction poll. The braid-matter program is high risk. It began as a long shot with only a slim chance of working out. It was not at all clear that braids (in this case in four-valent networks used to describe states of geometry and gravity) would turn out to reproduce some of the basic patterns of matter----key symmetries and invariants. This paper is, for me, the first sign that braid-matter might work. Others might see differently and I would be glad to have some comments.

    In any case the whole thing is very new. It goes back only to Bilson-Thompson's work in 2005----which had braids but without the context of four-valent networks.
     
    Last edited: May 12, 2008
  2. jcsd
  3. marcus

    marcus 24,730
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    I should list the paper by He and Wan which immediately precedes this one

    http://arxiv.org/abs/0805.0453
    Conserved Quantities and the Algebra of Braid Excitations in Quantum Gravity
    Song He, Yidun Wan
    25 pages, 2 figures
    (Submitted on 5 May 2008)

    "We derive conservation laws from interactions of braid-like excitations of embedded framed spin networks in Quantum Gravity. We also demonstrate that the set of stable braid-like excitations form a noncommutative algebra under braid interaction, in which the set of actively-interacting braids is a subalgebra."

    There is also a solo paper by Yidun Wan and another co-authored by Jon Hackett and Wan.

    One of the references says there is also a paper in preparation by Smolin and Wan.

    So far, to my knowledge, there is no evidence either that the 4-valent braid-matter approach of Wan et al is right, or that it is wrong.

    One thing that can be said is that, if it is right, matter arises as knots in geometry, in other words matter is a topological complication in space. It is a daring idea, with a high risk of not working out, and I think Yidun Wan and the others deserve a lot of credit for undertaking such a research venture. Yidun has posted several times here at PF, and subsequently set up his own blog.
     
  4. marcus

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    Here is a Perimeter online video lecture by Yidun about braid matter,
    https://www.physicsforums.com/showthread.php?t=184400
    it is a good easy audiovisual way to learn about braid matter.

    Here is our announcement of Yidun's blog back in May 2006. Has it been two years already?!
    https://www.physicsforums.com/archive/index.php/t-120127.html

    At that time Yidun was posting at PF with the name "lqg". I see a post from him there.
    The blog is named "Road to Unification".

    Perimeter has a new catalog of video talks called Pirsa. If you go here:
    http://pirsa.org/speaker/Yidun_Wan
    You will find TWO available video talks by Wan. One of them is more recent 31 January 2008.

    PIRSA:08010044 ( Windows Presentation, Windows Video File , Flash Presentation , MP3 , PDF) Which Format?
    Braid-like Chiral States in Quantum gravity
    Speaker(s): Yidun Wan - University of Waterloo
    Abstract: There has been a dream that matter and gravity can be unified in a fundamental theory of quantum gravity. One of the main philosophies to realize this dream is that matter may be emergent degrees of freedom of a quantum theory of gravity. We study the propagation and interactions of braid-like chiral states in models of quantum gravity in which the states are (framed) 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. These braids may serve as fundamental matter content.
    Date: 31/01/2008 - 2:00 pm
    Series: Quantum Gravity
    URL: http://pirsa.org/08010044/


    PIRSA:07090011 ( Windows Presentation, Windows Video File , Flash Presentation , MP3 , PDF) Which Format?
    Propagation and interaction of topological invariants on embedded 4-valient spinets
    Speaker(s): Yidun Wan - University of Waterloo
    Abstract: The study of particle-like excitations of quantum gravitational fields in loop quantum gravity is extended to the case of four valent graphs and the corresponding natural evolution moves based on the dual Pachner moves. This makes the results applicable to spin foam models. We find that some braids propagate on the networks and they can interact with each other, by joining and splitting. The chirality of the braid states determines the motion and the interactions, in that left handed states only propagate to the left, and vice versa.
    Date: 07/09/2007 - 3:00 pm
    URL: http://pirsa.org/07090011/

    Over the years I've found the Perimeter online video lectures quite helpful, so if anyone wants to learn more about braid-matter and the current research, I'm suggesting this. there is also online talks at the ILQGS (international loop quantum gravity seminar).
     
    Last edited: May 13, 2008
  5. What dynamical stuff constitutes the braids ??? Or is it just old fashioned symmetry braking ?
     
  6. marcus

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    Careful, glad to see you! I saw your recent posting on arxiv. Good luck with it!
    This is a useful question. I don't think anyone has spelled out what dynamical stuff.

    One response would be the same primitive "material" that embedded spin networks themselves are made of. You get braids whenever you have the network embedded.
    A braid is like a knot. You get the possibility of knots whenever you have a circle that is embedded in R3.

    You Careful know this. I'm saying it in case anyone else is reading the thread and doesn't know.

    I personally don't like that response to the question either, but that would be one answer.

    We should think about it, but for now I think there is no answer. A spin network is too fundamental for it to be "made" of any "material". Likewise braids in a spin network, they don't seem to be made of any thing. they are mathematical ways of representing information, I guess.
    =======================

    A 4-valent network can be thought of as a simplicial complex. but as you mentioned there is a kind of generalized symmetry breaking in the way you glue the simplexes together. You can glue them together in some naive straightforward way, I suppose, or you can twist them as you are bringing face to face. There can be crisscross contorted ways that you join face to face.
    =======================

    Something I am curious about, well two things:
    One is how this braid-matter business might parallel Connes Chamseddine NCG-SM. They say that spacetime is M x F where M is just a smooth 4D manifold and F is a finite discrete sort of geometry that is representable only algebraically (not as a manifold).
    Well it seems to me that 4-valent networks (conventionally representing 3D geometry in Loop-talk) correspond vaguely to the manifold M, and that MAYBE Connes finite geometry F corresponds to the TWISTS AND BRAIDS. The dimensions don't match perfectly and the fit may not be very good but I see some possibility of the two approaches joining.

    The other thing I am curious about is how braid-matter could tie in with Ambjorn Loll CDT. They both use Pachner moves.. Yidun Wan uses a dynamics of local moves made on the network which looks similar to the local moves on the simplexes that Ambjorn Loll use-----e.g. join two tets and then split the result into three (to take a lower dimensional example). It seems possible that the CDT spacetime brickworks are basically the same thing as braid-matter 4-valent networks and that Wan could be showing Ambjorn Loll a way that they could include matter in their CDT picture.

    this is very tentative on my part. havent thought it out much.
     
    Last edited: May 14, 2008
  7. Well, one of the reasons why I asked is because spin networks are merely kinematics and as such there is no way to attach physical information to it a priori. Moreover, what may appear to be knotted for one observer, could be unknotted for another one. Just like accelerated observers are seeing a thermal bath while freely falling ones nothing.

    There is a definite distinction between spin networks and say causal sets in this regard. The causet itself is a dynamical object and questions like braiding could in principle be asked (albeit it would be difficult) in such framework.
     
  8. marcus

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    Careful as always you raise interesting points. I would appreciate if anyone could help out by responding to this. (My thought was that topology shouldn't be observer-dependent or at least that topology is unchanged by the transformations one usually thinks of, but I'd like to hear someone else's comment.)

    I was reluctant to cover up your post, unresponded to, but want to continue with a bit more discussion.
     
  9. marcus

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    There is another bit of unfinished business, so to speak, from a previous braid-matter thread. That thread got a lot of discussion going in different directions by different people and this comment by Saltlick didn't get a response. It also points up some potentially interesting topics and it would be great if anyone who knows the referenced literature could respond

    As it happens, that post was in context of talk about a trivalent braid-matter paper. But I think it may apply equally well to a discussion of the Wan-He paper, which is dealing with the 4-valent case.
     
  10. Well, intrinsic topology is (and the topology of knots is trivial), properties of knots however depend upon the embedding space R^3. In R^4, there exist no nontrivial knots; that is you can always find a global diffeomorphism which undoes the knotting.

    It might be -in this way- that particles change species if observers change, which would definetly be problematic. Since I haven't read the papers (or given it any further thought), I would welcome any comment on this (and set me straight if necessary).
     
    Last edited: May 16, 2008
  11. The problem is that people continue to associate the embedding space with some fixed classical geometry that is supposed to reflect the nature of an emergent spacetime. Bad idea to put in by hand what you want to get out. The only way to treat braids in a truly observer dependent way (this is seen as a feature, not a problem), is to view the imbedding space as a reflection of the measurement constraints for that particular observer, ie. as an abstract template completely independent of the properties that we like to attribute to space on large scales. I don't see how you can do this without incorporating category theory, so that the embedding space can be, eg., a configuration space.
     
  12. marcus

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    that is an appealing suggestion. I have always been puzzled by that very thing about braids, you need an embedding of the network for them to have meaning, but we were always trying to get rid of an embedding space. So can you sketch out in more detail how you could associate the embedding space with the observer? So then the knots and braids exist for him and him alone? Please explain as simply as you can---rather than refer me to some paper where I would have to labor to dig it out
     
  13. I agree that within a quantum mechanical context such view could be entertained although I see no a priori reason why such embedding should be space-like unless you break diffeomorphism invariance from the start (we shall never agree upon the role of the observer, but that should not be a conversation killer). Nevertheless, I have no quick understanding for how one could avoid different observers to see one and the same braid as different species of particles (even in the Everett interpretation where you would treat the second observer as a state living on a huge spin network, this would be an issue).
     
    Last edited: May 16, 2008
  14. Well, this is where I completely part company with a spin foam point of view: for the observer's status to be correctly encoded in the logical diagrams (ie. generalized braids) one would have to specify different observables for different classes of observer. And there is no problem with different observers viewing a given diagram in different ways, because the context also contains physical meaning. Of course, this is not at all a classical point of view, and cannot be made so. The recovery of classical geometry (ie. GR) would be far more complex than the simplest possible QG statements expressible via braids. But this is kind of nice, because maybe the particle spectrum is in fact simple.
     
  15. But how could one expect getting out GR of such a scheme in some semi-classical limit ? I could assume that the braid is an eigenstate for the observables O_1 , O_2 and as such observers 1 and 2 have deterministic measurement outcomes (even quantum mechanically). Hence, I would arrive at two classical observers doing the same experiment while getting two different answers. It is therefore unclear to me what you mean by "And there is no problem with different observers viewing a given diagram in different ways, because the context also contains physical meaning".
     
  16. Exactly, and I don't see a problem with this. The observers' classicality is still defined abstractly and independently of a universal spacetime. Everybody has their own universe (so there is a multiverse, but it's very different to the usual kind, which is still supposed to be out there somewhere). Riemannian geometry would arise as a subtle non linear kind of superposition of categorical geometries for observers on all scales (scale being the main index of observer type).
     
    Last edited: May 17, 2008
  17. The state I alluded to is a product state, so multiversing should not matter here, so it should be equivalent to the case of two classical observers in the same universe. A non linear kind of superposition ???
     
    Last edited: May 17, 2008
  18. Sorry, without the maths I'm not exactly sure what you mean, but perhaps you could define 'same universe' for me in a background independent way. Are we talking about 2 mathematically identical observers viewing the same experiment together? Or are we talking about 2 different observers viewing a certain precisely definable measurement problem? In either case there is a product of effective universes because if we insist on there only being one universe, then we can formalise the notion of an observable for the entire universe, but this seems physically non-sensical. I think it makes more sense for everything to be relative.

    Well, I'm constantly trying to come up with novel simple descriptions instead of launching into a tirade about operads and topos theory. Apologies if that one doesn't work too well.
     

  19. The traditional way of doing that would be to quantize the Dirac algebra in an anomaly free way and constrain states S by HS = 0 = H_a S (but that is obviously not my personal opinion). First, let me treat things classically: you can compute diffeomorphism covariant quantities such as two point functions A(x,y) satisfying Diff(A)(Diff^{-1}(x), Diff^{-1}(y)) = A(x,y). Classically, you might be able to measure things like lim_{y \rightarrow x} \nabla_{V(y)} A(x,y) where V is a local vectorfield and after you did some observation, you have to take the map of the entire mathematical 4-D universe (in some coordinate system and diff gauge) and pinpoint those points x where your observation matches this calculation (as well as the observer taking this map afterwards :-) ). This could imply that your theory is weakly unpredictive in the sense that there exist plenty of places in the universe where you could be (in some fixed diff gauge) and incoming electromagnetic radiation might fall in at one place at some later time but not at the other, but obviously the behaviour of the planets would remain the same for a very long time in the future. This is to be expected, a deterministic theory of the universe should not lead to unique predictions for an observer in it (because that would imply the observer to know things beyond the observable universe). Now quantum mechanically, there are further complications but no ''real'' problems (what the interpretation is concerned :-) ). Since you need extra (non dynamical) ingredients, diff invariance goes through the window and the predictive power (as well as beauty) of your theory decreases by a factor of infinity (but hey: that is quantum mechanics :-)). Now I have to turn to my own thoughts about this, otherwise it does not make sense. I am convinced that it is possible to give a STATIC four-dimensional formulation of quantum gravity which is fully covariant (not that I dream of that but who cares). That is: no observers, only space-time algebra: you might see it as a universal envelopping algebra for all observers. Now, putting in a foliation is nothing but at trick to identify the algebra's induced on the hypersurfaces. This allows you to introduce creation/annihilation operators, the associated Fock spaces, time evolution, hamiltonians and so on. So, given two different foliations, natural (generalized) Bogoliubov transformations can be constructed (which ought not to give rise to unitary equivalent theories if the map from one foliation to another is not globally well defined - as is the case for the Unruh effect). More to come, have to go now.
     
    Last edited: May 18, 2008
  20. So, what does this foliation mean ? Semi-classically, it has a double function : it serves as a reduction of the state devise and (b) the curves of constant space coordinates correspond more or less to the wordlines of classical observers. (b) is a priori difficult to uphold since all observers are material entities themselves : that is, the state of the universe contains exitations of material fields which can be characterized by gauge non covariant localized projection operators giving outcomes such as : | human being with quantum hair > , | bad local realist > , | mutant > and so on... Now, we should be only interested in gauge covariant operators which we can assume to be living on a hypersurface of the foliation by using the isomorphism described above. Such operators of course forbid outcomes of the kind |bad local realist > but allow for | human being with quantum hair > sees |bad local realist>. Now, what e.g. the |mutant> ''knows'' simply depends upon the maximal set of gauge covariant operators (with partial support on the mutant) containing the projection operator associated to the entire universe in its spectral decomposition (we assume here that a measurement changes that state and the latter are therefore only important if the state of the universe does not correspond to an eigenstate...). Problems with such theory are legio, for example there is no guarantuee that increasing t means to go forwards in time (since the latter consists of a measurement too). Another example woud be: if conscious observation is discrete and by no means triggered by any dynamics; why don't we observe an entirely discontinuous universe (something which penrose and GRW might be worried about) ?

    Anyhow, coming back to our knots: suppose a spin network-knot which lives in the leaf sigma (and which is characterized by a gauge non covariant operator associated to sigma) and two classes of material observers, which we may assume to be classical, that is they correspond to eigenvectors of such gauge covariant operators as |class1 has sigma as a surface of constant time > and | class2 does not contain sigma as a surface of constant time but the knot belongs to such surface > . Now, a gauge covariant observable then corresponds to measuring the Alexandrov polynomial of the knot with respect to both physical hypersurfaces of constant time containing the knot. Assuming it is possible that the knot is unknotted with respect to the second hypersurface; I don't see how one can get out of this issue.

    As for the non-linear superposition principle : when I speak about superposition being not in contradiction with a non linear theory; I mean of course that a suitable linearization gives rise to an appropriate probability interpretation associated to the full non-linear theory (and this is not a contradiction). Do you intend something similar or what?
     
    Last edited: May 18, 2008
  21. OK, that is an interesting point. (In fact, I see a lot of determinism in what we are doing, too. It just isn't obvious). But of course I prefer to interpret any situation with such multiple outcomes as quantum, even though not all observables will be quantum in the usual sense.

    Static meaning that all possible outcomes are predetermined and fixed for all Time, where Time is, what exactly? I am quite happy with the algebraic perspective, only an algebra of all observers sounds just as problematic to me as a universal observer. The beauty of the categorical point of view is that one cannot even discuss algebras of all observers, because the relational nature of things makes it nonsensical.
     
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