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

by marcus
Tags: braid, excitations, gravity, quantum, song, yidun
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marcus
#1
May12-08, 01:54 PM
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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.
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marcus
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May13-08, 12:09 AM
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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.
marcus
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May13-08, 12:22 AM
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Here is a Perimeter online video lecture by Yidun about braid matter,
http://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?!
http://www.physicsforums.com/archive.../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).

Careful
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May14-08, 02:27 PM
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C, P, and T of Braid Excitations in Quantum Gravity (Song He, Yidun Wan)

What dynamical stuff constitutes the braids ??? Or is it just old fashioned symmetry braking ?
marcus
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May14-08, 03:10 PM
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Quote Quote by Careful View Post
What dynamical stuff constitutes the braids ??? Or is it just old fashioned symmetry braking ?
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.
Careful
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May14-08, 03:54 PM
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Quote Quote by marcus View Post
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.
.
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.
marcus
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May15-08, 11:26 AM
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Quote Quote by Careful View Post
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.
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.
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May15-08, 11:43 AM
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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

Quote Quote by Saltlick View Post
...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.
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.
Careful
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May16-08, 04:52 AM
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Quote Quote by marcus View Post
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.)
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).
Kea
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May16-08, 01:23 PM
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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.
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May16-08, 01:47 PM
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Quote Quote by Kea View Post
... 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.
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
Careful
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May16-08, 03:08 PM
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Quote Quote by Kea View Post
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.
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).
Kea
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May17-08, 01:17 AM
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Quote Quote by Careful View Post
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...
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.
Careful
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May17-08, 02:45 AM
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Quote Quote by Kea View Post
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.
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".
Kea
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May17-08, 01:36 PM
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Quote Quote by Careful View Post
Hence, I would arrive at two classical observers doing the same experiment while getting two different answers.
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).
Careful
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May17-08, 05:25 PM
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Quote Quote by Kea View Post
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).
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 ???
Kea
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May18-08, 01:49 AM
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Quote Quote by Careful View Post
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.
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.

A non linear kind of superposition?
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.
Careful
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May18-08, 04:23 AM
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Quote Quote by Kea View Post
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.

Quote Quote by Kea View Post
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.
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.


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