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The braid matter program is a difficult long-shot gamble but they keep forging ahead on it.
It started at Perimeter around November 2006 and there were so many obstacles, so many things that might not have worked out, that it could have reached an impasse any time in the past year and a half and been abandoned.
but instead, two of the team have just posted a new paper. And TWO MORE are in preparation! There is one coming out by Yidun Wan and Lee Smolin, and another one on the way by Jonathan Hackett, Louis Kauffman, and Sundance B-T!
Here is the one they just posted:
http://arxiv.org/abs/0803.3203
Conserved Quantities for Interacting Four Valent Braids in Quantum Gravity
Jonathan Hackett, Yidun Wan
18 pages, 7 figures
(Submitted on 21 Mar 2008)
"We derive conservation laws from interactions of actively-interacting braid-like excitations of embedded framed spin networks in Quantum Gravity. Additionally we demonstrate that actively-interacting braid-like excitations interact in such a way that the product of interactions involving two actively-interacting braid-like excitations produces a resulting actively-interacting form."
==========================================
The idea is assume that you can realize gravity----that is the quantum state of geometry---by means of 4-valent ball and tube networks. You are allowed to TWIST the tubes. You can picture the tubes as ribbons if it makes the twists more graphic and easier to imagine. Four-valent just means that every ball-joint has exactly four tubes meeting it.
OK so assume that the quantum state of geometry can be represented by this kind of fourvalent twist-network. Now we are interested in UNIFYING geometry with matter, so how do we add matter to that picture?
The braid-matter team is struggling to show that you can represent particles by something analogous to KNOTS in that ball-twisted-tube network. Knots can interact. One knot can undo another. Two knots can do themselves up to make a third, or a fourth. Certain kinds of knots can PROPAGATE around in the rest of the network without getting hopelessly tangled up and stuck somewhere.
Someone with patience and mathematical skill should be able to CLASSIFY all the GOOD knots. The ones that can propagate and interact. I am using "knot" in a not very technical sense. I'm not rigorously defining anything. I mean some crisscross twisty braiding of some nearby tubes connected to some neighboring balls.
It wasnt obvious that there were going to turn out to be ANY GOOD KNOTS AT ALL! But there are. So then the next part of this hard game is to classify them and study their interactions. And then the very longshot gamble is that when you have them all classified you might find that they correspond to KNOWN PARTICLES!
If not, well you have done some interesting mathematics and discovered yet another way that Nature isn't. But if it turns out there's a match, well something very strange is going on. The longshotness of this research----the remoteness of reward---impresses me, as well as the combinatorial/algebraic difficulty. Algebraically it is unplowed ground. They have had to construct new tools.
So it's amusing for us bystanders to watch.
=======================================
By the way suppose we forget about tubes and twisting for a moment and just think about fourvalent balls joined by simple wires. A network of that sort is dual to a WAY OF STICKING TOGETHER TETRAHEDRONS. Think of tetrahedral lego blocks. Each ball is replaced by a tet, and a wire connecting two balls means that those two tets snap together. So a given fourvalent network could describe a TRIANGULATION with some sort of geometry. Working with fourvalent networks is somewhat akin to what Jan Ambjorn and Renate Loll do called "Causal Dynamical Triangulations". They impose special conditions on how their 3D triangulations can evolve in time, which amount to having the whole process realized as an assemblage of simplexes. The 4d simplex analog of a 3d tetrahedron. And they run Monte Carlo computer simulations of little universes made of shuffling simplexes. This produces interesting results.
So what Yidun Wan and Jonathan Hackett are doing with fourvalent networks is not too far removed from CDT, although superficially it looks quite different. I suppose that as a long-shot gamble the Braid-Matter group's work could eventually give Ambjorn and Loll's group some ideas of how to incorporate matter fields into Causal Dynamical Triangulations.
It started at Perimeter around November 2006 and there were so many obstacles, so many things that might not have worked out, that it could have reached an impasse any time in the past year and a half and been abandoned.
but instead, two of the team have just posted a new paper. And TWO MORE are in preparation! There is one coming out by Yidun Wan and Lee Smolin, and another one on the way by Jonathan Hackett, Louis Kauffman, and Sundance B-T!
Here is the one they just posted:
http://arxiv.org/abs/0803.3203
Conserved Quantities for Interacting Four Valent Braids in Quantum Gravity
Jonathan Hackett, Yidun Wan
18 pages, 7 figures
(Submitted on 21 Mar 2008)
"We derive conservation laws from interactions of actively-interacting braid-like excitations of embedded framed spin networks in Quantum Gravity. Additionally we demonstrate that actively-interacting braid-like excitations interact in such a way that the product of interactions involving two actively-interacting braid-like excitations produces a resulting actively-interacting form."
==========================================
The idea is assume that you can realize gravity----that is the quantum state of geometry---by means of 4-valent ball and tube networks. You are allowed to TWIST the tubes. You can picture the tubes as ribbons if it makes the twists more graphic and easier to imagine. Four-valent just means that every ball-joint has exactly four tubes meeting it.
OK so assume that the quantum state of geometry can be represented by this kind of fourvalent twist-network. Now we are interested in UNIFYING geometry with matter, so how do we add matter to that picture?
The braid-matter team is struggling to show that you can represent particles by something analogous to KNOTS in that ball-twisted-tube network. Knots can interact. One knot can undo another. Two knots can do themselves up to make a third, or a fourth. Certain kinds of knots can PROPAGATE around in the rest of the network without getting hopelessly tangled up and stuck somewhere.
Someone with patience and mathematical skill should be able to CLASSIFY all the GOOD knots. The ones that can propagate and interact. I am using "knot" in a not very technical sense. I'm not rigorously defining anything. I mean some crisscross twisty braiding of some nearby tubes connected to some neighboring balls.
It wasnt obvious that there were going to turn out to be ANY GOOD KNOTS AT ALL! But there are. So then the next part of this hard game is to classify them and study their interactions. And then the very longshot gamble is that when you have them all classified you might find that they correspond to KNOWN PARTICLES!
If not, well you have done some interesting mathematics and discovered yet another way that Nature isn't. But if it turns out there's a match, well something very strange is going on. The longshotness of this research----the remoteness of reward---impresses me, as well as the combinatorial/algebraic difficulty. Algebraically it is unplowed ground. They have had to construct new tools.
So it's amusing for us bystanders to watch.
=======================================
By the way suppose we forget about tubes and twisting for a moment and just think about fourvalent balls joined by simple wires. A network of that sort is dual to a WAY OF STICKING TOGETHER TETRAHEDRONS. Think of tetrahedral lego blocks. Each ball is replaced by a tet, and a wire connecting two balls means that those two tets snap together. So a given fourvalent network could describe a TRIANGULATION with some sort of geometry. Working with fourvalent networks is somewhat akin to what Jan Ambjorn and Renate Loll do called "Causal Dynamical Triangulations". They impose special conditions on how their 3D triangulations can evolve in time, which amount to having the whole process realized as an assemblage of simplexes. The 4d simplex analog of a 3d tetrahedron. And they run Monte Carlo computer simulations of little universes made of shuffling simplexes. This produces interesting results.
So what Yidun Wan and Jonathan Hackett are doing with fourvalent networks is not too far removed from CDT, although superficially it looks quite different. I suppose that as a long-shot gamble the Braid-Matter group's work could eventually give Ambjorn and Loll's group some ideas of how to incorporate matter fields into Causal Dynamical Triangulations.
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