The riddle of longshot links (new version of Smolin's '07 unification paper)

[marcus]

Recently (25 July) Lee Smolin posted an update of his December 2007 unification paper
http://arxiv.org/abs/0712.0977
The Plebanski action extended to a unification of gravity and Yang-Mills theory

"We study a unification of gravity with Yang-Mills fields based on a simple extension of the Plebanski action to a Lie group G... [which] may be applied to Lisi’s proposal of an E8 unified theory, giving a fully E8 invariant action. The extended form of the Plebanski action suggests a new class of spin foam models."

The persistent intuition that keeps creeping back into consciousness here is the idea of non-local links in a spin network.

This is something that other QG approaches either do not have or have not yet exploited. It is worth keeping an eye on IMO. All the more because Smolin indicates there is a followup paper in the works, with Garrett Lisi and Simone Speziale. In my estimation, the implied prospect, if it materializes, would be solid contribution to Physical Review D putting this unification scheme (with its nonlocal links) on the map.

On the face of it, nonlocal links is a very strange notion. That a spin network can describe the world and that in ancient days the network was disorderly with connections every which way----not like a regular 3D lattice. With the passage of time the network smoothed itself out somewhat and evolved into a more regular configuration giving the semiclassical illusion of the 3D space we know and love. But there persisted this RESIDUE of long-range connections. Some pairs of nodes that were paradoxically both near and far.

To a local observer who cannot see the other end, these look like severed links----culdesacs---singletons---unmatched socks.

This strikes me as being of the nature of a just-so-story creation myth or better a creation HUNCH.

Because, O ye of insatiable curiosity, the unmatched socks are matter. They are what scholars call FERMIONS.

 

[marcus]

Thanks to Berlin for letting us know about the new version of Smolin's paper

Just seen the new version of Smolins paper on the Plebanski action. It says that a new paper is in preparation together with Lisi and Speziale on gravity+EW unification, building on Smolins framework.

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0977v2.pdf

I would call this "exceptionally" good news! E8 is still alive.

berlin

and also to MTd2 for calling attention to Berlin's post---which I otherwise might have missed!

 

[MTd2]

"That a spin network can describe the world and that in ancient days the network was disorderly with connections every which way----not like a regular 3D lattice. With the passage of time the network smoothed itself out somewhat and evolved into a more regular configuration giving the semiclassical illusion of the 3D space we know and love."

It sounds like Loll's QG, in the begining. When the universe was too small, there wasn't a notion of locality.

"ut there persisted this RESIDUE of long-range connections. Some pairs of nodes that were paradoxically both near and far.

To a local observer who cannot see the other end, these look like severed links----culdesacs---singletons---unmatched socks.

This strikes me as being of the nature of a just-so-story creation myth or better a creation HUNCH.

Because, O ye of insatiable curiosity, the unmatched socks are matter. They are what scholars call FERMIONS."

I think the dimension (in Loll QG) s never really close to 4, if you don't go to infinity, that is, when you stay in microscopic realms. The erros in the emerging latice are the fermions. What do you think?

 

[marcus]

What do you think?

I don't dare think, at this point.

But look at Speziale's publication trackrecord. He tends to prefer solid ground. I think if he gets involved in a collaboration it is because there is a substantial result in sight. I am hopeful and would like to see this idea become a mainstream research topic. But I have to remember that right now it is an exotic leap into midair. Also I do not see the connection that you see with Loll Triangulations. Loll requires that the simplexes march in strict causal formation and these longshot links seem in radical noncompliance with her orders. But I could easily be wrong--maybe Triangulations gravity does after all allow for maverick linkages.

 

[MTd2]

Also I do not see the connection that you see with Loll Triangulations. Loll requires that the simplexes march in strict causal formation and these longshot links seem in radical noncompliance with her orders.

The fact that something is causal does not imply that is local in Loll Triangluations. The 4-simplexes does not have dimensions, although they are "4 dimensional". They don't have spatial dimensions, you even told us that before. The spatial dimensions emerge when you iterate the simplexes. Such it is the case the most famous example of loll's QG works like this, the de-sitter space emerges at an increasing X continuous of hausdorf dimensions until you get to 4.

Microscopicaly, dimensions are bad defined, so that you can get non-local links. And you get that for the simple reason that the physical dimensions do not matter, but to what and how vertexes are linked.

For example. Suppose you get two 4-simples, A and B, linked by a single vertex V. Now, around A, compute the relations with other vertexes except for Vab. The more you compute, the more macroscopic you become. You would get a 4-d space Ma around A. After, repeat the procedure with B, excluding Vba. You would see emerg 4-d space Mb around B.

Now, my idea it is that if you now analize the neighborhood of Ma, you will see yor lab. And after, if you analize the neighborhood of Mb, you will see the surface of a planet at andromeda galaxy. They are casualy linked.

Of course this sounds ridiculous, but you have to remember that this is such the case of euclidian schroendinger equation. You have this kind of casuality relation, that is, and sometimes that denotes entanglement. You follow a parameter t is just a parameter for a solution of the wave equation. But fortunantely, no information is transmited instantly, because t is not quite a dimensionaly defined as in the larger scale, that is, in special relativity or general relativity.

EDIT.: I corrected some mistaeks

 

[MTd2]

What do you think, Marcus?

 

[marcus]

MTd2 what worries me are things you mentioned in your post. entanglement. apparent possibility of instantaneous transmission of information. Maybe these issues have been addressed in some earlier papers but I don't remember seeing them resolved.

 

[MTd2]

MTd2 what worries me are things you mentioned in your post. entanglement. apparent possibility of instantaneous transmission of information.

Wow, am I didn't say such things happens. Just that it would mimick what we apparently see in QM. That's why the transmission of information is apparent, not real. I tried to just see an intermediate situation that you could describe mathmaticaly, not just by arguing, as people usualy do in the discussion causalityXentanglement.

The way you talk, I feel like a stupid bastard '

 

[marcus]

Wow, am I didn't say such things happens. Just that it would mimick what we apparently see in QM. That's why the transmission of information is apparent, not real. I tried to just see an intermediate situation that you could describe mathmaticaly, not just by arguing, as people usualy do in the discussion causalityXentanglement.

The way you talk, I feel like a stupid bastard '

Please, I was not criticising what you said. I told you before I don't know what to think about this question. Until I see more written on it I don't want to hazard any guess. You shouldn't feel embarrassed, you seem smart (not stupid!) but also you seem less cautious.

The question we were asking, I think, is if one can picture this idea of Smolin's of a lattice with a few random longshot links carried over to a CDT context. I can't cross that bridge.