Best CDT expo so far + new results (Goerlich)

[marcus]

The best online slide-set exposition of Causal Dynamical Triangulations that I have seen so far is the one that Goerlich presented at the QGQG conference on 30 June.

It makes excellent use of graphics to get across some basic features of CDT that are often missed. Such as for instance the extreme irregularity of the lattice representing a typical spatial slice.

Here's the QGQG menu of slide-sets (with audio for some of the talks as well)
http://echo.maths.nottingham.ac.uk/qg/wiki/index.php/QGsquared-slides

Here is the link for Andy Goerlich's slides in particular---or just scroll down to Monday session C19
http://echo.maths.nottingham.ac.uk/qg/wiki/images/1/1e/GoerlichAndrzej1214824381.pdf

This presentation is geared for a wide physics audience---accessible but more detail and math than you would get in a SciAm introductory piece.
Highly recommended.

Also have to mention that Freidel's talk is fantastic (one of several fantastic talks at QGQG)
Slides
http://www.maths.nottingham.ac.uk/r...rence/uploaded/tuesday/FreidelLaurent1234.pdf
Audio
http://www.maths.nottingham.ac.uk/r...nference/audible/02Tuesday/LaurentFreidel.mp3

 

[marcus]

One quick and easy way to get a lot of insight into CDT (if you haven't done this before) is to go to Andy Goerlich's slide #7
and to think about the fact that all those triangles are actually equilateral.

It is topologically a 2-sphere---representing a spatial slice of a 2+1 dimensional toy universe. The familiar balloon surface analogy you always get in cosmology. However the geometry is extremely bumpy. The curvature of the surface is concentrated at POINTS ( in higher D cases it will be concentrated at the D-2 simplices sometimes called the bones or hinges but here D-2 = 0 so it is at points, especially simple.)

The curvature can be seen by how many equilateral triangles fit around the point.
In some cases you can see that 10 or 20 fit around one point---that is positive curvature. In other case you can see that only 4 fit around a point---that is negative curvature.
If you see a place where exactly 6 are around a point that would be a flat place. In Goerlich's slide #7, I didn't happen to notice a point with just 6 triangles around it. Maybe you will spot one.

 

[marcus]

It is worth knowing a little about the CONTEXT----the QGQG conference where the talks by Freidel, Rovelli, Goerlich and so many others were presented. One indicator, for me, is that the first plenary talk was given by Vincent Rivasseau on NCQFT---noncommutative quantum field theory. And Rivasseau also gave the summarizing talk at the end. I noticed that several of the other plenary speakers referred back to themes that Rivasseau highlighted.

I'd say the NCQFT program is to get rid of dependence on a spacetime continuum and produce a deeply background-independent QFT. Geometry and matter degrees of freedom should be treated on the same basis----everything is generalized feynman diagrams or ribbon graphs or spinfoams or something new along those lines---in any case no continuum. You may have a different handle on it. Here is Rivasseau's final slide, of his QGQG talk:

===quote Vince R. conclusions slide===
CONCLUSIONS

The GW model may be considered the Ising model of NCQFT

NCQFT lies "in between" quantum gravity and ordinary QFT

4D Moyal space is really 2+2. 4D NCQFT remains at the complexity
level of 2D gravity. 3D and 4D gravity, eg in the GFT formulation with
their more complicated "Barett-Crane"-type vertices require a more
sophisticated analysis.

The main challenge in my view is now to invent a new RG adapted to
quantum gravity. With this tool we should understand how ordinary
space-time emerges from a background independent formulation of QG
(-> Rovelli and collaborators). The discovery of the noncommutative
RG associated to the GW model, which is nonlocal and mixes ordinary
scales is an encouraging step in this direction.

==endquote==

 

[wolram]

I wish them luck, but i am willing to bet that non background Independence theories will never work, or string theory, if anyone wants a subscription to playboy they can take the bet.

 

[marcus]

I wish them luck, but i am willing to bet that background Independence theories will never work.

:rofl:

You certainly are not alone in thinking that!

I on the other hand think that only background independent theories have a chance.

By background independent, I mean what the non-string QG community usually means by this namely the theory doesn't involve a pre-arranged geometry----no pre-established metric on a manifold.
Vince Rivasseau is more extreme---he seems to be asking that the theory doesn't requre ever assuming a continuum: no spacetime manifold at all.

I wonder if Loll's CDT could be formulated so as to meet Rivasseau's specifications. I guess it probably could.

 

[wolram]

:rofl:

You certainly are not alone in thinking that!

I on the other hand think that only background independent theories have a chance.

By background independent, I mean what the non-string QG community usually means by this namely the theory doesn't involve a pre-arranged geometry----no pre-established metric on a manifold.
Vince Rivasseau is more extreme---he seems to be asking that the theory doesn't requre ever assuming a continuum: no spacetime manifold at all.

I wonder if Loll's CDT could be formulated so as to meet Rivasseau's specifications. I guess it probably could.

Sorry Marcus i edited my post after you replied it seems, some times i forget how fast the Internet works.

 

[marcus]

i edited my post after you replied it seems, some times i forget how fast ...

This is constantly happening to me too! I like to edit. Reading a post suggests changes and other things to say.

I wish them luck, but i am willing to bet that non background Independence theories will never work, or string theory, if anyone wants a subscription to playboy they can take the bet.

That is a very sporting offer. I hope that one of the string fans takes you up on it.

 

[marcus]

Thanks for reminding me to look back, Wolram! In post #2 I was typing fast and made a careless mistake, switching the words positive and negative. Too late to edit. I will quote the post and make the correction here in *asterisks*

... Andy Goerlich's slide #7
and to think about the fact that all those triangles are actually equilateral.The curvature can be seen by how many equilateral triangles fit around the point.
In some cases you can see that 10 or 20 fit around one point---that is *negative* curvature. In other case you can see that only 4 fit around a point---that is *positive* curvature.
...

In the graphic of slide #7 some of the triangles look all skinny and pointy. that is so that in our world we can draw them with 10 or more fitting around a point.

equilateral triangles have angles of 60 degrees----so if 10 fit around a point that is 600 degrees around that point (negative curvature)

And some of the triangles in the graphic are drawn look like they have 90 degree angles so that only four can fit around a point----but remember all those triangle are really equilateral. So that means if 4 fit there are only 240 degrees around the point (positive curvature).

the curvature is associated with the angle deficit----the amount by which 240 is less than 360, in the example.