Exploring Causal Set Approach to Quantum Gravity

[Rebel]

Is somebody here involved with the causal set approach to QG?

http://arxiv.org/abs/gr-qc/0309009 is a nice introduction to the theme, and I liked among the introduction with some quotes of Riemann.
If so or any of the good people like to give opinion, I would like to make some questions:

Someone figures out how things would have evolved if things were not based in stathistics concepts as havig a Poisson distributions for the causets, the sprinkling, ideas of Random graphs and so on? For instance, having more things like a direct binomial distribution in the causets describing systems, could have the Hauptvermutung a more precise statement than the actual one? I think that the idea of having random graphs as inherent in many ideas developed till now has some atractive features as phase transitions (and I guess it was initially the idea to get the continuum as limit and even for the inclusion of matter), but maybe for advances more than focusing in quantum measures it could be nice for some people working on it to review the fundamentals of the theory.

Also, I think that in the status quo of the theory it could be checked if it has some relations with others, like CDT, since there could be links among path integral approach working with discrete structures. What do you think?

 

[marcus]

...
Also, I think that in the status quo of the theory it could be checked if it has some relations with others, like CDT, since there could be links among path integral approach working with discrete structures. What do you think?

There is good communication between Causets and CDT. Some top young people in Causets are or used to be Joe Henson and David Rideout. They have worked in other QG approaches with other researchers. Look up their papers in arxiv.

One of the top two or three leaders in CDT is Renate Loll, at Utrecht. After Henson got his PhD at UC San Diego, Renate Loll invited him to Utrecht for a two-year postdoc, as I recall, around the time 2005-2007. He didn't have to do her stuff, he continued Causetting at Utrecht.
He gave Causet seminars attended by Loll's CDT doctoral students. This is a close association. He continued doing Causet research while supported as a member of a CDT team. After that, in 2008, he went on to another postdoc position at Perimeter Institute (where as you know there are Lee Smolin and Laurent Freidel and others).
Perimeter is strong in Loop/Spinfoam. But it has Causet research too: Rafael Sorkin is there a lot of the time. And for some reason I don't see Henson doing Causet so much now. In fact in 2009 Henson came out with a very interesting paper in CDT! http://arxiv.org/abs/0907.5602
It looks to me like the paper makes use of smart intelligence that he picked up working in Causets. Techniques and ability carry over.

You ask what I think? Young researchers go back and forth between the various approaches. There are relations and similarities, which are sometimes mentioned in papers, but differences as well.
My poorly informed subjective judgment is that Causets is philosophically appealing, and has some ingenious mathematics which allows it to work with minimal structure--a certain elegance in other words. But I think it lags behind. Fewer workers, fewer papers, fewer results. I don't think it is hot now, the way Loop/Spinfoam is hot, or AsymSafe QG, or various newer approaches.

To understand where I am coming from, have a look at this Emergent Gravity conference (called EG4, held at Vancouver this month):
http://www.emergentgravity.org/index.php?main=main_EGIV_about.php

You will see David Rideout presenting Causets, also Renate Loll will be there, Daniele Oriti, also various String people and plenty of Loop/Spinfoam people as well. Look at the topics. But in all the talks only one (Rideout) seems to be Causets.
"Rideout
deSitter Space from Causal Set Dynamics
We present evidence that the early universe of sequential growth dynamics for causal sets begins with a phase of super-exponential expansion, followed by a deSitter-like period of expansion."

Look at the EG4 Programme:
http://www.emergentgravity.org/index.php?main=main_EGIV_programme.php
The single Causet talk is grouped with 3 others in the "Networks" topic on Monday afternoon:
14:30 Loll
14:45 Conrady
15:00 Bilson-Thomson
15:15 Rideout
A lot of the conference will be given to open discussion, for everybody from all the different approaches. The chairs of the 7 discussion sessions are:
Renate Loll
Dan Oriti
Matt Visser
Fotini Markopoulou
Bill Unruh!
Silke Weinfurtner
Ralf Schuetzhold (who does analog gravity experiments like hydrodynamic "black hole" analogs where the speed of sound is analogous to the speed of light.)
and none of the chairs does Causet, maybe Renate Loll CDT would be the closest. Or maybe Markopoulou with the "quantum graphity" approach.
To me it looks like no matter how ingenious and exquisite mathematically and philosophically, Causets is currently marginal.
That's just what I think. You asked.
==========================

BTW here is something I think is interesting. You know that Florian Conrady is a young guy who has co-authored several papers with Laurent Freidel. I have gotten a high respect for Conrady. Now here is some completely new work on something I didn't ever see yet. Which also comes in the Monday afternoon session.
"Conrady
Simplicial complexes from condensation
I will talk about work in progress on a statistical model of graphs. The configurations are arbitrary graphs with a fixed number of links. The Hamiltonian is a simple function of the graph that favors the formation of 2d simplicial complexes. Monte Carlo simulations show that at low temperatures the system is in an ordered phase, where the links condense to 2d simplicial complexes. At high temperatures one has a disordered phase and the links form graphs of high connectivity."

So there is a Hamiltonian that governs the evolution of some graphs and at the "big bang" time when it is very hot there is no regular idea of space because of "high connectivity" meaning almost every point is connected to almost every other--a totally crumpled up chaos, not a real space.
And then as it cools down it evolves a regular dimensionality, and it looks like a simplicial complex (a more familiar idea of geometry). That seems like an interesting toy model of the emergence of (maybe not gravity but at least) geometry. I will watch out for a paper about this from Conrady, if the work makes it to that stage.

 

[Rebel]

Thank you for the very nice reply. I guess there could be some relation among CDT, Causets and others, for example it's direct to associate some models Ising-like that sometimes Ambjorn used for CDT and some discrete models that could evolve as graphs in general or posets in particular for causal sets... that's something in which I am wondering to add to my thesis; I'll check better about the talks of EG4 and the paper you mention, that reminded me another paper you mentioned f Rivasseau, although just for the use of graphs for computations. Best regards.

 

[Carey]

Hello Rebel, I have some findings that I think will interest you. My training is in philosophy of science and math, with a focus on Russell and Whitehead's doctrine of space-time called "eventism." From this vantage point, I came to causal set theory without knowing of it by name. I developed it by diagramming the finite causal sets, starting with the simplest. I found that relative frequency ratios are formed in such diagrams, and that these may serve physics as energy ratios, in accord with Planck's E=hf. Each causal link is thereby a quantum of energy. With that motivation, I went on to construct space-time and its particles from quanta, using arrow diagrams. This is a more foundational development of causal set theory than the others have found. I think this is what you were promoting in your post. The theory and its diagrams are published this year in an article called "Finite Eventism." You can Google that phrase, or my full name, to find my work online. Google Books has a generous preview of the article on its website for the book "Mind that Abides," edited by David Skrbina. I could email a PDF of the complete article to anyone interested. -- Carey R. Carlson