How Does Summing Over Topologies Advance Quantum Gravity Research?

[marcus]

Sum over topologies---Loll Westra

this thread is about these three papers
http://arxiv.org/hep-th/0306183
http://arxiv.org/hep-th/0309012
http://arxiv.org/hep-th/0507012

the titles are "sum over topologies and..."
"spacetime foam in 2D and the sum over topologies"
"taming the cosmological constant in 2D causal quantum gravity with topology change"

I want to discuss these papers, if someone wants to with me.
I think they are important.

what happened before with Loll was she got something (CDT) to work in 2D in 1998 (she and Ambjorn) and then gradually they cranked it up to 3D and then finally in 2004 they got it working in 4D.

and the way you understand Loll work in 4D is NOT approach it directly but begin studying how it works in lower dimensions. when she finally gets this "sum over topologies" to work in 4D and the paper comes out, then if you want to understand it you will STILL have to go back to these three here!

I guarantee as much as anyone can guarantee about the future. In 2006 or so you are going to wish you had read these 3 papers, or if you did read them then you will be glad.

 

[marcus]

the easiest to start with is this one
http://arxiv.org/hep-th/0309012

the reason is the pictures

it is more expository. it is a talk that Willem Westra (Loll grad student) gave at a Krakow workshop on Random Geometry. lot of networking going on in that general area--not just applied to quantum gravity, although quantum gravity IS one kind of random geometry.

Willem's talk is more expository and has more pictures than the initial paper which more starkly reports the research results.

they are working very much in the causal-layered CDT method and they use that layering to limit the kind of wormholes that spacetime can get in it. the wormholes they allow are very tiny and very brief and so you almost don't know they are there. ordinary macro causality is not perceptibly violated.

you don't get that a beam of light disappears over here and unexpectedly reappears over there. you don't get weird wormhole stuff. look at the pictures and see why.

they are being very careful and cautious about how they introduce microscopic soufflé topology. they allow that spacetime can be a soufflé down at Planck scale, but the way they introduce the wormholes it is very controlled, so nothing weird happens to Galileo and Newton and the rest of us sitting around playing cards and drinking beer.

 

[Mike2]

I want to discuss these papers, if someone wants to with me.
I think they are important.

what happened before with Loll was she got something (CDT) to work in 2D in 1998 (she and Ambjorn) and then gradually they cranked it up to 3D and then finally in 2004 they got it working in 4D.

I'm not sure what they are trying to prove. They start with 4D simplexes and they produce the 4D spacetime in the large scale. They use 4D to get 4D. What does that prove? I'm sure it proves they have a consistent theory. But I don't see that it proves that it is the right theory.

 

[marcus]

I'm not sure what they are trying to prove...

Which paper have you read, of those I mentioned wanting to discuss in this thread? I gave links to 3 papers. let's pick one, read it, and talk about what they are setting out to prove in that paper.

 

[Mike2]

Which paper have you read, of those I mentioned wanting to discuss in this thread? I gave links to 3 papers. let's pick one, read it, and talk about what they are setting out to prove in that paper.

So you want to talk about the intricacies of the mathematical procedure introduced in these papers irrespective of whether they are the correct theory of reality or not? Is that what I am to understand? It doesn't matter which paper you are talking about. I question the legitimacy of the whole approach. I haven't declared it wrong. But an argument that asserts A proves A is true no matter what A is. Such arguments are called "begging the question" or "petitio principii", a form of common logical error.

Perhaps an argument can be made for its legitamacy on the basis of it being a "path integral" formulation which derives spacetime as we know it. If you can show that this is the only "path integral" formulation possible, that would make for an even stronger argument for its legitamacy, though not a complete proof of its correctness. I thought I may have read something in the introduction of one of those papers to this effect. I can't remember which one.

 

[marcus]

Which paper have you read, of those I mentioned wanting to discuss in this thread? I gave links to 3 papers. let's pick one, read it, and talk about what they are setting out to prove in that paper.

In this thread I would like to discuss one or more of those 3 papers, with anyone who is interested in those particular papers and wants to understand them better.

these papers are specifically about the 2D case and sum over topologies

anyone who wants to discuss some other topic, like whether the overall CDT approach is valid (if one can tell ahead of time before empirical tests of predictions which may not yet have been derived from the theory ) is welcome to start their own thread. I will be apt to ignore off topic discussion here.

And if no one here at PF wants to discuss these 3 "sum over topologies" papers that is all right too.