How close to QG now with cellular quantization?

[marcus]

There is an issue with the new paper by Bonzom and Smerlak on cellular quantization of geometry, which surfaces in an obscure footnote #5 on page 5 at the end.

The paper http://arxiv.org/abs/1201.4996 appears to resolve most or all of the outstanding doubts concerning the Loop program. That would be too good to be true, so what's the catch?
In what ways does their paper fall short of a full resolution?

If you have some ideas about this, I hope you will share them. I'll start off by saying what I think is the main unresolved issue: concerning that footnote at the end.

 

[marcus]

Part of it depends on what you think the goal of QG is. Some people would say it is to understand the structure of geometry at very small scale. I would say it is to understand geometry at very high energy density. The two goals seem identical but there may be a subtle difference.

In terms of a standard cutoff k (standing for energy, wavenumber, inverse length...) energy density is simply the fourth power k⁴ so what's the difference between taking k to infinity and taking k⁴?

For me there is a difference because I think of a nonperturbative background independent QG achieving three things:
to recover GR in appropriate limit
to be tested against early universe observation
to resolve the GR glitch at the start of expansion, probably with a bounce.

So a successful theory of quantum geometry would have to model the bounce, an evolution through extremely high energy density that you can't put in a box. And the results of which we can observe after the fact.

The paradigm is slightly different from what one automatically thinks of as a quantum experiment---a box with a cat in it, or some other such boxed system with the experimenter and his classical paraphernalia outside.

I think if you look at footnote 5 on page 5 of the paper you will see that Bonzom and Smerlak are being told a reservation about their results which goes more or less as follows. The aim of QG is to put some geometry in a box and study it as a quantum system so that we can understand the *microscopic structure* of geometry. What you, Bon and Smer, are doing is not directly relevant to that, because a box and its contents are topologically TRIVIAL and a 2004 paper of Freidel Louapre already told how to deal with that situation.
http://arxiv.org/abs/hep-th/0401076 .
The reservation is that we don't need what they are doing (with this cellular quantization paper) because our main business is to learn about the microscopic degrees of freedom of geometry in a box and this doesn't advance that particular program.

But I think this may be the wrong perspective. It does not reflect what I think is the most interesting thing, namely the behavior of geometry at extreme energy density at the start of expansion, which we can actually OBSERVE because we see the ancient light that came from it---the microwave background---and maybe other stuff too.

Of course it could be the right perspective. In footnote 5 they are reporting comment by a very smart expert, A. Perez, so I feel a bit odd being in disagreement. I could easily be wrong about this. I hope some other people have thoughts on the matter.

 

[marcus]

the main thing about the Bonzom Smerlak paper is that it is a "proof-of-concept" of cellular quantization. It applies CQ to the pure BF theory a kind of dry run or test case and it gets the right thing..

Now pure BF is supposed to give you a topological invariant. It only sees the broad form of the space, is it sphere, is it torus etc. It has no freedom to detect ripples and suchlike local variation. Spinfoam quantum geometry is founded on BF---it takes it as a starting point and adds a constraint that breaks the BF topological invariance. It adds a term to the action that cripples its ability to ignore local variations and see only topology. And by happy good fortune the broken BF theory turns out to be General Relativity! So the spinfoam approach is based on that "lamed" form of BF.

Now BF theory can be quantized using cell-complexes: either what is called a 2-complex (foam) consisting only of the 1-cells and 2-cells, or the full cellular decomposition consisting of 1-, 2-, 3-, and 4-cells.

We are used to spinfoam QG where you just use the 2-complex, it has been in the spotlight for the past 3 or 4 years. Now Bonzom and Smerlak have proposed, and tried out, an extension of that where you quantize GR using the full cellular decomposition.

Actually you take any TRIANGULATION Δ of the 4d spacetime into simplices, and you take the DUAL to that triangulation, which is a cell complex K.

I have to go, supper. Back later.

 

[marcus]

Here's a good way to get a rough sense of what Matteo Smerlak is like.

Video seminar talk (lots of Q/A dialog with Laurent Freidel and Lee Smolin)
Is temperature the speed of time? Thermal time and the Tolman effect.
Matteo Smerlak

Google "smerlak pirsa" and get http://pirsa.org/10110071/