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Rovelli's talk at Perimeter 4/4/12: video online, comment?

by marcus
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marcus
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Apr4-12, 04:36 PM
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http://pirsa.org/12040059
Fine presentation today, room packed, good questions from audience (esp. from Turok but also from others.)

Rovelli will spend several weeks at Perimeter during which time he also makes a side trip to Princeton Institute for Advanced Study to give a slightly different talk:

http://www.princeton.edu/physics/eve...ent.xml?id=347
High Energy Theory Seminar - IAS - Carlo Rovelli, Aix-Marseille University, France
Loop quantum Gravity: Recent Results and Open Problems
Description: The loop approach to quantum gravity has developed considerably during the last few years, especially in its covariant ('spinfoam') version. I present the current definition of the theory and the results that have been proven. I discuss what I think is still missing towards of the goal of defining a consistent tentative quantum field theory genuinely background independent and having general relativity as classical limit.
Location: Bloomberg Lecture Hall
Date/Time: 04/23/12 at 2:30 - 3:30 pm

He will also be giving a series of lectures on QG at the University of Vienna during the first week of September:
http://www.coqus.at/events/summerschool2012/
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genneth
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Apr4-12, 09:47 PM
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Very interesting. The thing which is new (in that one had to read between the lines rather than hear him say in papers) is that essentially commuting the classical and continuum limit is currently tricky, if not outright unknown. I think this is essentially the problem that Tom has been drawing our attention to, in the form of properly (whatever that might mean) quantising the constraints in the canonical formalism. Whilst I completely agree with the sentiment, I personally (betraying my roots in condensed matter) think that the proof will be in the eating of the pudding --- I think that before we have the necessary mathematics to properly quantise those constraints we will find by pure computation and comparison with experiment whether the theory as written is viable (not withstanding all the recent excitement about perhaps needing to restrict the type of triangulation allowed in order to get the right bit of the state sum).

Summarising: very nice talk with honest appraisal of the state of play --- something which can be hard to glean from papers.
atyy
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Apr4-12, 11:49 PM
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Quote Quote by genneth View Post
Very interesting. The thing which is new (in that one had to read between the lines rather than hear him say in papers) is that essentially commuting the classical and continuum limit is currently tricky, if not outright unknown. I think this is essentially the problem that Tom has been drawing our attention to, in the form of properly (whatever that might mean) quantising the constraints in the canonical formalism.
Here's a paper which has a very brief discussion about it:
http://arxiv.org/abs/0809.2280
"In a sense, one needs that the large spin limit and the integration over the spins commute with each other. Whether this happens or not is not obvious: one might be worried, for instance, that the summation over spins is much less restricted than a summation over discrete geometries and that this will lead to stronger equations of motions. It might be, on the other hand, that the exponential suppression of non Regge–like configurations is strong enough to effectively reduce the summation to a sum over geometries. This is an important question that deserves to be studied further."

I think the FGZ paper is somehow related, but am not sure.

marcus
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Apr5-12, 02:23 AM
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Rovelli's talk at Perimeter 4/4/12: video online, comment?

Quote Quote by genneth View Post
... Whilst I completely agree with the sentiment, I personally (betraying my roots in condensed matter) think that the proof will be in the eating of the pudding --- I think that before we have the necessary mathematics to properly quantise those constraints we will find by pure computation and comparison with experiment whether the theory as written is viable ...
Yes and yes! While I too share the sentiment that all should be done properly (whatever that means), I also think, as you say, that the primary test of whether the theory as written is viable will probably be empirical. "The proof of the pudding is in the eating."

It's nevertheless interesting to watch the struggle around that rectangular diagram, to get from the lower left corner to the upper right, involving two kinds of limits. At the moment my attention is focused on the Warsaw group's proposal (SN-diagrams) to make systematic the process of summing amplitudes of spinfoams up to a certain level of complexity---a number N of vertices.

I hope that proposal can be implemented as a computer algorithm. It seems to give a way to systematically generate all the spinfoam histories up to a certain complexity "cutoff" level (of course just those histories bounded by a certain spin network giving initial and final state information.) To me that seems like part of empirically "proving the pudding". Have the computer calculate and sum transition amplitudes up to some N. Then increase N, and see. I think you understand even more clearly the kind of thing I have in mind.

If anyone else is reading and is curious about this, google "puchta feynman arxiv" to get the Warsaw group's spinfoam feynman diagrams paper. In any case thanks both Atyy and Genneth for comments. I had to be out this evening so could not reply until now, which is past midnight here. Let's see how it looks in the morning.
marcus
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Apr5-12, 12:56 PM
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Let's look at the PDF slides for Rovelli's talk and identify a few important ones.
There are 49 slides. The most important is surely going to be #19, but there will be a few others (e.g. #9) to mention as well.

Slide #19 is the rectangle diagram titled The general structure of a parametrized (general covariant) quantum theory.
Quantum theory                                              Classical theory
Transition amplitude           hbar→0                   Hamilton function
W(x,x')                                                          S(x,x')

∞                                                                 ∞
↑                                                                  ↑
N                                                                  N

Discretised                                                     Discretised 
quantum theory              hbar→0                      classical theory
WN(x,x')                                                        SN(x,x')
The horizontal left to right limit is taken as hbar→0, the usual classical limit.
The vertical upwards limit is taken as N, the number of steps or more generally the complexity of the discretisation, goes to infinity. Since there is no prior metric, there can be no idea of a "lattice scale" to shrink to zero. But one can, for example let N→∞ where N is the simply the number of vertices in foam histories contained in a given spin network boundary result.

In Rovelli's case, the lower right corner of the quad is REGGE CALCULUS and that path from Loop to GR does seem workable. Indications are the classical limit of LoopN (lower left) is Regge (lower right) for fixed finite discretisation cutoff N, although that can still be argued about. And then the upwards limit from Regge to GR, as N→∞, takes you the rest of the way.

But we'd like more than that. We'd like it to be clear that you can start in lower left with LoopN and let N→∞ and run straight up to a nice finite well-defined limit theory Loop at the upper left corner of the quad. With no limit, then, on how complex the spinfoam histories can be.

Personally I would not mind seeing that explored numerically in several cases, by machine.
The Warsaw group seems to be examining prospects of a computable algorithm that would let N be systematically increased. Both Rideout and Christensen have each applied heavy duty cluster computing to this kind of thing. I wonder if something analogous will happen in this case. My private sense is the Warsaw algorithm is ingenious and *deserves* to be run. We'll see.
atyy
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Apr7-12, 02:10 AM
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I haven't had time to watch the whole thing - does Rovelli say anything about the Rovelli-Smerlak proposal to take the continuum limit (summing = refining)?
genneth
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Apr7-12, 05:23 AM
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Quote Quote by atyy View Post
I haven't had time to watch the whole thing - does Rovelli say anything about the Rovelli-Smerlak proposal to take the continuum limit (summing = refining)?
Arguably the whole talk is based around it. The way Rovelli puts it is that in a generally covariant theory the discretised version reaches the continuum by just increasing the number of sampling points without a need to tune any parameters. This is in distinction to lattice QCD, for example.
marcus
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Apr7-12, 07:46 AM
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Quote Quote by atyy View Post
I haven't had time to watch the whole thing...
It's tough not having time to watch an hour lecture. Demands on my time change from week to week and fortunately right now are light, but I know what you mean.

If anyone else has the time right now there's a related hour lecture that R. gave that morning which is meant to serve as a supplement (with additional examples and detail about the Hamilton function and mechanics without treating time specially.)

He tells the students they can treat the morning talk as "part of" the colloquium.
The relevant lecture is number 3 in what will probably turn out to be a series of 12 lectures--
four a week for three weeks or so, starting 2 April.

http://pirsa.org/C12012

Perimeter has these 3-week or so courses, the eleventh one they started this year would I guess be C12011.
R.'s is the twelfth course they started this year so it is C12012. I'm guessing that this one is just Mon-Thu, with a Fri-Sun break. We'll see. Anyway the morning talk for the dozen-or-so students on 4 April was a considerable help to understand the afternoon 4 April colloquium.

The individual URL for that day's morning talk is http://pirsa.org/12040021/ but you don't really need that if you have the C12012 URL for the whole three(?) week course series.

Bianca Dittrich was in the audience at the colloquium.
atyy
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Apr7-12, 08:59 AM
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Quote Quote by genneth View Post
Arguably the whole talk is based around it. The way Rovelli puts it is that in a generally covariant theory the discretised version reaches the continuum by just increasing the number of sampling points without a need to tune any parameters. This is in distinction to lattice QCD, for example.
Did he say anything about the existence of such a limit? I think most people thought the Rovelli Smerlak limit didn't exist, and was actually divergent.
genneth
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Apr7-12, 02:42 PM
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Quote Quote by atyy View Post
Did he say anything about the existence of such a limit? I think most people thought the Rovelli Smerlak limit didn't exist, and was actually divergent.
Yes, at the end, as one of the open problems --- he considers it a question of well-behaveness of radiative corrections. To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below). His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.
marcus
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Apr7-12, 04:04 PM
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Quote Quote by genneth View Post
... To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below)...
You could be right. I didn't hear any explicit mention of that q-deformed version, with positive cosmo constant. But it would make sense. I may have missed something and should listen to the talk again. I like what you say here:

*His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.*

This seems like a good way to put it. For instance, restrict to the N=1 case (as I recall a Lewandowski et al paper does) and see what you get. With just one internal spinfoam vertex. And simple S3 geometries for initial and final.

Or pick some other finite N as limit of the number of internal vertices, and repeat what you did for N=1. Frank Hellmann's thesis was along these lines---I forget the details, like what N was. Lewandowski seems to be a leader in equipping for this research direction. Jack Puchta gave a ILQGS talk on it.

As I recall they already have some interesting results for very basic cases. So we'll see: is it useful?

======EDIT to reply to next post======
Genneth thanks for catching that!

Quote Quote by genneth View Post
It's not in the slides, but his (spoken) words refer to it. In addition, when discussing the finiteness issue, he clearly states (but again, only spoken) that it is UV finite always but only IR finite if one takes the q-deformed version.

A potential snag with the non-q-deformed version might be that it is difficult to say what UV vs IR limit really means -- precisely because it is just refinement either way. Nevertheless, I hope it is obvious (which probably means it is not) that the deformed theory is simply finite for any finite boundary state.
I just listened to the whole talk (not including questions at the end) and heard the points you mentioned. Right now I don't have anything to add to your post #12, so will not spend a post simply to say Amen.
genneth
#12
Apr7-12, 06:11 PM
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Quote Quote by marcus View Post
You could be right. I didn't hear any explicit mention of that q-deformed version, with positive cosmo constant. But it would make sense. I may have missed something and should listen to the talk again.
It's not in the slides, but his (spoken) words refer to it. In addition, when discussing the finiteness issue, he clearly states (but again, only spoken) that it is UV finite always but only IR finite if one takes the q-deformed version.

A potential snag with the non-q-deformed version might be that it is difficult to say what UV vs IR limit really means -- precisely because it is just refinement either way. Nevertheless, I hope it is obvious (which probably means it is not) that the deformed theory is simply finite for any finite boundary state.
marcus
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Apr7-12, 10:27 PM
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I can see I'm going to have to get to know Pirsa 12040059 better and also the paper that is closest to it in concept and content: Arxiv 1108.0832
The paper paralleling the talk is On the Structure of a Background Independent Quantum Theory

It has the quadrangle diagram that I copied in post #5, which is slide #19 of the talk. It's Table I of "On the Structure"

And it also has, as its table II, the corresponding diagram that you get when the concepts are applied to a CELL COMPLEX C, and you take the limit in the sense of nets, since cell complexes form a directed set. (This is common enough as mathematics but may not be familiar to everybody.) This appears a half-dozen times in the talk, as slides #26, #30, #34, #39, #43, #44, ... and more. This quadrangle diagram comes under the heading General Structure of Quantum Gravity--see slide #48:
Exact quantum gravity                                   General Relativity
transition amplitudes           hbar→0                Hamilton function
W(hl)                                                          S(q)

∞                                                                 ∞
↑                                                                  ↑
C                                                                  Δ

LQG                                                             Regge
transition amplitudes             hbar→0               Hamilton function
WC(hl)                                                          SΔ(libdry)
source paper http://arxiv.org/abs/1108.0832
colloquium talk http://pirsa.org/12040059
concurrent beginner course http://pirsa.org/C12012 e.g. http://pirsa.org/12040019 , 0020, 0021,...

It's nice how things are coming together. There is that excellent introductory course for beginners, running concurrently in online video, that develops this same material at simpler level over several mornings---and there is the oneshot higher level presentation in colloquium, also online video. And there is the August 2011 paper, which in effect the colloquium is explaining, and which gives the gist in compact form you can print out.
atyy
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Apr9-12, 09:54 AM
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Quote Quote by genneth View Post
Yes, at the end, as one of the open problems --- he considers it a question of well-behaveness of radiative corrections. To be concrete, the system he really has in mind is the q-deformed version with a cosmological constant, which makes the sum obviously finite (the representations are bounded from above as well as below). His phrasing of the problem is then that of whether the N-vertex expansion is a useful one, i.e. does the first few terms really provide a good approximation to the full theory.
Isn't the q-deformation supposed to solve a different divergence than the continuum limit, ie. the continuum limit still seems divergent after q-deforming?

By continuum limit, I'm thinking of Eq 26 in http://arxiv.org/abs/1010.1939. The discussion following talks about q-deformation, and the limit of Eq 26 as different things.
genneth
#15
Apr9-12, 01:14 PM
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Quote Quote by atyy View Post
Isn't the q-deformation supposed to solve a different divergence than the continuum limit, ie. the continuum limit still seems divergent after q-deforming?

By continuum limit, I'm thinking of Eq 26 in http://arxiv.org/abs/1010.1939. The discussion following talks about q-deformation, and the limit of Eq 26 as different things.
It would solve both. The sums that are in Eq 25 of that paper become completely finite --- there are literally only a finite number of terms which contribute.
marcus
#16
Apr9-12, 05:24 PM
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Links to Rovelli's online video course in LQG, which goes along well with the source paper On the Structure of a Background Independent Quantum Theory and with the colloquium talk Transition Amplitudes in QG
that we are considering, will be given here http://pirsa.org/C12012

Lecture 1 http://pirsa.org/12040019
Lecture 2 http://pirsa.org/12040020
Lecture 3 http://pirsa.org/12040021
Lecture 4 http://pirsa.org/12040022

Lecture 5 http://pirsa.org/12040026
Lecture 6 http://pirsa.org/12040027 expected
Lecture 7 http://pirsa.org/12040028 "
Lecture 8 http://pirsa.org/12040029 "

The first 5 lectures are now online. Hopefully there will be a third week as well.
For reference:
On the Structure... http://arxiv.org/abs/1108.0832
Transition Amplitudes...http://pirsa.org/12040059
atyy
#17
Apr9-12, 06:47 PM
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Quote Quote by genneth View Post
It would solve both. The sums that are in Eq 25 of that paper become completely finite --- there are literally only a finite number of terms which contribute.
Yes, Eq 25 would be finite under q-deformation, but how about Eq 26, where C -> ∞ ?
genneth
#18
Apr9-12, 07:40 PM
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Quote Quote by atyy View Post
Yes, Eq 25 would be finite under q-deformation, but how about Eq 26, where C -> ∞ ?
One needs to keep in mind that an amplitude is always associated with a boundary state. If you keep adding vertices then eventually the only way to satisfy the tetrahedral inequalities will be to force some faces to be of zero size due to area quantisation. In other words, you can't actually keep refining if the boundary state itself is finite.

The q-deformation just ensures that the boundary state will be.


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