What's happening with Loop? (new potential challenges)

[marcus]

Some new research has emerged as a potential challenge to the main Loop version of quantum geometry/gravity. We may disagree as to which new work presents the most interesting challenge, I want to know what you think.

I personally think that the Freidel Geiller Ziprick (FGZ) paper that just came out will have a strong impact on LQG. It studies the classical phase space that LQG is presumably built on and proves a lot of results with apparent rigor. I'm struggling to understand the paper. Anybody who thinks they can summarize or interpret please do! I cannot tell as yet if the FGZ picture of LQG phase space is compatible with the current version as presented for instance in 1102.3660.

FGZ is 1110.4833: "Continuous formulation of the LQG phase space". If in fact the current Loop version can be built on this phase space foundation, it will strengthen things all around.
But I'm still trying to ascertain this.

I see the Shape Dynamics (SD) phase space as a clear challenge. If you disagree please explain.
The main SD paper I'm thinking of is Gomes Koslowski 1110.3837. This is a totally different classical phase space for quantum geometry/gravity. LQG would need drastic modification to work on it. I think.

I have to go, back soon.

 

[marcus]

Back now. The remarkable thing about SD is that it just uses a 3D manifold. For SD a 4D spacetime does not exist. It can be constructed artificially to show equivalence to classical 4D GR, but it is not fundamental to the theory.

This is intuitively right. Since 4D spacetime geometry is a "smooth trajectory" it should not exist any more than quantum theory allows for the trajectory of a particle. One only ever makes a finite number of measurements and thus knows where the the particle was at only a finite number of points---the rest is uncertain. The 4D block universe geometry with its predetermined future eternity (including e.g. every last radioactive decay) is a repugnant unnatural notion. So that is a fine thing about SD. It lives on a 3D manifold.

But this raises it's own set of problems. How do Gomes Koslowski (authors of 1110.3837) cope with them? Page 8, section 6 "reconstruction of spacetime":

General Relativity is a theory of the spacetime metric, but the physical interpretation of the dynamical metric as the geometry of the universe arises through a clock and rod model given by the matter content of the theory. We can thus view the operationally defined geometry as fundamental and only accept it as a nice feature of General Relativity to use the spacetime metric as a fundamental field. Terms like “light cone“ put the operational meaning of geometry to the forefront. Shape Dynamics does not immediately provide a spacetime metric at a glance, but a spacetime interpretation of Shape Dynamics comes operationally out of a clock and rod model in the same way as it does in General Relativity. The simplest clock and rod model is a multiplet of massless free scalar fields, which we will consider here.​

Page 10 last paragraph of conclusions:

Second, we found that an operational spacetime picture of SD can be obtained straightforwardly through a clock and rod model constructed from matter fields. At a superficial level this is surprising, because SD has a notion of simultaneity and naively it would seem that SD breaks Lorentz invariance. This would violate the very idea of spacetime that is at the heart of our understanding of special and general relativity. However, this conclusion is premature. Let us assume for a moment that we had access to GR-matter trajectories but not to the spacetime metric. Then we would have to adopt an operational description of spacetime much like the idea that underlies noncommutative geometry (see opening quote). We would then recover spacetime precisely along the lines outlined in section 6. Hence the spacetime picture of SD is the same as an operationally defined spacetime picture in GR.​

One of the SD papers I have been reading has given me a special regard for James W. York, formerly of the University of North Carolina at Chapel Hill and now emeritus at Cornell. For references to York see 1010.2481 page 3.

 

[marcus]

The challenge from SD is already at the level of what the classical configuration space ought to be. Here is a quote from 1010.2481 page 3:

York began his 1973 paper [6] on the conformal approach to the initial value problem by stating: “An increasing amount of evidence shows that the true dynamical degrees of freedom of the gravitational field can be identified directly with the conformally invariant geometry of three–dimensional spacelike hypersurfaces embedded in spacetime.” He continues: “the configuration space that emerges is not superspace (the space of Riemannian three–geometries) but ‘conformal superspace’...​

What York says means by 'conformal superspace' is the space where each point is a conformal equivalence class of Riemannian three–geometries---then cross this with the real line (time) so you get paths through the space of all conformal 3-geometries. He did not develop the idea completely in that seminal 1973 paper.

Despite these bold claims, he does not show that the dynamics actually projects down to curves on conformal superspace nor does he provide an explanation for how the 4D diffeomorphism invariance of general relativity could be related to 3D conformal invariance. In this paper, we fill in these gaps.​

So there is a possible argument about what the true dynamical degrees of freedom actually are! and thus on what basis one should build the quantum theory of dynamically evolving geometry.

Either way, classical geometry/gravity is about paths through a space of 3D geometries, and the quantum version (QG) is about the analogous histories of evolving quantum geometry: paths through a realm of quantum geometries. But which superspace? Should it be the space of conformal-invariant geometries where local size is ignored? Or not?

I seem to recall Rafael Sorkin explaining that 9/10 of the d.o.f. in GR are causality, and only one is local size. If you know the causal relations between all the events, and in addition add one more piece of information, a local size factor, then you can reconstruct the metric. He could have been talking about "shape" instead of "causality"---perhaps they're related.

To me, SD does not sound at all compatible with LQG. I'm hoping someone can convince me otherwise.

On the first day of the Loops 2011 conference (Monday 23 May) much of the afternoon session--until 5 PM actually-- was devoted to talks on Shape Dynamics. There were five talks on it, including ones by Koslowski and by Gomes. Obviously the Loop researchers were interested in hearing about SD, which now seems to emerge as a competing approach with a different idea of the classical configurations or degrees of freedom to be quantized.
http://www.iem.csic.es/loops11/

Perhaps the overall most interesting development is the FGZ (Freidel Geiller Ziprick) paper that I mentioned in post #1, and not anything to do with Shape Dynamics. It will take me some time to assess this and make the comparison. Any help would be welcome.

 

[MTd2]

Marcus, this is the best introduction for http://arxiv.org/abs/1105.0183

Just like General Relativity, or Special Relativity, it is a world on its own in terms of philosophy. That paper explains the foundations very well.

SD is based on the Mach Principle and that instead of a clock and a ruler, the fundamental measurement device is the angle.

 

[marcus]

Please look back to post #2 where I quote the main SD paper I'm concerned with. The authors, Gomes Koslowski talk a lot about clock and rod construction.

Of course I know that conformal maps are angle-preserving and forget about linear size.
However it may not be as simple as you imagine. The conformal equivalence relation is only spatial. There still seems room for a clock in this picture .

Until I understand better I have to focus on what Gomes Koslowski say (it is their paper, not Father Julian's). And they talk about clock and rod operational definitions. What do they mean?

 

[MTd2]

The theory itself is free of clocks because all that there is curved 3 manifold with a Newtonian universal time. So, the concept of clock happen when you construct a clock with matter, literally.

 

[marcus]

Right! And I think this bears a strong resemblance to how it actually is in Nature, don't you?

 

[MTd2]

Right! And I think this bears a strong resemblance to how it actually is in Nature, don't you?

And since it has a preferential folliation, things faster than light will naturally warp, like in Star Trek, no kidding, since causality cannot be broken.

 

[tom.stoer]

I agree that there are challenges, but they are coming from the loop program itself, not from outside; and they are not new, unfortunately

 

[marcus]

Then would you say, Tom, that because there are some old challenges we should not think about new challenges?

 

[tom.stoer]

no, we should discuss both; but to me the situation looks as follows: we do not know (yet) whether LQG is complete, consistent, reproduces GR in the IR; so in order to compare LQG with other approaches we first must understand what to compare - and if there is something to compare at all

 

[martinbn]

no, we should discuss both; but to me the situation looks as follows: we do not know (yet) whether LQG is complete, consistent, reproduces GR in the IR; so in order to compare LQG with other approaches we first must understand what to compare - and if there is something to compare at all

What are the approaches for quantizing gravity that are complete, consistent and reproduce GR?

 

[tom.stoer]

What are the approaches for quantizing gravity that are complete, consistent and reproduce GR?

There are no such approaches :-(

 

[marcus]

Then would you say, Tom, that because there are some old challenges we should not think about new challenges?

no, we should discuss both;...

I'm content with that. I am eager to hear if you have anything to day about the Freidel Geiller Ziprick paper (FGZ) but I will also try to discuss other questions if you want. If I may (since that is an interest of yours) I'll also update us on the efforts to show LQG has the GR limit. As I recall Claudio Perini just posted something about that on arxiv yesterday.

But we have is a multifront program with simultaneous advances on several fronts. What, to me, is the most urgent and interesting to consider right now is FGZ. I see it as either a major challenge or a major step forwards. (If it helps to remember the initials, one can think of the antiwar rock band cofounded by http://en.wikipedia.org/wiki/Tuli_Kupferberg" in the 1960s.)

I've been reading this Rovelli Speziale paper cited by FGZ and it looks to me as if FGZ MIGHT have made some progress on an issue that has interested you sometimes.
This is the relation between on the one hand the (Zakopane, say) abstract spinfoam formulation and on the other hand the earlier Ashtekarian+LOST theorem+maybe even Hamiltonian version.
Anyway that seems to be what Freidel is trying to do. He got a break from Bianchi's recent "dynamics of topological defects" because that works with embedded networks. So not so abstract. Networks of topological defects, in fact. I think he is trying to bridge some kind of gap---I'm still trying to understand the significance of the FGZ paper. If you get around to examining it one of these days I'll be glad to hear your reflections on it.

The question for me is whether what FGZ is doing is compatible with the current formulation, or not.

 

[xristy]

1102.3660: Carlo Rovelli; http://arxiv.org/abs/1102.3660"

1110.4833 (FGZ): Laurent Freidel, Marc Geiller, Jonathan Ziprick; http://arxiv.org/abs/1110.4833"

1110.3837: Henrique Gomes, Tim Koslowski; http://arxiv.org/abs/1110.3837"

1010.2481: Henrique Gomes, Sean Gryb, Tim Koslowski; http://arxiv.org/abs/1010.2481"

1105.0183: Julian Barbour; http://arxiv.org/abs/1105.0183"

 

[marcus]

Xristy, thanks for assembling these links! They are some of the most important for the current discussion and very nice to have handy.

1102.3660: Carlo Rovelli; http://arxiv.org/abs/1102.3660"

1110.4833 (FGZ): Laurent Freidel, Marc Geiller, Jonathan Ziprick; http://arxiv.org/abs/1110.4833"

1110.3837: Henrique Gomes, Tim Koslowski; http://arxiv.org/abs/1110.3837"

1010.2481: Henrique Gomes, Sean Gryb, Tim Koslowski; http://arxiv.org/abs/1010.2481"

1105.0183: Julian Barbour; http://arxiv.org/abs/1105.0183"

I am beginning to think that since 2008 we are seeing a DOUBLE revolution in Loop gravity. First there clearly was a revolution in spinfoam dynamics, which resulted in the formulation that we see in the Zakopane lectures. Perhaps the first full presentation was in the "New Look" paper of early 2010, from which the Zakopane lectures, a year later, are an expanded version.

But I think we are now also having a revolution in the HAMILTONIAN side of LQG, with Laurent Freidel's initiative. I think a new LQG formulation will come out of this FGZ paper.
If I am right it could be one of the most highly cited LQG papers of 2011.

 

[atyy]

The question for me is whether what FGZ is doing is compatible with the current formulation, or not.

http://arxiv.org/abs/1110.4833" seem to think it is. In their final paragraph: "It also allows us to reconcile the tension between the loop quantum gravity picture, in which geometry is thought to be singular, and the spin foam picture, in which the geometry is understood as being locally flat. We now see that both interpretations are valid and correspond to different gauge choices in the equivalence class of geometries represented by the fluxes."

 

[tom.stoer]

Plesae have a look at https://www.physicsforums.com/showthread.php?t=544728; I plan to continue with SFs quite soon

 

[qsa]

Does SD say anything about singularity or cosmological scale behavior. If not .what is the point. Ok time is not important, so.

 

[Finbar]

Thanks marcus for bring the FGZ paper to my attention.

I think it touches on an important point which is often glossed over in loop papers.
Namely that discretization and quantization need to be disentangled. Discretization is
always a necessary when you want to quantize continuous degrees of freedom.

Maybe such a paper can teach us something about the continuum limit in LQG.

 

[marcus]

Thanks marcus for bring the FGZ paper to my attention.

I think it touches on an important point which is often glossed over in loop papers.
Namely that discretization and quantization need to be disentangled. Discretization is
always a necessary when you want to quantize continuous degrees of freedom.

Maybe such a paper can teach us something about the continuum limit in LQG.

Yes. This is such an important point!

I have taken your insight (without giving you credit ) as a help to make a couple of posts in Tom Stoer's original "prospects for canonical" thread.

Freidel and his collaborators have, in effect, invented Loop Classical Gravity.

I did not realize how much that needed to be done until I had been reading the paper for a couple of days.

 

[Finbar]

One thing that confuses me is whether " loop classical gravity" should have the same degrees of freedom as general relativity. Somehow at the classical level it should be the same at least in the continuum limit. Is this still an open question?

"We can now face the question of whether the dynamics of classical general relativity can be formulated in terms of these variables."

They also talk about how the difference between Regge geometries and the one coming from the loop variables...

 

[marcus]

You made the main point about this when you said LCG has to have a finite number of d.o.f. in order to be quantized. Or as you put it, it would have to be "discretized".
And then there is some limit process to recover the full infinite d.o.f.

I hope this is a fair interpretation of your post.

Types of limits are set by human convention on pragmatic grounds. Does a particular limit process/method let you calculate what you want and do your answers converge to the right thing? If so, then it is a good type of limit process.

The Ashtekar Lewandowski measure (which Bianchi has some good words about in his PIRSA talk) is a projective limit. there are a bunch of different limits defined in math. Limit in the sense of nets... I think you have mentioned a few in other posts. You know about that stuff. What type of limit is practical depends on the structure you are taking limits of. Usually there is at least a partial ordering on some set of things.

So perhaps what we should do is simply go look at the discretization presented in FGZ , which depends on some graph Gamma, and see how the limit goes. I'll look for the part of the paper where they address that issue.

BTW Finbar, you may have noticed this:there is a minor typo in the second line from the top of page 6 where it should say that g_v is a member of G_Γ
For our convenience here is the link http://arxiv.org/abs/1110.4833
G_Γ ≡ SU(2)^|V_Γ|

The notation is fairly familiar and transparent. |V_Γ| is the number of vertices of the graph, and you just cartesian that many copies of SU(2)

so g_v is really an n-tuple of one group element for each vertex, or more exactly a|V_Γ|- tuple

 

[marcus]

Further down the page on page 6 they give a clue how they are going to work the recovery of the infinite d.o.f.

==quote==
The question we would like to address is: What is the relationship between the continuous phase space P described in the previous section, and the spin network phase space P_Γ? More precisely, we would like to know if it is possible to reconstruct from the discrete data P_Γ a point in the continuous phase space P? In order to describe the relationship between the discrete and continuous data, we need a map from the continuous to the discrete phase space. We can then study its kernel and see to what extent it can be inverted. This is the object of the next sections.
==endquote==

 

[marcus]

Also Finbar the FGZ program is still in progress. As I recall at the end they basically said "to be continued". They still have to study some kind of refinement limit, I think.
They have a symplectomorphism that is invertible and goes back from the discrete phase space to a certain (dense?) subset of the continuous phase space.

By "dense?" I don't mean just for one fixed graph Gamma but if you consider all the graphs. And all the piecewise flat geometries. My understanding is pretty vague and sketchy here. I think they are telling us to expect a followup paper and I'm trying to imagine what direction it will take. So far what they have constructed is an invertible mapping between continuous and discrete phase spaces for a specific fixed graph or fixed cellular decomposition of the 3d manifold. I'd be interested to know your thoughts about this and if I'm missing something.
==================================

Tomorrow, 1 November, Tim Koslowski gives a talk on Shape Dynamics at the online ILQGS (international LQG seminar):
http://relativity.phys.lsu.edu/ilqgs/

 

[Diffeomorphic]

I would suggest checking out the new paper by Sean Gryb and a philosopher Karim Thebault discussing the problem of time, and how Shape Dynamics is free of the local problem of time!

http://arxiv.org/abs/1110.2429

 

[marcus]

Thanks for the pointer!
I see that Sean Gryb is now at Utrecht in Renate Loll's group.
I had not seen anything by Karim Thebault, he is new to me. Here is an earlier paper:
http://arxiv.org/abs/1108.4731
Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?
I see Karim Thebault is at the Sydney Center for Time
(Centre for Time, School of Philosophical and Historical Enquiry, University of Sydney, Australia)
I think one of Rovelli's PhD students (Florian Girelli?) has taken a postdoc at Sydney.

Just for reference I will copy the Gryb Thebault abstract:
http://arxiv.org/abs/1110.2429
The role of time in relational quantum theories
Sean Gryb, Karim Thebault
(Submitted on 11 Oct 2011)
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the classical dynamics of the full system. We propose a new strategy for consistently quantizing systems with a relational notion of time that captures the full classical dynamics of the system and allows for evolution parametrized by an equitable internal clock. This proposal contains the minimal temporal structure necessary to retain the ordering of events required to describe classical evolution. In the context of shape dynamics, an equivalent formulation of general relativity that is locally scale invariant and free of the local problem of time, our proposal constitutes a natural methodology for describing dynamical evolution in quantum gravity.
19 pages, 2 figures

 

[marcus]

1102.3660: Carlo Rovelli; http://arxiv.org/abs/1102.3660"

1110.4833 (FGZ): Laurent Freidel, Marc Geiller, Jonathan Ziprick; http://arxiv.org/abs/1110.4833"

1110.3837: Henrique Gomes, Tim Koslowski; http://arxiv.org/abs/1110.3837"

1010.2481: Henrique Gomes, Sean Gryb, Tim Koslowski; http://arxiv.org/abs/1010.2481"

1105.0183: Julian Barbour; http://arxiv.org/abs/1105.0183"

Tim Koslowski has given his International LQG Seminar talk and the PDF is posted online
http://relativity.phys.lsu.edu/ilqgs/koslowski110111.pdf

The audio is not yet available. He is forthright about pointing out the possible drawbacks and unresolved problems of Shape Dynamics. I think the openness gives the talk extra value. He talks about the LOOP QUANTIZATION of (classical) SD. He refers to a paper of his that is not yet out.

I have no clue as to where or how this SD business is going to go. Do some others here have a hunch about it?

 

[marcus]

Tim Koslowski seminar talk at ILQGS
http://relativity.phys.lsu.edu/ilqgs/
they just got the audio online too. So you click on the PDF to have the slides ready.Then you start the audio and he tells you "next slide" as he goes thru the talk.

Tim has a paper in the works about quantizing Shape Dynamics (which is classical so far).
He is using Loopy methods, but because the starting point is different it will be a different theory.

 

[Chronos]

The apparent lack of diffraction in light emitted by distant quasars at gamma ray frequencies is disturbing to me. I often wonder what test might be devised to incontrovertably resolve the issue of whether space is digital or analog.

 

[tom.stoer]

The FGZ paper is a great attempt to discuss as much as possible on the classical level, i.e. identifiying issues already at the classical level, and seperating them clearly from quantization issues. It shows clearly that there is a kind of discretization not related to quanization. It shows how to reconstruct spacetime.

It explains that there are two gauges, namey the LQG and the SF gauge! This questions the LOST theorem b/c
a) there may be even more gauge choices available
b) they may be missed by LOST just as the SF gauge was (which sems to be uncritical as this is a kind of duality)
c) there may very well be different and inequivalent quantizations

Looking at standard QFTs usually one fixes the dynamical variables, fixes a local symmery i.e. implements some constraints and quantizes the theory (or the other way round). In GR / LQG it seems that there are several steps where different dynamical variables are used, several steps where local symmetres are fixed (gauge, spacelike diff., ...) and it is by o means clear how many different choices and orders there are, at which point in time one should quantize and whether all these different steps and limits do commute.

 

[Diffeomorphic]

Well, I sure hope Shape Dynamics turns out as it seems to have a bright future. I had the privilege to talk with Sean Gryb for a few days when he was at PI and he was really excited about what him and the other people like Tim Koslowski had planned for it. He was really was astounded that within the SD formalism GR became re-normalizable, and he was talking about constructing a quantum theory of SD with some collaborators. I'm pretty excited that I get to publish a paper with him. :D

 

[marcus]

Well, I sure hope Shape Dynamics turns out as it seems to have a bright future. I had the privilege to talk with Sean Gryb for a few days when he was at PI and he was really excited about what him and the other people like Tim Koslowski had planned for it. He was really was astounded that within the SD formalism GR became re-normalizable, and he was talking about constructing a quantum theory of SD with some collaborators. I'm pretty excited that I get to publish a paper with him. :D

That's absolutely wonderful! What great news! Here's wishing you every possible success in your collaboration with Sean Gryb.

BTW, since other people may not have seen this, I recall that you introduced yourself in a Academic or Career thread (I forget which) as having a dual honors major at U. Calgary in Astrophysics and Appl. Math. and after finishing first year you went to Perimeter summer program. So it you and Sean would have had some conversations at PI this summer. Is there a PIRSA talk that describes the *SD renormalizable* result which Sean was excited about? Any particular PIRSA video you want to recommend, or a specific part of a particular SD paper? I can often use pointers. And about SD I don't know alot.

 

[tom.stoer]

Besides SD we should add AS.

There are recent attempts to apply AS to Ashtekar-like / first-order formalism of GR including the Holst-term and to study the scaling of G, Lambda and the IP.

 

[marcus]

Besides SD we should add AS.

There are recent attempts to apply AS to Ashtekar-like / first-order formalism of GR including the Holst-term and to study the scaling of G, Lambda and the IP.

Good point. A paper that appeared yesterday illustrates what you said about the Immirzi parameter (IP) coming up in Asymptotic Safety gravity:

http://arxiv.org/abs/1111.1000
Running Immirzi Parameter and Asymptotic Safety
Jan-Eric Daum, Martin Reuter
(Submitted on 3 Nov 2011)
We explore the renormalization group (RG) properties of quantum gravity, using the vielbein and the spin connection as the fundamental field variables. We require the effective action to be invariant under the semidirect product of spacetime diffeomorphisms and local frame rotations. Starting from the corresponding functional integral we review the construction of an appropriate theory space and an exact funtional RG equation operating on it. We then solve this equation on a truncated space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory. It is probably inequivalent to metric quantum gravity constructed in the same way.
To appear in the proceedings of CORFU 2010