If LQG now satisfactory, how to add matter?

[marcus]

Currently the two definitive papers are 1004.1780 and 1010.1939, with several others applying spinfoams to cosmology e.g. 1003.3483.

LQG is about where one could have predicted back in Fall 2008, with the merger of the canonical, covariant, and cosmological versions. I think in fact one or more people here at PF did observe that trend and predict that. It unifies the theory and brings it closer to testability, because early-universe cosmology is a potential venue for testing.

The present form of LQG is at the intersection of lines of work by Ooguri, Atiyah, Feynman, Regge, Penrose. The October paper mentions that it follows from 3 separate approaches:
1. Canonical quantization of the conventional phase space of General Relativity
2. Polyhedral quantum geometry
3. Covariant lattice quantization
For details, see 1010.1939

Thus there are signs that the present form of LQG is a satisfactory theory of quantum geometry/gravity without matter. Matter still has to be introduced.
So the question concerns the logical next step. Assuming that what we see will turn out to be satisfactory, how can matter be laid on to the spacetime foundation it provides?

At first sight, in the one-page formulation given in the October paper, you see a list of FEYNMAN RULES GOVERNING TWO-COMPLEXES.
There is a half-page section on page 1 of 1010.1939 called "Feynman Rules" which at the end says "This completes the definition of the model."

The 4 Feynman rules determine how to calculate transition amplitudes, for the two-complexes. That defines LQG.

So at first sight, and this may be correct as well, the theory is a theory of two-complexes, so if matter is to be added to the picture it must carried by the two complexes.

That's one possibility. I'd like to hear any ideas about how this could be done, or about other schemes for including matter.

 

[atyy]

LQG is not satisfactory. The physical innner product is probably divergent (in addition to the IR divergence). My own guess is that it needs GFT renormalization. And I would prefer if gravity and matter should both emerge together from a GFT.

 

[tom.stoer]

The physical innner product is probably divergent

Can you post a reference?

And I would prefer if gravity and matter should both emerge together from a GFT.

Emergence of matter - yes; but from GFT? How?

 

[bcrowell]

As an outsider and total ignoramus about LQG, the statement that LQG is OK except for the need for coupling to matter seems a little implausible. Maybe I'm just an idiot, but to me, this would seem to imply that LQG was currently able to reproduce any result that you could get in the classical limit from the vacuum field equations of GR, and to examine the quantum effects when the classical limit doesn't apply. Is this really true? Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

 

[atyy]

Can you post a reference?

http://arxiv.org/abs/1010.1939 "The second source of divergences is given by the limit (26)."
http://arxiv.org/abs/1010.5437 "We have observed that under certain general conditions, if this limit exist ..."

In a different but related context (GFT, not spinfoam LQG), http://arxiv.org/abs/gr-qc/0607032 "That such a sum can be defined constructively thanks to the simplicial and QFT setting is already quite an achievement, and to ask for it to be finite would be really too much!"

Emergence of matter - yes; but from GFT? How?

I don't know, of course, if I did ... But I am hoping for further developments following
http://arxiv.org/abs/hep-th/0512113
http://arxiv.org/abs/0903.3475
http://arxiv.org/abs/1004.0672

Some background as to whether gravity and matter should be unified is given in the last reference:
"Several approaches to coupling matter within spin foams were embarked upon [2–7]. The most tractable and indeed most successful of these procedures embedded the Feynman diagrams of the field theory into the spin foam. Remarkably, summing over the gravitational degrees of freedom, the effective matter amplitude was seen to arise as the Feynman diagram of a non-commutative field theory [8]. To add to this position, it was shown that an explicit 2nd quantised theory of this gravity matter theory could be provided by group field theory, while later the non-commutative field theory was seen to arise as a phase around a classical solution of a related group field theory [9]. Of course, one may approach the subject with the view that one should discretise the field directly on the spin foam, since in the continuum theory, we expect that the field has a non-trivial energy-momentum tensor, and should affect the state sum globally. This method has yielded to a succinct initial quantisation for Yang-Mills and fermionic theories [4–6], but due to the non-topological nature of the resulting amplitudes, further calculations proved unwieldy. Now, it was not our intention that this work would or should settle this debate, but we find that this theory is more in line with the arguments of the former way."

 

[marcus]

the statement that LQG is OK except for the need for coupling to matter ...

I am not making that statement. The author of the papers, which provide a kind of current status report, does not. You should look at the two papers, which have carefully qualified statements with a lot of references. I would say there are signs that the current form might be satisfactory----a kind of final version of LQG.

That does not yet mean that it is RIGHT. (One still has to derive predictions, and test.)
But if we are seeing something like a finished version of the theory, then a natural question to ask is how to add matter.

So this is a kind of speculative experiment. If the present form were satisfactory, how would matter be added?

I don't immediately see how,and I would like to get people's ideas of how it could go.

 

[atyy]

As an outsider and total ignoramus about LQG, the statement that LQG is OK except for the need for coupling to matter seems a little implausible. Maybe I'm just an idiot, but to me, this would seem to imply that LQG was currently able to reproduce any result that you could get in the classical limit from the vacuum field equations of GR, and to examine the quantum effects when the classical limit doesn't apply. Is this really true? Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

None of this has been achieved. The latest is summarized in http://arxiv.org/abs/1004.4550 . This is not sufficient, because eg. DT started from a similar point, but didn't produce anything sensible until it became CDT. Also, in CDT, although one starts with the Regge action, a continuum limit is supposed to be taken ultimately. Whereas in LQG, the Regge action is the classical limit, but that would seem to imply classical spacetime is discrete? Is another limit missing? Would that limit commute with the classical limit? Or will matching the free parameter in LQG make the discretization sufficiently fine?

The free parameter is discussed http://arxiv.org/abs/1010.1939 "Let's call LPl the unit of length in which all the equations above hold. LPl is a fundamental parameter of the theory, setting the scale at which the theory is defined, namely the scale of the quantum granularity of space"

 

[marcus]

Emergence of matter - yes; but from GFT? How?

I'd be interested to hear about that too. The reference Atyy gave, with the quote, was
http://arxiv.org/abs/1004.0672
The particle interpretation of N = 1 supersymmetric spin foams
V. Baccetti, E. R. Livine, J. P. Ryan
(Submitted on 5 Apr 2010)
"We show that N = 1 supersymmetric BF theory in 3d leads to a supersymmetric spin foam amplitude via a lattice discretisation. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3d gravity coupled to embedded fermionic Feynman diagrams."

Here's what was quoted in Atyy's post:

...
Some background as to whether gravity and matter should be unified is given in the last reference:
"Several approaches to coupling matter within spin foams were embarked upon [2–7]. The most tractable and indeed most successful of these procedures embedded the Feynman diagrams of the field theory into the spin foam. Remarkably, summing over the gravitational degrees of freedom, the effective matter amplitude was seen to arise as the Feynman diagram of a non-commutative field theory [8]. To add to this position, it was shown that an explicit 2nd quantised theory of this gravity matter theory could be provided by group field theory, while later the non-commutative field theory was seen to arise as a phase around a classical solution of a related group field theory [9]. Of course, one may approach the subject with the view that one should discretise the field directly on the spin foam, since in the continuum theory, we expect that the field has a non-trivial energy-momentum tensor, and should affect the state sum globally. This method has yielded to a succinct initial quantisation for Yang-Mills and fermionic theories [4–6], but due to the non-topological nature of the resulting amplitudes, further calculations proved unwieldy. Now, it was not our intention that this work would or should settle this debate, but we find that this theory is more in line with the arguments of the former way."

It isn't clear to me, and we are having company so I won't have time soon to try to figure it out. Would be grateful for any hints as to how this might work.

 

[MTd2]

Should matter emerge from the mismatch of tetrahedra in spin foam?

 

[marcus]

Atyy, I looked at the paper you indicated that you were quoting. I found this on page 15, in the conclusions:

==quote 1004.0672==
Finally, the most interesting application to our formalism would be to study the insertion of actual physical non-topological fermionic fields. Starting in 3d, in the present work, we have tracked from the initial continuum action down to the final discretised spinfoam amplitude how the explicit fermionic Feynman diagrams get inserted in the spinfoam amplitude. These fermionic observables come with precise weights (see e.g. eqn. (39)-(40)). These weights are fine-tuned so as to ensure that the full model ‘gravity+fermions’ is topological.

That shows that these spinfoam amplitudes provide the correct quantisation for our supersymmetric theory. As soon as we modify these weights, we would get non-topological amplitudes and it would be interesting to see how we could modify them in order to insert more physical fermionic fields. Then, we hope to apply the same procedure to the four-dimensional case by first deriving the spinfoam quantisation of supersymmetric BF theory and studying how the fermions are coupled to the spinfoam background, and then seeing how this structure is maintained or deformed when we introduce the (simplicity) constraints on the B-field in order to go from the topological BF theory down back to proper gravity.

Another interesting outlook is to push our analysis to N = 2 supersymmetric BF theory, already in three space-time dimensions, following the footsteps of [7]. Indeed, such a theory already include a spin-1 gauge field, and we could study in more detail how the full supersymmetric amplitudes decomposes into Feynman diagrams for the fermions and spin-1 field inserted in the gravitational spinfoam structure. Then we would see how it is possible to deform this structure in such a way that the spin-1 field represents standard gauge fields. This road would provide an alternative way to coupling (Yang-Mills) gauge fields to spinfoam models, which we could then compare to the other approaches developed in this direction [6]...
==endquote==

I am thankful for any indication of how the researchers imagine adding matter to the picture. The LQG literature goes back and forth between Group Field Theory (GFT) and spinfoam and BF theory. It is becoming all one. So whichever way you can get matter in, seems fine.
With this paper, they are working in 3D and so far can just hope to extend the method to 4D.

 

[atyy]

Or maybe something traditional (no unification) but still far out

http://arxiv.org/abs/gr-qc/0605087

 

[tom.stoer]

Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

Afaik neither Schwarzschild nor de Sitter has been reproduced so far.
The graviton propagator has been constructed over the last couple of years by Rovelli et al. and was shown to have thre correct limit. This is a kind of consistency check b/c one does not know whether the graviton propagator as constructed from standard GR at tree level is of any physical relevenace beyond (!) tree level (as standard GR fails to be consistend beyond tree level).

 

[marcus]

Do the LQG folks have a Schwarzschild metric with quantum corrections? Do they have plane gravitational waves with appropriate modes of polarization?

Tom responded as relates to plane gravitational waves (at least I think what he mentioned about the LQG graviton applies in that direction.)

In LQG there are BH models which reproduce classical results with quantum corrections. There are many papers and you can judge for yourself how complete the program is in that department by looking at recent ones. I doubt that this is all that relevant to the main topic question of how to add matter.

But here are some papers to glance at, if you are curious:
http://arxiv.org/abs/1007.2768
http://arxiv.org/abs/1006.0634
http://arxiv.org/abs/0905.3168

The first one here, for example:
Generic isolated horizons in loop quantum gravity
Christopher Beetle, Jonathan Engle
(Submitted on 16 Jul 2010)
"Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface."

From my perspective as outside observer, I reckon that matterless LQG is now reaching a satisfactory stable formulation, so that it is time to ask how they are going to include matter. What approaches will be tried?

What makes sense given the kind of "asymptotic" formulation (w/o matter) that we are now seeing emerge?

What I THINK is that the best clues, or hints come from looking at last year's Oberwolfach workshop "Noncommutative Geometry and LQG"

http://owpdb.mfo.de/show_workshop?id=783

What this shows me is a network of people, which includes Alain Connes and Vincent Rivasseau even thought they did not directly participate in the workshop.
So it is a window on a network of potentially fertile ideas. You see there elements of
GFT (group field theory)
Noncommutative field theory (e.g. Richard Nest, Thomas Schücker)
NCG (Marcolli and others).

One of the workshop participants was Thomas Krajewski, a member of Rovelli's QG team at Marseille. I'll list his papers to see what things he has worked on.

 

[marcus]

BTW I think it would be naive to start asking if the theory is right or wrong, or to start making bets.

What we see now are more like signs of maturity. What a I called an "asymptotic" version.
The formulation is mathematically extremely nice.
It is at a convergence of several lines of QG research, that I mentioned in the opening post. It is at an intersection, making contact with other things I mentioned (NGC, Ooguri, BF, Feynman diagrams, GFT, Regge).
Notably also we see a strenghtened coherence, it's clear now that canonical=covariant=cosmology. A loose association has fused and taken shape.

This is still happening, which is why I called the formulation asymptotic. But AFAICS it is time to assume that the main outlines (of matterless LQG) will remain as they are and to look ahead. It is how matter is added that could change things now.
================

So, looking for clues as to how that could go, I looked at Krajewski's list of papers. He has 24 on Spires going back to before his 1998 PhD thesis. Look at the network of topics and collaborators:
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+Krajewski%2C+Thomas&FORMAT=WWW&SEQUENCE=

My sense is that somewhere in that "hotbed" of mathematical topics, that you see in the list, there are the seeds of how to put matter into LQG. And it is not the person (Krajewski in this case) but the web of mathematically fertile ideas that you see. The person or persons could be anybody---someone we have heard of or not heard of. I am trying to comprehend what is comprised in this mathematical "hotbed".

BTW Alain Connes and Vaughn Jones were on Krajewski's 1998 Thesis committee, at Marseille. The more I hear about CPT Luminy at Marseille the more I like it. It seems to enjoy a good intellectual climate.

 

[atyy]

My sense is that somewhere in that "hotbed" of mathematical topics, that you see in the list, there are the seeds of how to put matter into LQG. And it is not the person (Krajewski in this case) but the web of mathematically fertile ideas that you see. The person or persons could be anybody---someone we have heard of or not heard of. I am trying to comprehend what is comprised in this mathematical "hotbed".

I think this particular cluster is spinfoams-GFT-non commutative field theory and comes from a paper http://arxiv.org/abs/hep-th/0512113 and a manifesto http://arxiv.org/abs/hep-th/0505016 .

 

[marcus]

Two more graduates of the ENS Lyon! Must be something in the water at the École Normale :-D.

But then tell me if you see: what mathematical form would the matter take?

The basic object here is the set of square-integrable complex-valued functions on a cartesian product of (just any number) K copies of a compact group G.

L₂(G^K)

(It looks good already: L₂ spaces and compact groups are some of the really nice things in mathematics.)

In matterless LQG the group G is SU(2). And K is the number of links in a graph. Afterwards the "graph goes to infinity" but the theory is initially built on finite graphs.

Could it be that one adds matter to the picture simply by enlarging the group G?
This could have been what was happening in the paper you quoted only a few posts back. Baccetti Livine Ryan.
As I recall the group UOSP(1|2) appeared in that paper. I don't know that group.

I suppose there are other possibilities. the L₂ space could be a set of functions not from G^K to the complex numbers x+iy but to some other number system, or to matrices. That does not immediately make sense to me, so I am inclined to prefer thinking about the first possibility---an enlarged group G manifold---for the time being.
=====================

Here is a 1980 paper about the group UOSP(1|2) by Berezin and Tolstoy
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103908695
Free open access provided by Project Euclid.

To recall the paper that uses UOSP(1|2):

...The reference Atyy gave, with the quote, was
http://arxiv.org/abs/1004.0672
The particle interpretation of N = 1 supersymmetric spin foams
V. Baccetti, E. R. Livine, J. P. Ryan
(Submitted on 5 Apr 2010)
"We show that N = 1 supersymmetric BF theory in 3d leads to a supersymmetric spin foam amplitude via a lattice discretisation. Furthermore, by analysing the supersymmetric quantum amplitudes, we show that they can be re-interpreted as 3d gravity coupled to embedded fermionic Feynman diagrams."
...

 

[S.Daedalus]

Whatever happened to the idea that matter is already included in LQG (and similar approaches) via the Bilson-Thompson topological preon construction (see, e.g. http://arxiv.org/abs/hep-th/0603022" )? I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.

 

[czes]

Skyrmions have been used to model baryons. It has been predicted that they could be created in a multicomponent Bose–Einstein condensate.
Skyrmion is a particular case of a topological soliton.
Is this theory a mainstream now or something beyond the mainstream ?

 

[MTd2]

I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.

And they are. The problem they still lack things like gluons.

 

[tom.stoer]

Skyrmions have been used to model baryons.

Skyrmions are valid in the context of chiral effective theories using pions (and other mesons) as degrees of freedom. Afaik there is no reason why Skyrmions should be treated as something more fundamental.

But that is certainly not relevant in the LQG context.

 

[tom.stoer]

Whatever happened to the idea that matter is already included in LQG (and similar approaches) via the Bilson-Thompson topological preon construction (see, e.g. http://arxiv.org/abs/hep-th/0603022" )? I seem to recall a claim by Smolin that such models may be 'already unified', and thus, one wouldn't have to add matter as much as to just find it.

They don't get all particles (I thought gluons are there but no second and third fermion generation). They don't get the (low-energy effective) dynamics, only algebraic rules. For me this approach is "Einstein's dream"; it would be at least as revolutionary as GR and QM. But as of today it's work in progress - with only a small number of players, I am afraid.

 

[suprised]

Most of this seems pretty much wishful thinking. I see a huge list of "may" , "promising", "future research" in all those papers, with no real concrete demonstration that any of these zillions of vague proposals may actually work. Kicking around ideas is easy, but getting something to work, even approximately, is not a minor detail, but actually the main part of the problem!

I understand that this is work in progress, but to be fair one should note that if string physicists would get much heat for hype of similar caliber; while the theory is much further developed.

I can understand the title of the thread only as ironic - didn't the recent paper of Alexandrov and Roche exhibit that there are serious problems with LQG at a basic level, so before one looses oneself in speculations about how to possibly add matter, shouldn't one first make sure that any of these many different attempts that one may loosely call "LQG" make sense at all?

 

[MTd2]

This horse is so beaten that even the carcass is waiting for paleontologists.

 

[czes]

Skyrmions are valid in the context of chiral effective theories using pions (and other mesons) as degrees of freedom. Afaik there is no reason why Skyrmions should be treated as something more fundamental.

But that is certainly not relevant in the LQG context.

Are Skyrmions a kind of the mathematical tool then ?

 

[Haelfix]

Most of this seems pretty much wishful thinking.

The other problem is that even if they can finagle their way into making something consistent (eg we can add a scalar here, a vector there, etc), the ultimate problem of QG remains in force. Namely that you have no idea what matter fields to add without actually doing the experiment!

So I would consider it somewhat dissappointing even if the succeeded in showing that their theory was consistent for all arbitrary matter couplings, b/c it would imply a lack of predictivity in nature (eg Nature is consistent even as a superset of itself) and that at best the current constraints on Bysm physics were all that we could get from pure theory.

The alternative, is to add constraints (new physics/symmetries/selection principles) to the mix, which gets right back into supersymmetry, conformal field theory, NCQ and so forth and we're right back to the old 1970s criticism of all the quantization of gravity approaches.. Namely that one way or the other, you have to add stuff to it until you can get control (and ultimately predictions)

 

[tom.stoer]

The other problem is that ... the ultimate problem of QG remains in force. Namely that you have no idea what matter fields to add without actually doing the experiment!

I don't know to which idea you are referring here (I think LQG + "something"), but the Bilson-Thompson preons are not "added by hand" but are emerging from the quantized geometry itself. Of course tis is a rather speculative idea and by no means maisntream but it should be taken into account as an approach to unify geometry and matter degrees of freedom.

 

[MTd2]

This horse is so beaten that even the carcass is waiting for paleontologists.

 

[tom.stoer]

Are Skyrmions a kind of the mathematical tool then ?

Originally Skyrme proposed that nucleons (proton, neutron) can be described in terms pion fields \pi^a(x) where a=1..3 counts the three pions in SU(2)_flavour. Now instead of using a linear field theory (Klein-Gordon) he introduced a non-linear field theory (non-linear sigma model with some extra terms) in terms of the SU(2) matrix

U(x) = e^{i\tau^a\pi^a(x)}

Then he showed that the field equations allow for a "radial" static "hedhog" solution

\pi^a(x) = \hat{r}^a f(r)

with a certain profile function f(r).

This solution in a topological soliton (the nucleon) b/c it has a "winding number" one which guarantuees its stability against decays into pions (mathematically this is due to the homotopy group defined by the mapping from compactified space S³ to SU(2)). A simple example is a field living in U(1) on a space defined by a circle S¹. As x runs around the circle the field runs around the the U(1).

One can show that these topological Skyrmions plus improved phenomenological models including vector mesons can be used as so-called chiral effective theories to describe
- nucleon masses
- nuclean form factors
- nucleon-nucleon scattering
- pion-nucleon scattering
- photo-pion production

Similar solitons can be constructed whenever there is a field living in a manifold (like the group SU(2)) which allows a topologically non-trivial mapping betwen spacetime and the manifold. In that sense it is by no means restricted to phenomenological models for the strong interactions. But I have never seen that solitons are used in LQG.

 

[Haelfix]

I don't know to which idea you are referring here (I think LQG + "something"), but the Bilson-Thompson preons are not "added by hand" but are emerging from the quantized geometry itself. Of course tis is a rather speculative idea and by no means maisntream but it should be taken into account as an approach to unify geometry and matter degrees of freedom.

When this idea (its really a variant of an old idea by Wheeler) was proposed several years ago, people immediately asked if it put any constraints at all on particle physics. Like for instance, does it enforce chirality? The answer was a vague 'I don't know'! So for now, it seems that if it works at all, its essentially equivalent to matter being added by hand since the exact nature of the geometry is uncertain.

 

[atyy]

LQG already has matter, and it can find gravity by AdS/CFT http://arxiv.org/abs/0907.2994

 

[qsa]

Most of this seems pretty much wishful thinking. I see a huge list of "may" , "promising", "future research" in all those papers, with no real concrete demonstration that any of these zillions of vague proposals may actually work. Kicking around ideas is easy, but getting something to work, even approximately, is not a minor detail, but actually the main part of the problem!

I understand that this is work in progress, but to be fair one should note that if string physicists would get much heat for hype of similar caliber; while the theory is much further developed.

I can understand the title of the thread only as ironic - didn't the recent paper of Alexandrov and Roche exhibit that there are serious problems with LQG at a basic level, so before one looses oneself in speculations about how to possibly add matter, shouldn't one first make sure that any of these many different attempts that one may loosely call "LQG" make sense at all?

LQG carries matter in the following way from Smolin's paper. It is 99% similar to my own idea coming from a very different angle. I am very astonished that nobody so far has mentioned this idea which he has been working very hard on it, and he even tied it to Lisi's idea.

http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0977v2.pdf



Consider a graph as in
Figure (1) which is regular and therefor may occur in the superposition of states making
up a semiclassical state associated with a flat metric. There is in loop quantum gravity,
no apparent energy cost to contaminating that lattice-like graph with non-local links as
shown in the figure. Nor is there an incompatibility with the semiclasicality of the state.
As there are many more ways to add a link to a lattice that connects two far away nodes
than two nearby nodes, there is an instability for the formation of such non-local links
as the universe expands from Planck scales. Moreover, once inserted in a graph, nonlocal
links are trapped, as they can only be eliminated if two of them annihilate by the
coincidence of their ends arriving by local moves at neighboring nodes. The proposal
is then that these act as Planck scale wormholes, carrying quantum numbers associated
with gauge fields carried by the non-local link.

Let us consider observations made by a local observer in the neighborhood of x. From
their point of view the edge exy simply comes to an end, that is it appears to connect
to a one valent node. But ends, or one valent nodes in loop quantum gravity represent
matter degrees of freedom. Thus, the dislocations due to disordered locality appear in the semiclassical limit as matter degrees of freedom.
Let us suppose that the gauge group is SU(2)⊗H, where H is an internal gauge symmetry.
Then the edge exy carries representations of these groups, (j, r). Local observers will describe exy as a particle of spin j and charge r.This leads to a picture in which for every generator of G, the gauge symmetry, the
semiclassical limit has a gauge field plus a set of particle excitations given by the representations of G.

 

[tom.stoer]

But still "most of this seems pretty much wishful thinking".

In a second paper Smolin tried to explain the cosmological constant via these non-local links. In addition Smolin proposes Bilson-Thompson. And then one can add matter by hand ...

The conclusion is that LQG carries a rich and (to a large extend) unexplored structure. Some known effects may be explained via these structures, some new effects may arise. Some unwanted effects may rule out LQG, ..., everything is possible.

 

[suprised]

If I remember correctly, the Bilson-Thompson model is a preon model which is equivalent to Haim Harari's Rishon model. That model had suddendly disappeared many years ago... why? because a smart student of Harari, Nathan Seiberg, had shown that this model is inconsistent due to anomalies. Well, since anomalies seem to be neglected in the LQG community, I am not surprised that they revive the Rishon model. Indeed, back to the 70s...

Incidentally, the question of matter is an interesting one also from the following perspective. If string theory is any right, matter is necessary for internal consistency. Pure gravity would not be consistent. It would be interesting to see whether LQG comes up with a similar consistency constraint. If not, then this would be a clear dividing line between strings and LQG. I guess it is too early to see because LQG seems so far to be plagued by all sorts of problems; but perhaps some day this issue can be sharpened.

 

[marcus]

Haven't heard much about braid matter for the past couple of years. I hope that in this discussion thread we can get back to the main topic---the ways currently being considered to include matter.

It seems fairly obvious that matterless (or simple scalar matter) LQG has matured to the point of being testable with the next generation of CMB spacecraft . The proposed NASA B-Pol mission for example--how soon such steps are taken depends mainly economic and political conditions, there are no technical barriers.
http://www.b-pol.org/index.php

Since there are evidently differing opinions regarding the theory's maturity, I'll copy two recent abstracts bearing on that:

http://arxiv.org/abs/1011.1811
Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters
Julien Grain, A. Barrau, T. Cailleteau, J. Mielczarek
12 pages, 5 figures
(Submitted on 8 Nov 2010)
"Cosmological models where the standard Big Bang is replaced by a bounce have been studied for decades. The situation has however dramatically changed in the last years for two reasons. First, because new ways to probe the early Universe have emerged, in particular thanks to the Cosmic Microwave Background (CMB). Second, because some well grounded theories -- especially Loop Quantum Cosmology -- unambiguously predict a bounce, at least for homogeneous models. In this article, we investigate into the details the phenomenological parameters that could be constrained or measured by next-generation B-mode CMB experiments. We point out that an important observational window could be opened. We then show that those constraints can be converted into very meaningful limits on the fundamental Loop Quantum Cosmology (LQC) parameters. This establishes the early universe as an invaluable quantum gravity laboratory."

http://arxiv.org/abs/1007.2396
Constraints on standard and non-standard early Universe models from CMB B-mode polarization
Yin-Zhe Ma, Wen Zhao, Michael L. Brown
(Submitted on 14 Jul 2010)
"We investigate the observational signatures of three models of the early Universe in the B-mode polarization of the Cosmic Microwave Background (CMB) radiation. In addition to the standard single field inflationary model, we also consider the constraints obtainable on the loop quantum cosmology model (from Loop Quantum Gravity) and on cosmic strings, expected to be copiously produced during the latter stages of Brane inflation. We first examine the observational features of the three models, and then use current B-mode polarization data from the BICEP and QUaD experiments to constrain their parameters. We also examine the detectability of the primordial B-mode signal predicted by these models and forecast the parameter constraints achievable with future CMB polarization experiments. We find that:
(a) these three models of the early Universe predict different features in the CMB B-mode polarization power spectrum, which are potentially distinguishable from the CMB experiments;

(b) since B-mode polarization measurements are mostly unaffected by parameter degeneracies, they provide the cleanest probe of these early Universe models;

(c) using the BICEP and QUaD data we obtain the following parameter constraints:
r=0.02^{+0.31}_{-0.26} (1 sigma for the tensor-to-scalar ratio in the single field inflationary model);

m < 1.36\times 10^{-8} \text{M}_{\text{pl}} and k_{*} < 2.43 \times 10^{-4} \text{Mpc}^{-1} (1 sigma for the mass and scale parameters in the loop quantum cosmology model);

G\mu < 5.77 \times 10^{-7} (1 sigma for the cosmic string tension);

(d) future CMB observations (both satellite missions and forthcoming sub-orbital experiments) will provide much more rigorous tests of these early Universe models."

 

[qsa]

But still "most of this seems pretty much wishful thinking".

In a second paper Smolin tried to explain the cosmological constant via these non-local links. In addition Smolin proposes Bilson-Thompson. And then one can add matter by hand ...

The conclusion is that LQG carries a rich and (to a large extend) unexplored structure. Some known effects may be explained via these structures, some new effects may arise. Some unwanted effects may rule out LQG, ..., everything is possible.

1-Consider particles as lines extending from the particle to everywhere in the universe.

2-generate these lines by throwing a random number, make it on a line i.e. 1D as an example
do above for two particles sitting each at the opposite side of a universe of 10^40 in atomic units-size of the proton-(size of our universe). Throw 10^41 times.

3-if you consider gravity as when both lines meet you have a probability of 1 in 10^40

4-if you consider EM force as when these lines cross one another p is close to .99

you can see the ratio, can't you. trust me ,forces are related to these probabilities.

increasing(decreasing) the universe size changes the ratio, EM stays .99. This is Diracs large number hypothesis(Google). Numbers are approximate. I hope I show details soon.

Quantum gravity in four lines.

 

[flatcp]

I hope that in this discussion thread we can get back to the main topic---the ways currently being considered to include matter."

You opened the thread with this description "If LQG now satisfactory, how to add matter?" . Seems reasonable for people who are definitely smarter then me (and from what I have read on this forum, you as well) to focus on the qualifier prior to considering the smuggled in concept.

If the moon is made of cheese, what kind?

 

[marcus]

...

If the moon is made of cheese, what kind?

Heh heh, great comment.

Actually the theory is essentially ready to test (with very simple matter) and ready to add matter. "If" is just an attention-getter. I have to go. Back later today.

 

[marcus]

I could have titled the thread Since matterless LQG satisfactory, how to add matter?

The theory has reached the point where it is reasonably coherent (LQG cosmology is being done with spinfoam) and makes a robust prediction of cosmo bounce---something that can be tested.

A concise simple discussion of this begins here:
http://www.math.columbia.edu/~woit/wordpress/?p=3262&cpage=1#comment-67952
Bee Hossenfelder, a reputable QG phenomenologist, entered the discussion here:
http://www.math.columbia.edu/~woit/wordpress/?p=3262&cpage=1#comment-67988

A more credible objective expert on QG phenomenology can't be found. Bee has organized two conferences on "Experimental Search for Quantum Gravity"---the world's first. One at Perimeter Institute, when she was there. The second one where she is working now, at NORDITA in Stockholm. She invited QG and string alike, across the board. She is a phenomenologist---that means develops and evaluates TESTS of theories---not playing favorites.

It's clear. You can falsify LQG if the CMB shows no evidence of cosmic bounce. The theory has to face the music of the ancient light---the CMB music. Bee is not the kind that takes prisoners or pulls punches.

It's not like some of Smolin's gambits, where people like Rovelli and Ashtekar didn't see the point and declined to sign on. There was never a proof that LQG implies energydependent speed of light, even when some people tried hard to derive one. But the bounce is robust. Ashtekar's people get it every time they solve the equations or run a computer simulations of the early universe. Time doesn't stop, in LQG, as you go back. A top density is reached and contracting distances re-expand.

I think it may be personally difficult for people like Rovelli and Thiemann to sign on to the bounce as an implication of LQG (because it puts the theory at risk of falsification) but I don't see any way they can avoid doing that. Rovelli already hinted, or mentioned that in his October paper 1010.1939.

Anyway, reluctantly or not, matterless LQG is going to be tested---actually most of the early universe models have some kind of simplified matter, like a scalar field. What I mean by "matterless" LQG is the theory with only this radically simplified form of matter.

And it may survive. That's why I say the next question to ask is how to add matter to the picture.

 

[MTd2]

Why aren't the tetrahedron when connection to other tetrahedron free to permute connecting vertices, change the chirality of connecting edges amd orientation of connecting faces?

 

[atyy]

It's clear. You can falsify LQG if the CMB shows no evidence of cosmic bounce. The theory has to face the music of the ancient light---the CMB music. Bee is not the kind that takes prisoners or pulls punches.

It's not like some of Smolin's gambits, where people like Rovelli and Ashtekar didn't see the point and declined to sign on. There was never a proof that LQG implies energydependent speed of light, even when some people tried hard to derive one. But the bounce is robust. Ashtekar's people get it every time they solve the equations or run a computer simulations of the early universe. Time doesn't stop, in LQG, as you go back. A top density is reached and contracting distances re-expand.

I think it may be personally difficult for people like Rovelli and Thiemann to sign on to the bounce as an implication of LQG (because it puts the theory at risk of falsification) but I don't see any way they can avoid doing that. Rovelli already hinted, or mentioned that in his October paper 1010.1939.

So if Rovelli has not yet signed on, how do we know this is not another "prediction" that will falsify LQG?

 

[marcus]

So if Rovelli has not yet signed on, how do we know ...?

We don't know for sure. He's careful and will not base anything on guesswork. He won't say something is a prediction until there is a watertight case, all spelled out. But it looks unavoidable to me.

Maybe I should be more cautious!

What must be shown is that a bounce occurs in the full spinfoam theory.

Let's glance at two October 2010 papers to gauge how far we are from that:

http://arxiv.org/abs/1010.1258
Big Bounce in Dipole Cosmology
Marco Valerio Battisti, Antonino Marciano
(Submitted on 6 Oct 2010)
"We derive the cosmological Big Bounce scenario from the dipole approximation of Loop Quantum Gravity. ... This model thus enhances the relation between Loop Quantum Cosmology and the full theory."

The dipole cosmology is simplified spin foam. It is not the full theory. The initial and final states are restricted. OK so the bounce has been derived only in a TOY spinfoam model, so far.

Then also, the authors of the next paper have found something wrong with the way time is handled in LQC. This also applies to the Battisti Marciano paper although it is not usual LQC---they treated time the same way.

http://arxiv.org/abs/1010.0502
Local spinfoam expansion in loop quantum cosmology
Adam Henderson, Carlo Rovelli, Francesca Vidotto, Edward Wilson-Ewing
(Submitted on 4 Oct 2010)
"...In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local."

I think this paper points out a technical matter that needs fixing. By my reckoning it doesn't invalidate the general impression that the bounce is a robust characteristic of Loop early universe. The Penn State work under
Ashtekar's direction has repeatedly confirmed this. I have a hard time imagining that it will not finally be confirmed.
I'll have to look at this again in the morning when I am fresh.

 

[marcus]

Atyy, I "slept on it" and can return a little fresher. One way to address the question is that it is now to a considerable extent out of Rovelli's hands and over in the court of the phenomenologists.

On the theorists' part there is an ongoing effort to link the full theory with LQC. Rovelli's group will continue doing that---there are already two years of papers. Thiemann has written on that too and he has a group at Erlangen. You already see Erlangen and Marseille people collaborating on completing the job. I think it is a done deal. The full theory (spinfoam) will be applied to cosmology.

For that matter, you see Penn State people working on the same thing: full theory-->cosmo.
Specifically it is the spinfoam formulation applied to cosmo. The theorists are bound to do that, it is out of anyone person's hands.

We have 10 years of experience teaching us to expect that the full theory applied to cosmo will give a bounce. They've tried all kinds of variations already including non-isotropic and that feature appears robust. As you saw, Battisti Marciano just tried it with spinfoam dynamics (toy version) and got a bounce.

So what happens after that is ultimately up to the phenomenologists.

I think there is a kind of moral wisdom in having a division of labor here. Phenomenologists have a professional interest in seeing if a theory is "ready" and if it smells ready to them they go about seeing how to test it.

The parent of a theory may not even want to see his construct go to the front and take its chances. I don't know what it feels like---it could actually be hard. The way professional specialization works, the parent is relieved of some of the responsibility of deciding. The theory goes up for testing when the phenomenologists decide---or so I think. That is one way it can work anyway.

 

[marcus]

So let's see who some of these phenomenologists are, who have recently weighed in. It makes a big difference what we think of them.
http://arxiv.org/abs/1007.2396
Constraints on standard and non-standard early Universe models from CMB B-mode polarization
Yin-Zhe Ma, Wen Zhao, Michael L. Brown

The paper was recommended by Bee Hossenfelder (NORDITA) whom we know, along with one of her own. Looks like she might think the work is solid, otherwise why recommend it? Who are the authors?

Wen Zhao has 35 papers going back to 2005. A substantial number of them are in observational early-universe cosmology, CMB analysis. So this is "right down his alley".
http://arxiv.org/find/astro-ph/1/au:+Zhao_W/0/1/0/all/0/1
He is at Cardiff U with joint appointment at the Wales Institute of Mathematical and Computational Sciences.

Yin-Zhe Ma and Michael Brown are Cambridge. Both are at the Kavli Institute for Cosmology. YZM has joint appointment at the Inst. of Astronomy. MB belongs to the Cavendish Lab Astrophysics group.
I guess the main institutional handle for both would be KICC (Kavli Inst. Cosm. Cambridge)

Webpage at Cavendish Astrophysics for Michael Brown:
http://www.mrao.cam.ac.uk/people/mbrown.html
(title is Senior Research Associate)

Yin-Zhe Ma papers going back to 2007 when YZM was at Beijing Kavli Inst. for Theoretical Physics (KITP China):
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=a+Ma%2C+Yin-Zhe&FORMAT=WWW&SEQUENCE=
I'll get back to this as time permits.

 

[marcus]

...
http://arxiv.org/abs/1007.2396
Constraints on standard and non-standard early Universe models from CMB B-mode polarization
Yin-Zhe Ma, Wen Zhao, Michael L. Brown

The paper was recommended by Bee Hossenfelder (NORDITA) whom we know, along with one of her own. Looks like she might think the work is solid, otherwise why recommend it? Who are the authors?

Wen Zhao has 35 papers going back to 2005. A substantial number of them are in observational early-universe cosmology, CMB analysis. So this is "right down his alley".
http://arxiv.org/find/astro-ph/1/au:+Zhao_W/0/1/0/all/0/1
He is at Cardiff U with joint appointment at the Wales Institute of Mathematical and Computational Sciences...

This is the real sign that Loop has reached a satisfactory state---phenoms are spontaneously gathering around scrutinizing it. They want to test (whether or not Loop people like the idea, opinions may differ) and think that they can.

I just learned that SHINJI TSUJIKAWA a Tokyo U phenomenologist has a "Loop falsifiable by CMB" paper in preparation. In this case it will be co-authored with a central Loop cosmology figure, Martin Bojowald.

I'll get the tip-off quote. It is reference [51] on page 34 of a Bojowald Calcagni that just appeared

http://arxiv.org/abs/1011.2779
Inflationary observables in loop quantum cosmology
Martin Bojowald, Gianluca Calcagni
40 pages
(Submitted on 11 Nov 2010)
"The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comoving curvature perturbation is shown to be conserved at large scales, just as in the classical case. Its associated Mukhanov equation is obtained and solved. Combined with the results for tensor modes, this yields the scalar and tensor indices, their running, and the tensor-to-scalar ratio, which are all first order in the quantum correction. The latter could be sizable in phenomenological scenarios. Contrary to a pure minisuperspace parametrization, the lattice refinement parametrization is in agreement with both anomaly cancellation and our results on background solutions and linear perturbations. The issue of the choice of parametrization is also discussed in relation with a possible superluminal propagation of perturbative modes, and conclusions for quantum spacetime structure are drawn."

==quote==
In this final section we discuss how they can be used to restrict models of loop quantum cosmology, making the framework falsifiable. Details will be provided in a separate publication [51]. For such an endeavor, it is crucial to obtain independent information on the main correction parameter δ_Pl...
==endquote==

[51] is a paper by Bojo Calcagni and Tsujikawa "to appear"

I think I might start compiling an "Honor Role" of phenomenologists who have published papers on this topic (most without collaboration by Loop people) or otherwise got the word out. Outstanding would be Sabine Hossenfelder (NORDITA Stockholm) who has organized two conferences on the experimental search for QG and published a number of papers on QG phenom. She's the one who pointed Wen Zhao out to me. Also outstanding are Aurelien Barrau, and a former PhD student of his, Julien Grain.

You can look up these people's work by name on Arxiv. Something that matters, I think, is that they don't play favorites. They explore testing possibilities of theories with implications for cosmology, any and all alike (including "string-inspired", braneworlds and all that.) Professional attitude .

Here's my provisional Early-Universe QG Phenomenologist Honor Role alphabetized by surname :

Aurelien Barrau
Julien Grain
Sabine Hossenfelder
Shinji Tsujikawa
Wen Zhao

 

[marcus]

To recap, if one just considers Loop QG with limited or no matter, the theory has to significant extent reached a stable configuration where it makes robust predictions that can be tested. The application of the full theory to cosmology is being carried out--one knows generally what the theory's consequences are and what to look for. Phenomenologists have taken over part of the job.

I do not expect the formulation of the theory to change much except as it changes to accommodate more complex realistic matter. From now on, I'm suggesting, what drives the development of the theory will be the need to add matter to the picture.

I'm not talking about "unification". I mean simply putting additional fields into the existing quantum-geometrical framework and having them interact with the geometry. So far Loop cosmology simulations have tended to use massless scalar fields---simple toy matter, not the real stuff---and the same with analytic solvable models.

There are some exceptions and Atyy has pointed out a bunch of them. Feynman diagrams for conventional field theory unearthed in a spinfoam QG context by Freidel, Livine, and others. But still the situation isn't clear enough for me to know, or even guess, what to expect.

I think I will make a tentative bet that the following paper, when it appears, will have some clues. This could be something that MTd2 has hinted at but I wasn't sure at the time if he was talking about this or something else.

This paper is in preparation:

Quantum Twisted Geometries and Coherent States
Laurent Freidel and Simone Speziale

I'll give some background on this. The paper was cited in a January 2010 paper by the same authors called:
Twisted Geometries: A Geometric Parametrization of SU(2) Phase Space.
http://arxiv.org/abs/1001.2748

 

[marcus]

As with any prediction I am foolish enough to make, you are welcome to make fun of me if proven wrong---assuming you remember what I say today and can compare it with the Freidel Speziale when it finally comes out. Just keep an eye open for something called
Quantum Twisted Geometries and Coherent States.

The main topic of that paper will of course not be matter, but I'm betting that it will contain a hint as to how Freidel and Speziale think matter can be brought in.

The January paper http://arxiv.org/abs/1001.2748 has an limitation worth noticing: it seems to be restricted to 4-valent spin networks. Correct me if you know otherwise. I don't see this explicitly stated. "Twisted" could also be called "squished". In the dual to the network, where two tetrahedra butt up against each other, the two triangle faces don't necessarily match. You might have to squish one of them in order to make it like the other.
=====================

One or more people in this thread mentioned Bilson-Thompson and braid matter. I haven't heard much of anything about braid matter for over 2 years and I don't expect the subject to be brought up. Let's put that one on "ignore" until further notice.

Last I heard, Song He (one of those who worked earlier on braid matter) was doing something with covariant Regge at Albert Einstein Institute---Dittrich's group. It actually relates to this Freidel Speziale work. From Song He track record I have a lot of expectations from him---if there were immediate results to be gotten from braid he would be on that but he is doing something else. It doesn't mean that something LIKE braid in some unknown sense couldn't have potential. I have no clue what that could be.

The main thing for now is probably just to decide simply how to put matter into the spin network and spinfoam picture, not any kind of "unification" or recovery of the standard model. Please correct me if you see that I'm wrong about that for some reason.
==============
The Freidel Speziale paper of January 2010 has been cited 16 times.
http://www.slac.stanford.edu/spires/find/hep?c=PHRVA,D82,084040
What did they say they were going to do in the paper that is in preparation? Let's call it something, for short, like QTG+CS (for quantum twisted geometries and coherent states.)

 

[marcus]

More on the adding matter front:

John Barrett posted a November 2010 update to this April 2010 entry in his blog:

http://johnwbarrett.wordpress.com/

Quantum gravity with matter

I gave a short talk at IHES in December (and a rather longer one in Marseille, too) on the topic of modifying quantum gravity models so that they contain realistic matter. A lot of work on quantum gravity is done without any matter fields and one gets the impression that matter fields are an optional extra which just make the system more complicated. The icing on the cake, as Chris Isham used to say about topology.

In my talk I suggested that, on the contrary, quantum gravity models with matter can actually be rather simpler than models without matter. This is because the Einstein action is induced by the matter fields, so removing the requirement to put the Einstein action into the theory from the beginning.

Some slides from my talks at Bayrischzell and Oxford are available. I am writing a short paper expanding this.

Update (Nov ’10) I’ve found a good result about this since those talks, hence the delay (and also I’m trying to finish a different paper first).

​

http://johnwbarrett.wordpress.com/2010/04/22/hello-world/

 

[atyy]

Ha, ha! So much for (Rovellian) LQG!

OK, that's premature, but I'm glad Barrett is going this way too!

http://arxiv.org/abs/1009.4475
"The above discussion suggests that it would be more natural to have some fundamental quantum theory of spin networks or spin foams which knows nothing about the Einstein action, except that it appears in the infrared limit, and is defined instead using some natural symmetry or other principles."

http://arxiv.org/abs/1004.0672
"Now, it was not our intention that this work would or should settle this debate, but we find that this theory is more in line with the arguments of the former way."

http://arxiv.org/abs/0909.1861
"In this essay we have taken a new step: geometry is nothing but the collective organization of emergent matter. This leads to a new way to view the Einstein equations: there is no surprise that T and R are inter-related, they are different facets of the same thing. In quantum graphity, matter becomes both geometry and matter."

http://arxiv.org/abs/0906.1313
"If gravity is induced [9], which means that Newton’s constant is zero at tree level and arises as a one loop correction, then the entanglement entropy is responsible for all of the entropy, and reproduces the area law with the correct coefficient [7,10]."

 

[marcus]

OK, that's premature,...

Indeed.

And Roche, Livine, Markopoulou, and Strominger don't make a very coherent ensemble.
You might find that current (Rovelli) LQG was more compatible with each one separately than the four are amongst themselves.

Your post just now appeared to be in response to this one of mine, and yet does not really connect to it:

More on the adding matter front:

John Barrett posted a November 2010 update to this April 2010 entry in his blog:

http://johnwbarrett.wordpress.com/

Quantum gravity with matter

I gave a short talk at IHES in December (and a rather longer one in Marseille, too) on the topic of modifying quantum gravity models so that they contain realistic matter. A lot of work on quantum gravity is done without any matter fields and one gets the impression that matter fields are an optional extra which just make the system more complicated. The icing on the cake, as Chris Isham used to say about topology.

In my talk I suggested that, on the contrary, quantum gravity models with matter can actually be rather simpler than models without matter. This is because the Einstein action is induced by the matter fields, so removing the requirement to put the Einstein action into the theory from the beginning.

Some slides from my talks at Bayrischzell and Oxford are available. I am writing a short paper expanding this.

Update (Nov ’10) I’ve found a good result about this since those talks, hence the delay (and also I’m trying to finish a different paper first).

​

http://johnwbarrett.wordpress.com/2010/04/22/hello-world/

Barrett works closely with Rovelli, whose PhDs may postdoc either at Nottingham or at Perimeter. Barrett just announced the setting up of a QG Masters degree program at Nottingham (see his blog, I gave the link above.)
And he says that he gave a long talk at Marseille in December 2009 laying out his ideas, as they were then, about how to include matter. Now, November 2010, he says he has found a result, material for a follow-up paper. It might be an agreeable surprise, I hope so.

What I was thinking was you might have some clue as to what direction Barrett is going, what his ideas on putting matter into the QG picture might be. If so please spell it out a bit for me. Paraphrase in your own words. So we have more than isolated short quotes out of context.

 

[atyy]

What I was thinking was you might have some clue as to what direction Barrett is going, what his ideas on putting matter into the QG picture might be. If so please spell it out a bit for me. Paraphrase in your own words. So we have more than isolated short quotes out of context.

I couldn't understand a word of his talk, once the category theory started! It seems to have something to do with http://arxiv.org/abs/hep-th/0608221. But all I got was that it has something to do with Sakharov's induced gravity, the exact same reference as Strominger's.