Criticism of LQG - What do we miss?

[tom.stoer]

It may be more intersting to identify open issues from our perspective instead of "translating" Lubosz. A brainstorming from my side:

• LQG starts with a quantization of spacetime which is topologically M³*R; it is by no means clear if this "background-dependence" does not throw away physical relevant sectors (of different topologies) of theory space
• in the most general form the new SFs can to some extent go beyond this topology (as they do not specify a topology at all - only in a kind of classical limit), but again it's not clear if all topological sectors can be considered in this context
• LQG uses SU(2)-colored graphs w/o the notation of "dimension"; up to now I see no reason how dim=4 could be singled out from these graphs
• LQG uses SU(2)-colored graphs w/o the notation of "dimension"; up to now I see no reason why especially SU(2) shall be used - why not any other gauge group? restricting to SU(2) can be justified only b/c one knows about the starting point dim=4 - which is a cat hunting its own tail; in that sense LQG suffers from a kind of "landscape problem"
• it is clear that 4-dim spacetime has some interesting properties, namely that it allows for an uncountable set of smooth structures; LQG uses exactly one smooth structure in the very beginning!
• I indicated in another thread that the very existence of uncountably many smooth structures in dim=4 could single out dim=4; my idea was to construct a measure counting all different smooth structures on top of all topological manifolds in all dimensions; that would single out non-compact M⁴ immediately simply due to "counting" w/o any additional dynamical input; LQG has nothing to say about that
• I am convinced (but of course I can be wrong) that matter (fields) do emerge from spacetime; up to now the results about framed graphs in LQG seem to be a dead end (no new results since years)
• adding matter on top of the SFs is the wrong way; it will never result in a unification of spacetime (gravity) and matter
• the asymptotic safety approach indicates that gravity may be non-perturbatively renormalizable; due to that approach all possible couplings constructed from g, R, ... should be taken into account and should be subject to renromalization group flow similar to Kadanoff's block spins; up to now LQG does not say anything about that
• LQG treats the BI parameter (or the BI field) in a rather special way; there are indication that the BI parameter is related to the theta-angle in QCD, but I think final results are still missing (this is of course of major interest as the BI parameter plays a prominent role in the spectra of certain operators; it is strange that a semi-classical calculation a la Hawking w/o quantum gravity should be used to fix the value of this parameter!)
• LQG treats the cosmological constant in a very special way (e.g. approaches via quantum deformations of SU(2)); it is unclear why the cc should have such a special role, whereas the AS approach indicates that all couplings can be treated in a harmonized manner
• taken together it is not clear if the cc is an algebraic input (via q-deformed SU(2)) or a dynamical output (e.g. via renromalization group) of the theory
• the LQC results are very encouraging; but afaik this theory says nothing about the initial conditions of the universe, especially regarding its entropy; up to now LQC treats the evolution of the universe near the big bounce as time-symmetrical; results using infinitly many degrees are required
• there are indications that the holographic principle is a fundamental principle of nature, but LQG does not use this principle at all, e.g. in order to define "boundary Hilbert spaces" to define the theory; the holographic principle shows up only in very special calculations, e.g. in calculating the states and the entropy of a black hole

 

[MTd2]

tom.stoer, why do you think LQG should be in harmony with AS QEG?

 

[tom.stoer]

I don't think that "it should be in harmony", but comparing condensed matter Hamiltonians with LQG suggests immediately to apply Kadanoff's block spin renormalization; Kadanoff's approach generates more complicated spin couplings; if you start with a nearest neighbor interaction then (afaik) integrating out short-range fluctuations generates from "elementary" nearest-neighbor, next-to-nearest-neighbor etc.; in addition it generates "running couplings"; this block-spin approach is related to momentum-space renormalization with cutoff; I expect something like that for LQG as well.

 

[MTd2]

What would be a short-range fluctuation in LQG? What is a cut off for LQG?

 

[tom.stoer]

:-)

I know that the momentum-space approach does not make sense; but the block-spin approach does. Do you knwo how it works?

 

[MTd2]

Just the very basic stuff in 2 dimensions. But LQG, parametrized by spin foams, is not a locallized lattice like in a solid. And not only that, the concept of neighbor is dubious since new vertices are created and destroyed randomly. So, this is not much different of a gas...

 

[tom.stoer]

But LQG, parametrized by spin foams, is not a locallized lattice like in a solid.

That doesn't matter; for the spin-Hamiltonians you do not need a background, localization in space etc.; all you need is the definition of an interaction between two spins.

... the concept of neighbor is dubious since new vertices are created and destroyed randomly.

I didn't say it will be straight forward :-)
I agree it is different due to the creation of new links and vertices.

The reason why I suspect that there is some truth behind it is the way a black hole is modeled in LQG; it is just a single, huge intertwinder with many edges penetrating a "horizon" defined by these edges; from outside there is no reason to "resolve" the intertwiner into different single spins; from the inside it may be reasonable to "zoom into the black hole" to see finer details; so the horizon hides the details from the observer located outside that horizon; I see no reason why one should not apply the same concept to every single vertex, regardless whether it is part of a black hole or not.

 

[atyy]

Maybe along the lines of

http://arxiv.org/abs/gr-qc/0203036
Coarse graining in spin foam models
Fotini Markopoulou

http://arxiv.org/abs/0909.5631
Algebraic structures in quantum gravity
Adrian Tanasa

http://arxiv.org/abs/1008.0354
EPRL/FK Group Field Theory
Joseph Ben Geloun, Razvan Gurau, Vincent Rivasseau

 

[MTd2]

Why not just to consider a vertice just as a scattering event, like 2 molecules in a gas? Thinking in this way, it sounds natural by just thinking the classical limit in terms of scattering amplitudes.

 

[Fra]

The more I think about this and the more of this nice discussions that take place the more does it seem that the three pillars on which somehow modern physics rests upon are entangled with each other.

The three things I mean is "quantum mechanics", "relativity" and "renormalization".

Recent threads tried to see what Rovelli's view on the CORE of relativity and QM is. But what is REALLY the core lession of the renormalization game? They are really inseparable, it's not possible the clarify one without the others. At least not physically.

I'll save my further thoughts for another thread. But maybe we can ask, what is the CORE lesson of renormalization? Or is it too early to draw that yet? It seems the QG issues can't be properly analysed without also thinking about what it means to scale the theories.

/Fredrik

 

[erkokite]

Here's something to add- I'm not a physicist so I could misunderstand, but Penrose brought this up in his Road to Reality book (and he is a physicist :D). LQG makes a transformation prior to quantization from the GL(2) group of General Relativity to the SU(2) by means of the Immirzi parameter. While this is a valid classical transformation, it does not hold in QFT.

 

[MTd2]

That's because SU(2) is the euclidean realization for GR! SL2(C) is the lorentzian :D

 

[marcus]

This is potentially an interesting topic! To focus discussion, could we take the most recent review's formulation as definitive? That way we will all be talking about the same thing.

Here is the most recent review:
http://arxiv.org/abs/1012.4707

The theory is defined by the three equations on page 2.

 

[marcus]

It seems to me that if you actually look at LQG. How the theory is formulated. (And don't just imagine things about it.) You see that it is not about how smooth manifolds behave, or about their metrics and such stuff.

It is about clusters of geometrically related measurements---I would say just from taking an objective look.

According to references in the paper, (observations concerning?) fermions and Yang-Mills fields can be included. Somehow the possibility of including information about matter in the picture is beginning to emerge. But the main thing dealt with so far is a cluster of related measurements of geometric stuff like area, volume, angle...

The important underlying principle is, I suppose, what Bohr said: physics is not about what nature IS but rather it is about what we can SAY of it.
Or you could rephrase it the way Rovelli has: that this is not about what nature "is" but rather about how nature responds to measurment.

So it is not about smooth manifolds (which are mythical creatures which we never actually observe but can only imagine). The theory is first of all based on graphs, because a graph is the skeleton that organizes a cluster of related measurments.
The primary object in the theory is the graph. And then one starts talking about the symmetries of measurements made involving the graph, and the Hilbertspace summarizing the information about those measurements... Anyway that is a start.

 

[tom.stoer]

marcus, nearly all topics I collected are about issues explicitly excluded by Rovelli; I am perfectly aware of this (as an example he does not want to talk about unification of gravity and matter ...)

 

[marcus]

marcus, nearly all topics I collected are about issues explicitly excluded by Rovelli; I am perfectly aware of this (as an example he does not want to talk about unification of gravity and matter ...)

That's fine. It's good to collect and bring up issues, in the context of the actual theory.
Since R. is a principal person defining and developing, simple courtesy would require one to acknowledge what is now the definitive formulation.

As you know, LQG has been completely reconstructed after 2007. Even Rovelli's 2008 review is partly out of date. No one else has written a review paper (after 2007) describing the theory and summarizing the status so far. All we have, since Rovelli's May 2008 "Living Reviews" survey is his 2010 papers, of which the most recent "LQG the first 25 years" is obviously intended to be definitive and supersede the other two.

There is, at present, no other author and no other competing formulation presented in comprehensive review-article form.

So it is very good to bring up topics and issues, but one should not make statements about what one fantasizes or imagines LQG might be, or what one fancies it might have been in 2004. One should raise topics and issues and bring them explicitly point-on-point to bear on what the theory IS.

After all, this is very easy to do--here is what LQG is:

http://arxiv.org/abs/1012.4707

 

[qsa]

This is potentially an interesting topic! To focus discussion, could we take the most recent review's formulation as definitive? That way we will all be talking about the same thing.

Here is the most recent review:
http://arxiv.org/abs/1012.4707

The theory is defined by the three equations on page 2.

To understand LQG original idea and its philosophy this paper is a must read.


http://arxiv.org/abs/gr-qc/9903045

Quantum spacetime: what do we know?

Authors: Carlo Rovelli

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in philosophy of science which are are raised by, or a relevant for, the research on quantum gravity.

 

[atyy]

Also, to show that some Regge-like thing is obtained does not imply the correct classical limit. That was the starting point of DT, and it did not work. With more constraints, CDT produced an intriguing result, but the discretization is still probably above the Planck scale, and the philosophy is markedly different from LQG in that the discretization does not remain in the fundamental theory that CDT approximates.

 

[tom.stoer]

I tried to express my ideas "close to LQG" b/c this is somehow the best (best developped) candidate (from the QG perspective - not from the string perspective); it is clear that many issues do not fit into this (rather narrow) LQG context as defined by Rovelli; nor do I expect that these issues can be solved in the current LQG framework

 

[atyy]

I'm very much in sympathy with your comment about matter on top of spin foams - there is no unification that way. It is true that in the original LQG idea pure gravity is a fundamental field, in which case it seems reasonable to add matter on top of spin foams. From this point of view additional generally covariant terms in the action would be consistent with LQG's own motivation of general covariance and with AS ideas.

However, I do suspect that current physical interpretation of the mathematics of LQG is not correct, and that some sort of unification could occur, perhaps along the lines of Freidel, Livine, Oriti and Ryan's work. In this case, the motivation for renormalization would come from GFT rather than AS since gravity isn't fundamental.

 

[marcus]

To understand LQG original idea and its philosophy this paper is a must read.


http://arxiv.org/abs/gr-qc/9903045

Quantum spacetime: what do we know?

Authors: Carlo Rovelli

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in philosophy of science which are are raised by, or a relevant for, the research on quantum gravity.

I think you are right. I just read the first two sections--up to about page 10--and skimmed the rest. I'm glad you pointed it out (I had missed the paper). It lays out the conceptual issues, as he sees them, with exceptional clarity.

 

[marcus]

I tried to express my ideas "close to LQG" b/c this is somehow the best (best developped) candidate (from the QG perspective - not from the string perspective); it is clear that many issues do not fit into this (rather narrow) LQG context as defined by Rovelli; nor do I expect that these issues can be solved in the current LQG framework

AFAICS your intent went in just the right direction. What one wants to do is inspect the current LQG framework and see if there are lacks, or shortcomings---fundamental inadequacies.

You might have a look at the goals expressed in this remarkable 1999 paper. It is surprisingly "clairvoyant" as regards the current framework
http://arxiv.org/abs/hep-th/9910131

He says right up front that the goal is to formulate QFT without a (pseudo)Riemannian manifold. And he explains why that has to be the goal. Basically right in the first paragraph.

The LQG as currently formulated could be wrong, but it is important to realize how bold it is. He is saying that physics should not be concerned with the flopping-around of a smooth manifold. (with or without particle fields painted on it.)

If you throw out the manifold (with stuff smeared on it) you get rid of quite a lot of phony "issues" that simply should not concern us---I think it boils down to that*.

GR describes the flopping around, waving, buckling, flapping of a manifold. Well no, even in GR you throw away the manifold eventually (E. said it has no objective reality) and pass to an equivalence class of metrics. The gravitational field is what is real and, as an equivalence class, it has no underlying manifold. In GR all the other fields should be defined on the gravitational field. (But as a practical matter one picks one representative of the class.)

So now we have a proposal of how to define QFTs without a spacetime manifold. Using finite graphs----showing contiguity between real things/events/measurments.
This proposal may be good or bad, we don't know yet.

BTW notice that it uses both SU(2) and SL(2,C)
and the Immirzi parameter is a relation between the representations of SU(2) and a countable subset of reps of SL(2,C).

p <--> (p, gamma*p)

Meanwhile the cosmo constant appears as q-group deformation parameter.

You mention the "landscape" represented by the choice of these two groups SU(2) and SL(2,C) that the theory is built on. Right. And even the two free parameters have their meaning in terms of the groups.

And it is a pragmatic issue which groups to choose. We will see, as more complicated matter is added to the picture, whether the groups change. One can imagine a process of "intuitively groping" for the right groups---a "group grope"

We should keep in mind that the LQG formulation consists of THREE EQUATIONS given right at the beginning of 1012.4707. Equations appropriately numbered (1), (2), and (3).

There is not much freedom in those equations. Perhaps the main freedom is in the choice of the two groups they are based on.

*or one may be able to translate a question originally expressed in terms of smooth manifold into the more minimalistic terms of LQG.
If a question requires manifolds in order to express it, I would suggest that it is physically meaningless.

 

[marcus]

So I would say that the real threat to the status quo which LQG poses is that if it is confirmed empirically then people will have to re-learn the quantum field theory of matter in a manifoldless formulation based on finite graphs.

On the other hand, if LQG fails observational tests, then such a shock may be avoided.

Because (as GR already indicated in 1915) spacetime is nothing else than the gravitational field.

LQG says that a quantum mechanical version of the gravitational field should live on finite graphs (carrying the finite information from measurements, particle detectors, etc that we either have or want to lay odds on.)

Because LQG says there is no other spacetime besides the quantum information represented by the spin-network graphs (and the two-complexes describing their evolution by giving transition amplitudes) it is absolutely essential to its success that we learn how to put matter on the graphs.

Something is not a good representation of the gravitational field (i.e. the geometry) if you cannot put matter on it. Because there is nothing else besides the gravitational field that matter CAN be defined on. So if LQG is to be a successful theory we must find a way to do this.
So far, it looks like one avenue towards this is that fermions are represented by broken links. Stumps that don't go anywhere.
(or perhaps have some antithetical stump somewhere else.) There may be still other ways in which matter is naturally included in the picture. As an observer I have no reason to speculate---I just notice that this is a vital current research front.

 

[tom.stoer]

I don't think that we should "add matter on top of it"; I expect matter + spacetime to emerge (consistently & coherently) from some fundamental entity. Spin networks may point into the right direction, but they are not complete, neither in the restricted spacetime-sense (BI, cc, SU(n) instead of SU(2), dim=4, ...) nor in the broader sense (matter couplings).

There are many (nearly) unexplored roads; for example there is absolutely no reason not to quantize GR in dim>5 or SUGRA in dim<=11 along these lines.

 

[marcus]

I don't think that we should "add matter on top of it"; I expect matter + spacetime to emerge (consistently & coherently) from some fundamental entity...

Well if you take a spin-network and break a link, creating two stumps...and later the two rejoin...is that "adding on top of" or is that "emerging"?

It may be that there are differences of nuance in the words which don't correspond to a consistent objective distinction.

I agree with you in liking to think of geometry and matter as arising from the same ground.
A single object should give rise to both. Then one has a chance of really understanding how matter can affect geometry. How it bends it and interacts with it. So I would like it if someone would invent such a theory.

But we might not be able to recognize such a theory in its early stage of growth. It might be difficult to identify what is a "natural" way for matter to emerge from whatever represents the quantumgeometry of the universe.

Suppose you could get something like matter by simply enlarging the groups that are used in LQG? Enlarging the SU(2) or the SL(2,C) used for labeling/coloring parts of the graph, or the two-complex.

That is, get matter by making the colors more complicated? Is that a natural emergence or is it an ad-hoc "adding on"?

Well that would depend mathematical taste, I suppose. Whether the enlarged groups were beautiful. Whether they provided elegant surprises. Mathematicians, the good ones, have a way of deciding whether something is elegant or clunky. I couldn't say anything in advance about that. One cannot always say in advance what will or will not constitute an elegant solution, or how something must look in order to be naturally emergent.

 

[marcus]

Some responses to the issues Tom raised:

[*]LQG starts with a quantization of spacetime which is topologically M³*R; it is by no means clear if this "background-dependence" does not throw away physical relevant sectors (of different topologies) of theory space

see next

[*]in the most general form the new SFs can to some extent go beyond this topology (as they do not specify a topology at all - only in a kind of classical limit), but again it's not clear if all topological sectors can be considered in this context

Indeed the SF models do not allow topology at scales smaller than you can measure. To distinguish between an apple and a donut one must have continuous paths and try to shrink them to a point. Such fine structure is not available at small scale. One can think of it as geometry being "uncertain" at Planck scale.

Since topology is a largescale phenomenon (existing "in classical limit") I see no obstacle to realizing macroscopic topologies, if that can be given meaning.

[*]LQG uses SU(2)-colored graphs w/o the notation of "dimension"; up to now I see no reason how dim=4 could be singled out from these graphs

I think Leonardo Modesto has some paper(s) showing that dim=4 comes out at large scale and that there is dimensional reduction at very small scale. IIRC this is based on the area-volume relation (which is scale-dependent). I would have to check this.

The choice of groups ( SU2 and SL2C ) is ad hoc. If you choose different groups you get a different theory. But given this choice of groups, I think the dim=4 comes out.

[*]LQG uses SU(2)-colored graphs w/o the notation of "dimension"; up to now I see no reason why especially SU(2) shall be used - why not any other gauge group? restricting to SU(2) can be justified only b/c one knows about the starting point dim=4 - which is a cat hunting its own tail; in that sense LQG suffers from a kind of "landscape problem"

Indeed the choice of groups is ad hoc. Any physics theory depends on some ad hoc choice. There is no "theory of theories" by which you can justify every feature and assumption a priori. Always in some respect you must be pragmatic, and see how well your theory works.

LQG is defined by three equations (1, 2, and 3) at the beginning of the recent review paper http://arxiv.org/abs/4707 . These equations depend on the choice of groups, there is little freedom otherwise. So this is a new format for QFT. You choose what two groups to use, and you put in those groups, and you see how it works.

At this point the problem is not one of having too many choices. It is to see how well this one choice, the fairly obvious one of SU(2) and SL(2,C), works.

[*] it is clear that 4-dim spacetime has some interesting properties, namely that it allows for an uncountable set of smooth structures; LQG uses exactly one smooth structure in the very beginning!

In the definitive review paper, I do not see any use of a smooth structure. There is no smooth manifold basic to the construction of the theory. Manifolds, and the differentiable structures on them, do not seem relevant to the theory.

[*] I indicated in another thread that the very existence of uncountably many smooth structures in dim=4 could single out dim=4; my idea was to construct a measure counting all different smooth structures on top of all topological manifolds in all dimensions; that would single out non-compact M⁴ immediately simply due to "counting" w/o any additional dynamical input; LQG has nothing to say about that

Right. The diversity of differentiable structures on various manifolds is interesting mathematics, but not phyics. It has to do with axiomatic mental constructs.

[*] I am convinced (but of course I can be wrong) that matter (fields) do emerge from spacetime; up to now the results about framed graphs in LQG seem to be a dead end (no new results since years)

I like this idea too! matter fields and geometry should arise from the same ground! Also the possibility of matter being braids or knots in spin network graphs was explored in 2007-2008 and seems to be a dead end. If the LQG gravitational field (i.e. quantum geometry) is a good one, then matter must be definable on it. Matter lives nowhere but on the gravitational field. I do not know how this will ultimately be done, or if it can be done. We will see.
====================

I will try to reply to the others later:
[*] adding matter on top of the SFs is the wrong way; it will never result in a unification of spacetime (gravity) and matter
[*] the asymptotic safety approach indicates that gravity may be non-perturbatively renormalizable; due to that approach all possible couplings constructed from g, R, ... should be taken into account and should be subject to renromalization group flow similar to Kadanoff's block spins; up to now LQG does not say anything about that
[*] LQG treats the BI parameter (or the BI field) in a rather special way; there are indication that the BI parameter is related to the theta-angle in QCD, but I think final results are still missing (this is of course of major interest as the BI parameter plays a prominent role in the spectra of certain operators; it is strange that a semi-classical calculation a la Hawking w/o quantum gravity should be used to fix the value of this parameter!)
[*] LQG treats the cosmological constant in a very special way (e.g. approaches via quantum deformations of SU(2)); it is unclear why the cc should have such a special role, whereas the AS approach indicates that all couplings can be treated in a harmonized manner
[*] taken together it is not clear if the cc is an algebraic input (via q-deformed SU(2)) or a dynamical output (e.g. via renromalization group) of the theory
[*] the LQC results are very encouraging; but afaik this theory says nothing about the initial conditions of the universe, especially regarding its entropy; up to now LQC treats the evolution of the universe near the big bounce as time-symmetrical; results using infinitly many degrees are required
[*] there are indications that the holographic principle is a fundamental principle of nature, but LQG does not use this principle at all, e.g. in order to define "boundary Hilbert spaces" to define the theory; the holographic principle shows up only in very special calculations, e.g. in calculating the states and the entropy of a black hole

 

[marcus]

This is a good list of concerns. It could lead to further constructive discussion. What follows are the points Tom made that I have not responded so far. In many cases I can give only a tentative response. Anyone else is welcome to jump in with comments.

[*] adding matter on top of the SFs is the wrong way; it will never result in a unification of spacetime (gravity) and matter

I suppose there are various ways to put matter into the picture. they will be explored and tried out. You may have some definite idea of what it means to "add on top of". I'm inclined to wait and see what including matter actually looks like.
then decide whether or not it seems to emerge from the geometry in a way that suggests some kind of unification of matter with geometry.

[*] the asymptotic safety approach indicates that gravity may be non-perturbatively renormalizable; due to that approach all possible couplings constructed from g, R, ... should be taken into account and should be subject to renromalization group flow similar to Kadanoff's block spins; up to now LQG does not say anything about that

Up to now I haven't seen A.S. say what happened at the big bang. Weinberg said this year that he had been trying to apply A.S. to the early universe, and he listed some problems that need to be overcome.

I'm not convinced that A.S. avoids the need for something like LQG. If whatever obstacles are overcome and we find that A.S. can model the early universe around the start of expansion, then we will have two models. That might be interesting, a case where observation of the CMB could be decisive.

[*] LQG treats the BI parameter (or the BI field) in a rather special way; there are indication that the BI parameter is related to the theta-angle in QCD, but I think final results are still missing (this is of course of major interest as the BI parameter plays a prominent role in the spectra of certain operators; it is strange that a semi-classical calculation a la Hawking w/o quantum gravity should be used to fix the value of this parameter!)

In the current formulation of LQG, the BI parameter plays the key role of mapping SU(2) reps p into SL(2C) reps (p, gamma*p)
I think you are right that we have not heard the final story concerning the value of that parameter. There have been various speculations about its significance--and it comes up tantalizingly in several different contexts. You are pointing to a question mark. It could be fun.

[*] LQG treats the cosmological constant in a very special way (e.g. approaches via quantum deformations of SU(2)); it is unclear why the cc should have such a special role, whereas the AS approach indicates that all couplings can be treated in a harmonized manner

the cosmological constant is another big question mark. I regret that I have nothing useful to say on the subject. Not even a hunch or wild guess.

[*] taken together it is not clear if the cc is an algebraic input (via q-deformed SU(2)) or a dynamical output (e.g. via renormalization group) of the theory

In this new format for a QFT, given by equations (1, 2, 3) in the December review paper, the groups largely determine the dynamics. So at some level one might suspect that
algebraic=dynamic.

Sorry I don't have anything more helpful and definite to say about these last points. You have made an excellent list of issues. Many of these indicate just the sort of things we should expect LQG to answer as the research program proceeds. Some really critical, that it must answer or fail.

One thing we can conclude is that we do not know what a general relativistic QFT will look like. People who have a preconceived idea of how a QFT must look are liable to be confused by what they see emerging.
Quite possibly a gen. rel. QFT will not have a spacetime manifold---

Still have two other points to consider! Have to take a break for the time being.
Thanks for the list of things to think about!

[*] the LQC results are very encouraging; but afaik this theory says nothing about the initial conditions of the universe, especially regarding its entropy; up to now LQC treats the evolution of the universe near the big bounce as time-symmetrical; results using infinitly many degrees are required[*] there are indications that the holographic principle is a fundamental principle of nature, but LQG does not use this principle at all, e.g. in order to define "boundary Hilbert spaces" to define the theory; the holographic principle shows up only in very special calculations, e.g. in calculating the states and the entropy of a black hole

 

[genneth]

[*] the LQC results are very encouraging; but afaik this theory says nothing about the initial conditions of the universe, especially regarding its entropy; up to now LQC treats the evolution of the universe near the big bounce as time-symmetrical; results using infinitly many degrees are required

If I may be so bold:

My position is that I don't demand LQG has to answer that question. The LQC research direction has rather neatly answered a personal question of mine for a very long time: how can one model the universe quantum mechanically, if the observer is in the universe? In retrospect, the answer is not so difficult to imagine anticipating (esp. for a condensed matter theorist!): quantum cosmology simple models the degrees of freedom representing the *large scale* structure of the universe --- in effect there is a sort of universality which allows these degrees of freedom to considered in separation to the other (say, matter or microscopic) degrees of freedom. Thus conceptually, we are making the assumption that at some point the coupling between these weaken and eventually they can be theorized about separately --- c.f. fluid dynamics; the macroscopic fluid model says nothing about the molecular kinetics, the latter can be assumed to couple in a simple way via constitutive relations regarding viscosity, heat capacity, etc. Thus if we run the argument backwards (in time), we should expect that in the earliest universe (i.e. asking now about the "initial" conditions, whatever that might mean for that period), there will eventually come a time when the "microscopic" motion occurs on the same timescale as the "macroscopic" motion, at which point we no longer have an separation of length/time scales, and must face the full quantum universe conundrum again.

Of course, we might hope that our eventual ToE *will* provide an answer; but I would chalk that one so far up the theory list that I think it exceeds what I can reasonably expect LQG to deliver.

 

[tom.stoer]

If I may be so bold:

Of course, we might hope that our eventual ToE *will* provide an answer; but I would chalk that one so far up the theory list that I think it exceeds what I can reasonably expect LQG to deliver.

Let me respond b/c this topic was also from my list. I am not expecting that LQG will have answers to all issues mentioned in my list. Rovelli is rather clear about the restricted focus of LQG. But that's the point: There are questions related to quantum gravity which cannot be answered by the leading theory of quantum gravity.

Regarding the initial conditions and entropy: here the situation is simple: the most interesting results are derived in the LQC context using only finitly many degrees of freedom; answers regarding entropy, fluctuations etc. need to be addressed in the LQG context using infinitly many degrees of freedom eventually.

 

[marcus]

...
Regarding the initial conditions ... answers regarding entropy,... need to be addressed in the LQG context using infinitly many degrees of freedom eventually.

No doubt you've seen the LQG papers where the early universe is treated using spinfoams. This is an application of the full theory (not symmetry-reduced) but still using only the simplest graphs and foams.

Here is a simple intuitive argument regarding Penrose's entropy objection to the bounce. See if it makes sense to you.

I think what happens regarding entropy is this---as long as gravity is attractive the most uniform distribution of matter (with a level gravitational field) is LOW entropy.

Starting with a low-entropy level spread, the matter begins to collect in clumps---this is entropy increasing. Penrose has discussed this in numerous talks.

However P. does not mention that in LQG case for a brief period of time during the bounce, gravity is repellent. In that case, with the reversed sign, it is the clumpy gravitational field that has low entropy. Collections of matter blow apart and matter takes on a uniform distribution (which is high entropy as long as gravity is repellent).

So during the bounce the distribution of matter, and the grav. field level out. Entropy is always increasing, as the field becomes uniform. Then, after bounce, gravity is again attractive and uniform means low. So the new expanding universe starts out in a low entropy state.

It is the fact that gravity changes sign that causes what seems to be a paradox. The gravitational field entropy is the dominant form and its definition depends on the sign (whether attractive or repellent.)

I think that is probably the reason that Ashtekar, who is longterm friends with Penrose and must have heard Penrose talk about entropy and bounce on countless occasions, has never seemed worried by Penrose's thermo objection. Admittedly this is not spelled out rigorously, but it's in the context of a novel situation and I find that, to me, intuitively it makes sense.

 

[tom.stoer]

good point!

 

[inflector]

I think that is probably the reason that Ashtekar, who is longterm friends with Penrose and must have heard Penrose talk about entropy and bounce on countless occasions, has never seemed worried by Penrose's thermo objection. Admittedly this is not spelled out rigorously, but it's in the context of a novel situation and I find that, to me, intuitively it makes sense.

I have always thought it intuitive that gravity was driving entropy (and time itself really). It is very interesting to see this pointed out with respect to Ashtekar's perspective, especially the sign reversal for entropy itself when gravity's sign changes.

It also seemed to me that a bounce would "fix" entropy so I have favored that idea over a pure big bang. It certainly answers the question of why the universe got to be so ordered. It will be interesting to see if this idea holds up under observations over the next decade or so.

Thank you marcus.