What are the best introductory resources for learning Loop Quantum Gravity?

[space_cadet]

GFT is related to the Sundance braid proposal?

In GFT the basic building blocks are (n-1)-simplices (a 0-simplex is a point, a 1-simplex is a line-segment, 2-simplex is a triangle, 3-simplex is a tetrahedron ... and so on), which are glued together to form a simplicial complex (a discretized manifold), whose dynamics is given in terms of group elements assigned to each of the n faces of the (n-1)-simplex (see e.g. arXiv:0710.3276v1) The "field" is then taken to be a complex valued functions acting on these (n+1) group elements:
$$ \phi(g_1, g_2, \ldots, g_{n}) : G^n \rightarrow \mathbb{C} $$
Now, given (n+1) copies of a (n-1)-simplex, one can glue these together along their respective faces to form a n-simplex, e.g. for n=3, given four triangles (a triangle is a 2-simplex), one can glue them together along their edges to form a tetrahedron (which is a 3-simplex). One can write down an action for such a theory (see reference above) and explicitly compute various observable quantities. The resulting theory describes the dynamics of an n-dimensional manifold in terms of its constituent (n-1)-simplices.

The connection with the braid proposal arises from the observation that, a priori, there is no restriction on the form of the group G which is used to label faces of the simplices. G could be SU(2), SL(2,C) or even SL(2,Z) (the modular group) or B_3 (the three-stranded braid group). For instance, if one can write down a GFT action for 2-simplices, with edges labeled by representations of B_3, such an action would describe the dynamics of a manifold constructed by gluing the edges of triangles using 3-strand braids. This is the essence of the relationship I see between GFTs and the braid model. It may or may not turn out to technically feasible.

If you have further questions a new thread might be best, since this reply already takes this thread off-topic!

 

[space_cadet]

LQG for the Bewildered - arXiv:1402.3586

Hello again,

Almost precisely one year to the day that I posted the early draft of lqgbewil in this thread, I present for your reading pleasure the beta-version of lqgbewil submitted to arXiv in Feb, 2014.

http://arxiv.org/abs/1402.3586

The paper is not one hundred per cent perfect, but Sundance and I have labored to bring it up to a level where, at least as far as the topics we directly address are concerned, it is around 90% complete.

We hope it will serve its intended purpose and we solicit your undiluted criticisms and opinions in order to be able to improve upon the original.

Enjoy!

 

[friend]

OK. So it seems the existence of spin networks is the starting point of LQG. Are these spin networks a completely derived thing? Or are they a guess as to the connection between GR and QT? Where does the derivation from present theory end and assumption begin in LQG. Thanks.

 

[marcus]

There do seem to be more different ways to learn about Loop and Spinfoam gravity these days. A variety of introductions and accessible overviews are getting more available.
One good one by Sundance Bilson-Thompson and Deepak Vaid ("space cadet") is discussed in this thread. There's also the recent textbook by Gambini and Pullin that puts emphasis on developing necessary prerequisites at undergrad level.
I should also mention Wolfgang Wieland's thesis---it provides an overview of new directions that current RESEARCH is taking. For a PhD thesis it does a remarkably thorough and thoughtful job surveying the current status. He posted it at the beginning of March 2014, so it's pretty up-to-date.
http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf
https://www.physicsforums.com/showthread.php?t=746983
Here's another introduction to spin foam QG, this time by Jonathan Engle:
http://arxiv.org/abs/1303.4636
I'm doubtless forgetting other useful recent work that can serve as introduction to the subject.

Another way a newcomer can get a glimpse of Loop Spinfoam essentials in the context of the 2013 Oxford conference on Cosmology and Quantum Foundations (which is an interesting avenue of approach where you see its motivation among active rival lines of thought) is to watch a couple of talks Rovelli gave at the conference. Both are on YouTube and the camera work is good.

Google "rovelli cosmology view" and you get:

Cosmology and Quantum Theory: the Relational View
Google "rovelli loops spinfoams" and you get:

Cosmology and Quantum Gravity: Loops and Spinfoams
In each case you will see auxiliary links to YouTubes of the Q&A sessions that followed the talk. These are interesting as well.

 

[marcus]

OK. So it seems the existence of spin networks is the starting point of LQG. Are these spin networks a completely derived thing? Or are they a guess as to the connection between GR and QT? Where does the derivation from present theory end and assumption begin in LQG. Thanks.

In a quantum theory (whether geometry and/or matter) the "ontology" is LEANER i.e. sparser than in classical case.
Phenomena are intermittent and discrete always involving some type of interaction.
Continuities are inferred.
(BTW see around minute 15 of Rovelli's first Oxford talk. The story of Heisenberg in the Copenhagen park at night.)

Facts are interactions: one process affects another

A process occurs in a bounded region. Outsiders interact with the process at the boundary.
Imagine a web of facts spread over the boundary. This is where the outside interacts with the process, eg. makes measurements or is affected in some way.
A spin network is one example: consisting of measurements of volumes and contact areas of chunks of space which could be the web of geometric facts surrounding the process
In current research networks carrying OTHER KINDS of labels besides spins can be used, so what one is dealing with is not always strictly speaking a SPIN network. But however it is labeled, it is a web of (at least hypothetical) measurements and facts of various kinds that surrounds a process and represents the way the outside "knows about" the process or interacts with it.
This is just my impression, in part reinforced by watching the two Oxford talks and reflecting on the slide images and such.

 

[Demystifier]

Rovelli and Vidotto have written a new introductory textbook on loop quantum gravity:
https://www.amazon.com/dp/1107069629/?tag=pfamazon01-20

It is not yet officially published, but a draft can be freely (and legally) downloaded from
http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf

I have started reading it, so I can tell its excellent.

A lot of introductory material on loop quantum gravity can also be found at the wikipedia page
http://en.wikipedia.org/wiki/Loop_quantum_gravity
where I have found the link to the draft above.

 

[Physics Monkey]

Interesting. I like the technical material presented in the first few sections of the Rovelli-Vidotto book http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf, but I find some of the initial propaganda really irritating.

I wish we could avoid this kind of infighting and misrepresentation.

For example, Figure 1.3 is silly and the caption misrepresents the content of AdS/CFT. Even in quantum gravity an asymptotic boundary will be non-fluctuating. Table 1.2 is another silly bit of misinformation. String theory is also heavily influenced by the sum over geometries perspective, e.g. all the way back to the work of Polyakov, etc. on the string worldsheet. And no mention seems to be made of the fact that the loop gravity approach requires (or at least used to require) an unusual quantization scheme in addition to "taking geometry seriously". This weird quantization scheme has always been a stumbling block for me and I suspect many others.

I would really like to understand these developments better, but I just get a bad taste in my mouth when a book begins this way. Am I crazy?

 

[MathematicalPhysicist]

The old string-loop fight:

 

[Demystifier]

I would really like to understand these developments better, but I just get a bad taste in my mouth when a book begins this way. Am I crazy?

No, you are just a human being having not only a rational side, but also an emotional one.
Try to be more rational and less emotional, by simply ignoring those parts which are not worth reading. Even geniouses sometimes tell silly things, which does not diminish the value of their non-silly words.

I would even go that far to propose that someone who never says anything silly, probably has nothing important to say at all.

 

[atyy]

No, you are just a human being having not only a rational side, but also an emotional one.
Try to be more rational and less emotional, by simply ignoring those parts which are not worth reading. Even geniouses sometimes tell silly things, which does not diminish the value of their non-silly words.

I would even go that far to propose that someone who never says anything silly, probably has nothing important to say at all.

But the problem is that if we have to figure out which parts of the book are trustworthy and which are not, then is the book still worth reading? If LQG has truly solved the black hole entropy problem, why is this not generally acknowledged? More propaganda from the LQG folks, or a magnificent achievement unjustly neglected by the physics community?

"The entropy can be computed from first principles, including the famous 1/4 Hawking factor, it is finite and the calculation can be done for realistic black holes, such as a Schwartzschild or Kerr hole. This is beautiful achievement of the theory which for the moment is not matched by any of the other tentative quantum theories of gravity." http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf (p220)

Here, for reference, is "Bianchi 2012b" http://arxiv.org/abs/1211.0522.

 

[atyy]

Or things like footnote 6 on p51 "This does not mean that we adopt an instrumentalist interpretation of quantum theory. A process is what happens to a system S between interactions with other physical systems. The manner in which S affects the physical systems it interact with, is described by the quantities (q, t, q0, t0). This is discussed in detail in [Rovelli (1996b)], to which we refer the interested reader for an interpretation of quantum mechanics that make sense in the exacting context of quantum gravity."

So we need to adopt Rovelli 1996b to have an interpretation that makes sense in the exacting context of quantum gravity. Good bye Bohmians!

 

[atyy]

Does LQG have any consensus? Or are the major results all in doubt?

The discrete spectrum of the area operators was questioned by http://arxiv.org/abs/0708.1721 .

The correctness of the EPRL model and whether it has an appropriate semiclassical limit was questioned by http://arxiv.org/abs/1201.2187 .

The formulation of spin foam cosmology was questioned by http://arxiv.org/abs/1105.1334 .

 

[Physics Monkey]

The need to carefully think through all the relevant physics notwithstanding, I quite enjoy downloading a new subject rapidly into my brain from a trusted source. It's just so much fun, not to mention efficient. And you quickly get your subconscious working on all the puzzles and mysteries and so forth.

This is part of the reason why I hesitate when I see easily avoided misrepresentations in a new book.

Still, I did like the introductory technical bits, for what its worth.

Also, I'm all for personality in a book (which is my reading of your adjective "silly", Demystifier). I enjoy reading an author who believes things, who has quirks and tastes, and who is generally willing to stick their neck out for something. But let's at least get to something technical before we start quibbling about who is a real quantum gravity theorist!

 

[Physics Monkey]

"The entropy can be computed from first principles, including the famous 1/4 Hawking factor, it is finite and the calculation can be done for realistic black holes, such as a Schwartzschild or Kerr hole. This is beautiful achievement of the theory which for the moment is not matched by any of the other tentative quantum theories of gravity." http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf (p220)

I hope we can all agree that this statement of Rovelli-Vidotto is just false.

 

[martinbn]

@atyy: It seems that you have some issue with LQG. May be I simply misunderstand you, but it seems that that you have a personal problem with it. And you are not a string theorist. :)

 

[atyy]

Do you say it's false because string theory has calculated the entropy of Schwarzschild and Kerr black holes?

 

[atyy]

@atyy: It seems that you have some issue with LQG. May be I simply misunderstand you, but it seems that that you have a personal problem with it. And you are not a string theorist. :)

I would hope it's fair to say that lots of workers in LQG have personal problems with it. And I'm not an LQG theorist either:)

 

[martinbn]

@physicsmonkey: Which parts are the propaganda? I may be wrong but it seems that you are biased and searching for propaganda. For example figure 1.3 seems innocent to me. May be you are irritated because you assume that the last picture, the quantum gravity, is supposed to be LQG. But I don't think that's what they claim. It is meant to be the final and complete theory of quantum gravity, it may very well be string theory.

 

[martinbn]

I would hope it's fair to say that lots of workers in LQG have personal problems with it. And I'm not an LQG theorist either:)

That is why I don't understand you. They, the workers in LQG, may have problems, but you a side observer, why do you have a problem with it?

 

[atyy]

That is why I don't understand you. They, the workers in LQG, may have problems, but you a side observer, why do you have a problem with it?

I think many major claims of the Rovelli-Vidotto book are in doubt:

Does LQG really calculate from first principles any black hole entropy?

Is the EPRL model the consensus model, with the correct semiclassical limit?

Is the Rovelli-Vidotto approach to spin foam cosmology correct?

And an earlier major claim of LQG (but not, I think, in the Rovelli-Vidotto book) about the discreteness of the spectrum of geometric operators is also questioned.

I provided links above to show that all have been questioned by LQG insiders. I think the book should be more explicit about these problems and alternative viewpoints.

But dare I say, the real reason is I'm not a Jimi Hendrix fan!

 

[Physics Monkey]

Do you say it's false because string theory has calculated the entropy of Schwarzschild and Kerr black holes?

I think its fair to say that no one has really computed the entropy of a Schwarzschild black hole in flat space. To be sure there are many partial results, including semi-classical stories, hand-waving string calculations (described e.g. in Susskind's thin book on the holographic principle), and some LQG calculations. Regarding LQG stuff, I don't see that the issue of areas not being gauge invariant has been resolved, but I'd be happy to be corrected about this. For me, the conceptual bottom line is that we don't really know what this entropy even is, e.g. what is the hilbert space or whatever? We know S = A/4G but I think we don't really know the analog of S=tr(rho log(rho)).

Then there is Kerr/CFT. This does in principle describe Kerr black holes in flat space, but the CFT in question is associated with near horizon physics and is in general just part of a larger unknown structure. But at least one has a calculation of the entropy of the black hole and some better idea of the analog of S=tr(rho log(rho)).

One could also mention extremal black holes. Presumably Rovelli-Vidotto discount this case with their comment about "realistic", but I don't think we should dismiss these so quickly given that we understand the microstates.

Undoubtedly the nicest examples come from AdS/CFT. There the entropy of Schwarzschild black holes and Kerr black holes are precisely calculated and understood microscopically in the CFT. Fine, the asymptotics aren't right, but these results are clearly triumphs for quantum gravity.

Most of the successes above are string successes (or more generally holographic successes), and I don't see how LQG can claim anything like these successes. The state counting always requires tuning the IP and the other "dynamical" calculations are at best semi-classical statements that the whole community has been discussing in various forms for years.

I've been saying for years that the obvious thing to do is study LQG in AdS, but for some reason I can't fathom, almost no one works on this.

 

[Physics Monkey]

@physicsmonkey: Which parts are the propaganda? I may be wrong but it seems that you are biased and searching for propaganda. For example figure 1.3 seems innocent to me. May be you are irritated because you assume that the last picture, the quantum gravity, is supposed to be LQG. But I don't think that's what they claim. It is meant to be the final and complete theory of quantum gravity, it may very well be string theory.

I'm certainly biased, no doubt about that. However, I think you have to really bend over backwards to not see Fig. 1.3 as anti-string and anti-AdS/CFT propaganda. The crazy color picture even has little triangles in it and the surrounding discussion makes it clear, in my opinion, that Rovelli-Vidotto are claiming to be genuine quantum gravity theorists unlike the rest of us poor post-maldacenians :)

My claim is simply that such statements are unnecessary and seriously detract from my enjoyment of the book.

 

[atyy]

Undoubtedly the nicest examples come from AdS/CFT. There the entropy of Schwarzschild black holes and Kerr black holes are precisely calculated and understood microscopically in the CFT. Fine, the asymptotics aren't right, but these results are clearly triumphs for quantum gravity.

What are the references for these?

 

[martinbn]

You might be right. I may be too naive or uninformed to see the figure that way, but then I guess I am lucky because I am reading the book and so far no bad taste in my mouth. :)

 

[marcus]

Hi Atyy,
thanks for including the reference to Bianchi's 4-page paper. It's clear from the context, pages 219-220, that they are talking specifically about that paper and the derivation (from LQG first principles) there in that paper.

They are not talking about other attempts within Lqg to derive BH entropy.

I think that Rovelli Vidotto's statement is probably correct. That is, that Bianchi has given a valid derivation in that paper, of the S=A/4 formula. Now whether Hawking's formula is correct is another matter. It could be wrong. But Bianchi has derived this formula, and that is what they are saying. It is made explicitly clear from context that they are discussing Bianchi's derivation.

...
"The entropy can be computed from first principles, including the famous 1/4 Hawking factor, it is finite and the calculation can be done for realistic black holes, such as a Schwartzschild or Kerr hole. This is beautiful achievement of the theory which for the moment is not matched by any of the other tentative quantum theories of gravity." http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf (p220)

Here, for reference, is "Bianchi 2012b" http://arxiv.org/abs/1211.0522.

I hope we can all agree that this statement of Rovelli-Vidotto is just false.

No, I don't agree. I think Bianchi's derivation is OK. But it doesn't matter, you are very welcome to think it doesn't work, or whatever suits. Very glad to see all the interest in this new textbook! Thanks everybody for all the comments!

 

[Mordred]

I'm not positive if these articles have been posted, they are ones I've been studying.

http://arxiv.org/abs/1201.4598 "Introduction to Loop Quantum Cosmology by Abhay Ashtekar
http://arxiv.org/abs/1302.3833 Loop quantum Cosmology by Ivan Agullo, Alejandro Corichi
http://arxiv.org/abs/1108.0893 "Loop Quantum cosmology: a status report Abhay Ashtekar, Parampreet Singh.

by the way I like your article: Space_cadet

 

[Physics Monkey]

No, I don't agree. I think Bianchi's derivation is OK. But it doesn't matter, you are very welcome to think it doesn't work, or whatever suits. Very glad to see all the interest in this new textbook! Thanks everybody for all the comments!

I hate to get into this again, but fine:

There are a number of nice points in Bianchi's paper http://arxiv.org/abs/1204.5122, but I cannot agree that it provides a derivation of S=A/4.

For starters, there is no actual definition of S ever given in the paper until the end where a comment about spin foams is made. However, what the Euclidean spin form partition function he writes has to do with earlier manipulations is not clear.

A derivation should have a definition of S and then an argument to show that S=A/4.

The sudden appearance of Clausius from nowhere, the assumption that the horizon has a temperature because of an elementary transition rate calculation, and so on means that we cannot regard this paper as a derivation. The coupling V between the thermometer and the geometry is ad hoc. The fact that the spin foam area states are not gauge invariant is not obviously addressed. I could go on ...

Many of these points were raised by me and others years ago when we first discussed this paper on Physics Forums. And again, the paper has nice ideas and results, all I'm claiming is that it cannot be viewed as a full derivation of S=A/4.

We can compare all this with, say, the calculation of the BTZ black hole entropy in AdS/CFT. We say that the BH entropy is defined to be the thermal entropy of the quantum state of the CFT. One derives that the AdS radius is proportional to the central charge in Planck units. Then one evaluates the area of the black hole horizon and finds that it is precisely A=4S. One is also free to study the dynamics of matter in the usual ways to see that matter can experience thermal effects. And although this in the context of AdS/CFT, Bianchi says nothing about the asymptotics, hence we're free to transplant Bianchi to AdS and compare. All I can say is that I know which set of ideas looks more like a derivation to me.

 

[Demystifier]

Atyy, your examples demonstrate that the book should be read critically. There are claims in it which are controversial. But still, I find the book good because I find many illuminating explanations in it. Rovelli certainly has a talent to explain complicated technical stuff in a relatively simple and intuitve way, and that's what I like about this book.

 

[atyy]

I think one of the most interesting sections of the book is 2.4.2 on the boundary formalism and observables in quantum gravity, and its application on p241 & 242. I have never understood this properly, and would love to know whether others think it makes sense. What I don't understand about it is that it seems that the observer is outside the quantum region of spacetime, and so presumably spacetime is classical where he is?

 

[Demystifier]

I think one of the most interesting sections of the book is 2.4.2 on the boundary formalism and observables in quantum gravity, and its application on p241 & 242.

Yes, that's one of my favored parts too.

I have never understood this properly, and would love to know whether others think it makes sense.

I think it does.

What I don't understand about it is that it seems that the observer is outside the quantum region of spacetime, and so presumably spacetime is classical where he is?

I think one cannot say where and when spacetime becomes classical before studying measurement in terms of decoherence, which Rovelli doesn't. An important part of it are (almost classical) coherent states which he does study, but what is missing is an explanation how the wave function of the universe becomes decohered in the basis of coherent states.

 

[marcus]

I think one of the most interesting sections of the book is 2.4.2 on the boundary formalism and observables in quantum gravity, and its application on p241 & 242. I have never understood this properly, and would love to know whether others think it makes sense. What I don't understand about it is that it seems that the observer is outside the quantum region of spacetime, and so presumably spacetime is classical where he is?

Yes, that's one of my favored parts too.I think it does.I think one cannot say where and when spacetime becomes classical before studying measurement in terms of decoherence, which Rovelli doesn't. An important part of it are (almost classical) coherent states which he does study, but what is missing is an explanation how the wave function of the universe becomes decohered in the basis of coherent states.

I think it's similar to the fact that a map does not need to contain an accurate picture itself. And the idea there is no super observer or god's eye view. So the boundary formalism DOES NOT CONTAIN a "classical" rest-of-universe. There is the process being studied, which is defined as occurring in a bounded spacetime region. And there is the boundary. And nothing more. But if I learn that there is somebody else observing the process, I can redraw the boundary so that the region now includes THEM. Other observers are quantum and modeled like everything else. I'm the USER of the boundary formalism, not something formalized in it

So the boundary formalism does not need to contain any "classical" spacetime region.

I could be wrong, that is just how I interpret it. For more reliable clarification, people might google "relational cosmology rovelli" and get the talk Rovelli gave in June 2013 at Oxford conference on Cosmology and Quantum Foundations


If I remember right the first 15 or 16 minutes provides a kind of philosophical argument why there is no "wave function of the universe"

 

[atyy]

marcus, so if I am using this boundary formalism, am I inside the boundary or outside? I thought I'd be outside, since everything inside the boundary is quantum, but I the observer am not quantum.

 

[marcus]

marcus, so if I am using this boundary formalism, am I inside the boundary or outside? I thought I'd be outside, since everything inside the boundary is quantum, but I the observer am not quantum.

I would say that you, as user, are not in the spacetime region being studied, Atyy. If you consider yourself quantum, then you are quantum. But you are outside the process being studied and modeled.

Officially, "boundary formalism" is the work of Robert Oeckl. I think he is currently at Erlangen. Google him if you want and read one of his expositions of "boundary formalism". My impression is that the user is not represented in the formalism. So the user of the theory is neither "quantum" or "classical".

I could be wrong of course. Maybe Oeckl talks about a classical observer as part of his formalism.
Would you like to check? Or shall I?

 

[marcus]

I think that it is probably wrong to think of the world divided between "quantum" and "classical". this false dichotomy is a relic of the Copenhagen interpretation. There is no need to think that everything is this or that.
But I don't speak for these various experts.

My impression is that Rovelli conceives of the world composed of quantum processes separated by boundaries which are to some extent MOVABLE. And which interact (exchange info) across the boundaries.

there is nothing "classical" in such a world. However one does not try to study the whole shebang all at once. One defines a finite process in a bounded spacetime region. there are interaction "facts" or events on the boundary allowing one to study that process and compute enclosure amplitudes.

One COULD perhaps choose to study one's instruments, one's hands, one's eyes as themselves quantum processes. In principle there is some flexibility as to where one puts the boundaries. As I recall at the Oxford conference there was some talk about being faithful to ordinary scientific practice---what's customary lab practice.

There are probably some distinctions between the relational view and Oeckl's boundary formalism as he presents it, but they're certainly closely related.

The new introductory textbook that Demystifier linked to is a really good source on LQG, as he says! I'll repeat the link in case anyone is new to the thread.
http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf
But I also can't recommend too highly this video of the talk Rovelli gave at Oxford last June
on "Cosmology and Quantum Theory: the Relational View"

 

[atyy]

I think Rovelli in his earlier review http://relativity.livingreviews.org/Articles/lrr-2008-5/fulltext.html section 5.4 says to pick your favourite interpretation. As a Bohmian, my favourite interpretation is Copenhagen, so I should be able to use a classical observer, at least according to Rovelli in 2008.

Also, in Oeckl's http://arxiv.org/abs/gr-qc/0312081 (second bullet point at top of p3) he says it is not necessary to endorse a wave function of the universe, which is very much a Copenhagen point of view.

So presumably, if I am classical, the spacetime around me is classical, and a physically relevant boundary state should be one that is strongly peaked on a classical geometry?