Loop gravity Hamiltonian-for Jeff and/or Eigenguy

[marcus]

Loop gravity Hamiltonian---for Jeff and/or Eigenguy

Sources on the loop gravity Hamiltonian would include, I guess, these two sections of Rovelli's textbook "Quantum Gravity"

Chapter 4 Hamiltonian General Relativity pages 97-108

especially section 4.1.2 "The Hamilton function of GR and its physical meaning"

(in classical GR the physical meaning of the hamilton function is not what one has learned to expect, due to differences in definitions of energy and time)

Chapter 7 Quantum Spacetime: the Hamiltonian Operator pages 167-174


At different time both Jeff and Eigenguy have been asking along similar lines about the loop gravity Hamiltonian and have cited the same article by Thiemann---who around 1996/1997 constructed a form of the Hamiltonian with which almost immediately Lewandowski pointed out problems. This had repercussions.

On 30 October, actually just in a few days, Lewandowski will give a talk on the Hamiltonian of quantum gravity at the "Strings meets Loops" symposium near Berlin. If the talk is posted, it may give an authoritative view for a wide audience.

Also since Rovelli's textbook is intended an introductory graduate level text to a fairly new subject matter it is, at least in places, fairly accessible---not too heavily technical. At least worth a look since Rovelli generally has a realistic down-to-earth approach.

There are two different issues involved----the second, and less important I think, is Thiemann's trouble with his construction of the constraint and the unhappy consequences which he doubtless still feels. The first as I see it, is already latent in GR, and you get a taste of it in Rovelli's Dialog on page 17. I will type in an exerpt

 

[eigenguy]

Originally posted by marcus
Sources on the loop gravity Hamiltonian would include, I guess, these two sections of Rovelli's textbook "Quantum Gravity"

Chapter 4 Hamiltonian General Relativity pages 97-108

especially section 4.1.2 "The Hamilton function of GR and its physical meaning"

(in classical GR the physical meaning of the hamilton function is not what one has learned to expect, due to differences in definitions of energy and time)

Chapter 7 Quantum Spacetime: the Hamiltonian Operator pages 167-174


At different time both Jeff and Eigenguy have been asking along similar lines about the loop gravity Hamiltonian and have cited the same article by Thiemann---who around 1996/1997 constructed a form of the Hamiltonian with which almost immediately Lewandowski pointed out problems. This had repercussions.

On 30 October, actually just in a few days, Lewandowski will give a talk on the Hamiltonian of quantum gravity at the "Strings meets Loops" symposium near Berlin. If the talk is posted, it may give an authoritative view for a wide audience.

Also since Rovelli's textbook is intended an introductory graduate level text to a fairly new subject matter it is, at least in places, fairly accessible---not too heavily technical. At least worth a look since Rovelli generally has a realistic down-to-earth approach.

There are two different issues involved----the second, and less important I think, is Thiemann's trouble with his construction of the constraint and the unhappy consequences which he doubtless still feels. The first as I see it, is already latent in GR, and you get a taste of it in Rovelli's Dialog on page 17. I will type in an exerpt

Thanks!

 

[marcus]

The page references I gave earlier for Rovelli's textbook chapters 4 and 7 refer to the October 12 draft that you would get if you downloaded the book today from his website (google Carlo Rovelli to get there, the link to the PDF if on his home page)

But if you happened to have downloaded the book earlier and have the August edition, Chapters 4 and 7 are on pages 107-122 and 193-201

Getting back to the Sal/Simp dialog. It is familiar, anyway to everyone who would be reading this thread, and posted at
http://arxiv.org/hep-th/0310077
and it is also included in Rovelli's textbook as a kind of "dessert" course at the end, after the History chapter and before References. The dialog dramatizes (among other things) the situation of a graduate student who may wish to study loop gravity but who, at least in the USA, may not be able to manage it for carreer reasons---finding a thesis advisor, job prospects etc.
Anyone interested enough in loop gravity to look into Rovelli's textbook should certainly confront that issue.

And the dialog sketches various misunderstandings between a particle theorist viewpoint and a GR view. For example (as relates to the hamiltonian) page 17:

Simp - So, does loop gravity predict Lorentz violation or not?

Sal - I am not sure. I think so far it is like large extra dimensions for strings. Could be. Could not.

Simp - hmmm...But if you have no Lorentz symmetry, you may have no hermitian hamiltonian.
Is loop gravity unitary?

Sal – No, as far as I understand.

Simp – This is devastating.

Sal – Why?

Simp – Because unitarity is needed for consistency.

Sal – Why?

Simp – Because without unitarity probability is not conserved.

Sal – Conserved in what?

Simp – In time.

Sal – Which time?

Simp – What do you mean “which time?”. Time.

Sal – There isn’t a unique notion of time in GR.

Simp – There is no coordinate t?

Sal – There is, but any observable is invariant under change of t, therefore everything is constant in this t just by gauge invariance.

Simp – I am confused.

Sal – I know, it is always confusing. . . Nonperturbative GR is quite different from physics on Minkowski . . .

Simp – Do we really need to get in the conceptual complications of GR?

Sal – Well, if we are discussing the theory that is supposed to merge GR and QM . . .

Simp – String theory merges the two without these complications.

Sal – This is why I think that string theory does not really merge GR and QM.

Simp – But you agreed it does.

Sal – No, I agreed that strings provide a finite perturbation expansion for the quantum gravitational field and this expansion breaks down when things begin to become interesting: in the strong field regime.

Simp – So, why does string theory not merge GR and QM?

Sal – Precisely because GR tells us that there is no fixed background space with stuff over it. Strings are always about background spaces with stuff over them.

 

[marcus]

this may be the gist, as regards hamiltonian

Simp – The fully background independent theory is an immense task, we are far from it.

Sal – Loop gravity does it.

Simp – And what do field and things stand on?

Sal – On top of each other, so to say.

Simp – It is not quite similar to the physics I know.

Sal – It is beautiful. You talked about the beauty of string theory. The emergence of spacetime as excited states, as loop and spinnetwork states, is extremely beautiful. It is quantum theory and general relativity truly talking to each other . . .

Simp – If background spacetime is missing, so is time?

Sal – Yes sir.

Simp – And if you do not want to impose asymptotic flatness you do not have asymptotic background time either?

Sal – Yes sir.

Simp – And if there is no background time, there cannot be unitary evolution, right?

Sal – Yes.

Simp – I am not sure I can digest a theory where there is no space and no time to start with, and without unitarity. . .

Sal – I suppose this is why there is so much resistance to loop gravity . . . Again, everybody searches background independence, but when you see it, it is sort of scary. . . Anyway, we can all believe what we like, until experiments will prove somebody right and somebody wrong, and for the moment no experiment is talking to us . . . Future will tell . . . But my point is that the absence of unitarity does not imply that the theory is inconsistent. Only that the notion of time is intertwined with dynamics. It is similar to the fact that there is no conserved energy in a closed universe . . .

 

[marcus]

a few words from Rovelli's chapter 7

In chapter 7 Rovelli constructs the loop gravity hamiltonian (even has a picture to help convey the idea) and then he says:

"The striking fact about the hamiltonian operator is that it can be defined at all. But how unique is it? There are a number of possible variants of the operator that one may consider. These can be seen as quantization ambiguities, that is, they define different dynamics in the quantum theory, which, at least at first sight, have all the same classical limit. So far, it is not clear if these are truly all viable, or whether there is some physical or mathematical constraint that may select among them. I list here some possible modifications of the operator..."

and he proceeds to list a page or so of different ways to vary the definition of the hamiltonian.

 

[jeff]

Originally posted by marcus
At different time both Jeff and Eigenguy have been asking along similar lines about the loop gravity Hamiltonian and have cited the same article by Thiemann

Firstly, I wasn't asking about the Hamiltonian. I was pointing out to you and everyone else that contrary to what you we're saying at the time that LQG was in fact in big trouble. Actually, I initiated a thread just to make this point which tells you how important I thought it was since I start few threads.

Anyways, why did you feel you had to start a new thread for this? Couldn't you just reply directly to eigen guy?

 

[marcus]

there are these urban legends (I guess you call them, factoids or something) that loop gravity is "stuck" or "in bad trouble" when it is going great guns

So in 1997 Thiemann constructed a hamiltonian and Lewandowski almost immediately shot it down---so what? This, as far as I can see it, doesn't mean being in trouble it just means that the theory has a chance to grow deeper and more interesting.

I don't think a person can really learn if they have a closed mind and are only looking for reasons to say "see, loop is a dead end, 9 out of 10 doctors prefer M-theory". If someone already knows the answer they are looking for, what's the point?

right now BTW i think loop gravity development is being guided by
the success in cosmology---where they include matter and get the classical limit and predict inflation and remove the singularity and in a sense reach a goal John Wheeler and others set 40 years earlier---and by some odd success in "discrete quantum gravity" by Gambini and Pullin where they also get the classical limit but in a different way I don't understand---they have 5 or 6 papers and say Thiemann went the wrong way (very confusing but they get the classical limit, or say they do). And Rovelli seems to have an idea about the hamiltonian too. (Gambini and Pullin stuff is hamiltonian and so likewise is cosmology)

Thiemann tells the story as if everybody ran off and did spin foam in despair, but when I look at the recent literature it does not show this at all----most of the action I see 2002/2003 is not spin foam at all, it is hamiltonian!

And the development in Rovelli's textbook is hamiltonian (he throws in a later chapter on spin foams but it is a disconnected afterthought thing)

So the simple story, whoever made it up, is wrong. There is no correct story because reality is not a story. Also there is no correct reasoning that "proves" that loop gravity is uninteresting or stalled or stuck or at a dead end. This is all pretty clearly in the realm of tendentious mythology.

But if you, Eigenguy or Jeff or whoever want to study the Thiemann paper or any other to understand what's going on in quantum gravity (not just to prove some preconceived notion) that is great more power to you.

 

[selfAdjoint]

For that Matter even Thiemann didn't run off and hide. He has an almost unbroken string of papers between 1997 and last March. All of it within this little area, if he wasn't actually trying to build the standard model out of E, A, and nets, then he was building newer and better tools to use on that project. I think Jeff was referring not so much to Thiemann's own work as to his dissing of the path integral approach that caught up so many QGists during the last few years.

I hope we can all get over the childish "my theory is better than your theory" wars that are defacing the web physics sites. What's worse than cranks dissing physics? Physicists dissing physics.

 

[eigenguy]

Originally posted by selfAdjoint
For that Matter even Thiemann didn't run off and hide. He has an almost unbroken string of papers between 1997 and last March. All of it within this little area, if he wasn't actually trying to build the standard model out of E, A, and nets, then he was building newer and better tools to use on that project. I think Jeff was referring not so much to Thiemann's own work as to his dissing of the path integral approach that caught up so many QGists during the last few years.

I hope we can all get over the childish "my theory is better than your theory" wars that are defacing the web physics sites. What's worse than cranks dissing physics? Physicists dissing physics.

Firstly, I do appreciate your responses. But suppose LQG is more popular than m-theory. Would someone who asks why that might be be a crank and dissing? If it is true that m-theory is more popular and someone points that out would they be a crank even though they don't say that therefore m-theory is the best? Is anyone here saying don't study LQG or are you just interpreting according to emotions wherever they come from? If not I think I deserve to see specific examples of the dissing and defacing you refer to. I think maybe you are not being fair and you and marcus should simply respond to science questions with scientific answers and not defacing site with political posturing and crank attitudes and dissing people who are actually objective and very nice.

Originally posted by marcus
there are these urban legends (I guess you call them, factoids or something) that loop gravity is "stuck" or "in bad trouble" when it is going great guns

So in 1997 Thiemann constructed a hamiltonian and Lewandowski almost immediately shot it down---so what? This, as far as I can see it, doesn't mean being in trouble it just means that the theory has a chance to grow deeper and more interesting.

I don't think a person can really learn if they have a closed mind and are only looking for reasons to say "see, loop is a dead end, 9 out of 10 doctors prefer M-theory". If someone already knows the answer they are looking for, what's the point?

right now BTW i think loop gravity development is being guided by
the success in cosmology---where they include matter and get the classical limit and predict inflation and remove the singularity and in a sense reach a goal John Wheeler and others set 40 years earlier---and by some odd success in "discrete quantum gravity" by Gambini and Pullin where they also get the classical limit but in a different way I don't understand---they have 5 or 6 papers and say Thiemann went the wrong way (very confusing but they get the classical limit, or say they do). And Rovelli seems to have an idea about the hamiltonian too. (Gambini and Pullin stuff is hamiltonian and so likewise is cosmology)

Thiemann tells the story as if everybody ran off and did spin foam in despair, but when I look at the recent literature it does not show this at all----most of the action I see 2002/2003 is not spin foam at all, it is hamiltonian!

And the development in Rovelli's textbook is hamiltonian (he throws in a later chapter on spin foams but it is a disconnected afterthought thing)

So the simple story, whoever made it up, is wrong. There is no correct story because reality is not a story. Also there is no correct reasoning that "proves" that loop gravity is uninteresting or stalled or stuck or at a dead end. This is all pretty clearly in the realm of tendentious mythology.

But if you, Eigenguy or Jeff or whoever want to study the Thiemann paper or any other to understand what's going on in quantum gravity (not just to prove some preconceived notion) that is great more power to you.

I assume that there are research papers on LQG that you like very much and would like people to read. I don't mean comparisons with m-theory since I agree that playing my theory is better than your theory is no good. I haven't played this game since all I asked was for justification of what I heard at a lecture which was LQG is not popular like m-theory. I never said that m-theory is better since I don't understand either theory and I was just looking for some guidance on why LQG is not so popular as m-theory. Maybe LQG is more popular. if so I would be interested in hearing that and understanding why (I am not saying that popularity is the bottom line. But I have to decide which theory to spend time on and if no one will give me a good answer to my questions what else do I have to go on but what most experts think). Also, the comparisons of LQG with m-theory is written by LQG not m-theory people so maybe LQG people like to play my theory is better than your theory?

What I request is that you suggest one of the best introductory but technical LQG papers and I will try to understand it. All I ask is that you be willing to help me understand it. I'm actually a quick learner and my questions will not be insane. If you are unwilling to do this even though I let you choose what I read, this would be very strange and dissapointing and make me wonder about what physics expert 2003 means and also this site. At this point I am realizing that it is in fact strange that you have this award but are not a mentor. Maybe your treatment of people who disagree with you is the reason. selfadjoint is a mentor and he has responded to my questions and maybe you need to think about that. You owe me an apology.

PS. Sorry about my grammar. I am mildly dislexic and my grammer is terrible when I am upset and on LQG I feel I am being treated unfairly and disrespectfully as any normal person would.

 

[marcus]

Eigenguy writes:
-----------------------
But I have to decide which theory to spend time on and if no one will give me a good answer to my questions what else do I have to go on but what most experts think). Also, the comparisons of LQG with m-theory is written by LQG not m-theory people so maybe LQG people like to play my theory is better than your theory?

What I request is that you suggest one of the best introductory but technical LQG papers and I will try to understand it. All I ask is that you be willing to help me understand it.
-----------------------

What would be wrong with your trying to learn M-theory! You may misunderstand where I am coming from. I am glad for you if you are interested in M-theory and get into it and learn some.

I don't have any interest in "recruiting" you to something that interests me. What I like to do is find people already sharing my interests and study something that interests us together (hopefully without interruption and distraction by people who are not interested!)

I don't like the idea of playing "missionary" to you. You should not feel like you need to learn loop gravity! If you already have an interest in stringy topics you should go with it---you can find plenty of people to talk to at PF. I happen to find string/brane stuff not interesting because it doesn't address what I think is the most exciting problem now: quantizing GR

Maybe I do not understand you and you really are interested in loop gravity and want to learn it. In that case several people including myself who have already been reading in the literature on it will be happy to try to help you find reading material you can understand (at least I will be happy to try and probably others too).

This business of finding a match between a person and the online literature is not as simple as you may think. It requires that you SAMPLE different things to see what, for you, is the "introductory but technical" article that is right.

I am not really sure you are interested in loop gravity (you sound already convinced that you should learn M-theory) but perhaps I should assume you have more interest than I hear, and suggest some reading to sample. I will try to do this. I'll mention some things to taste and you tell me if you like them. (if you really want to try to do this)

 

[eigenguy]

Originally posted by marcus
Eigenguy writes:
-----------------------
But I have to decide which theory to spend time on and if no one will give me a good answer to my questions what else do I have to go on but what most experts think). Also, the comparisons of LQG with m-theory is written by LQG not m-theory people so maybe LQG people like to play my theory is better than your theory?

What I request is that you suggest one of the best introductory but technical LQG papers and I will try to understand it. All I ask is that you be willing to help me understand it.
-----------------------

What would be wrong with your trying to learn M-theory! You may misunderstand where I am coming from. I am glad for you if you are interested in M-theory and get into it and learn some.

I don't have any interest in "recruiting" you to something that interests me. What I like to do is find people already sharing my interests and study something that interests us together (hopefully without interruption and distraction by people who are not interested!)

I don't like the idea of playing "missionary" to you. You should not feel like you need to learn loop gravity! If you already have an interest in stringy topics you should go with it---you can find plenty of people to talk to at PF. I happen to find string/brane stuff not interesting because it doesn't address what I think is the most exciting problem now: quantizing GR

Maybe I do not understand you and you really are interested in loop gravity and want to learn it. In that case several people including myself who have already been reading in the literature on it will be happy to try to help you find reading material you can understand (at least I will be happy to try and probably others too).

This business of finding a match between a person and the online literature is not as simple as you may think. It requires that you SAMPLE different things to see what, for you, is the "introductory but technical" article that is right.

I am not really sure you are interested in loop gravity (you sound already convinced that you should learn M-theory) but perhaps I should assume you have more interest than I hear, and suggest some reading to sample. I will try to do this. I'll mention some things to taste and you tell me if you like them. (if you really want to try to do this)

I came here interested in M-theory but there are no threads like yours and selfadjoints. (Also I just got a response to my request for an explanation of what is wrong with M-theory (S&M theory as he called it) with a long discouraging report on the subject. Basically he said that "if it's correct we will know - in about 150 years" ha ha. Hopefully it won't take as long for LQG). I will therefore start with LQG and Rovelli's book which looks easier and more leisurely then Thiemann.

 

[marcus]

Originally posted by eigenguy
I came here interested in M-theory but there are no threads like yours and selfadjoints. (Also I just got a response to my request for an explanation of what is wrong with M-theory (S&M theory as he called it) with a long discouraging report on the subject. Basically he said that "if it's correct we will know - in about 150 years" ha ha. Hopefully it won't take as long for LQG). I will therefore start with LQG and Rovelli's book which looks easier and more leisurely then Thiemann.

as far as reading in Rovelli's book, great idea! Be advised that there is plenty in that book which yours truly either has not read yet or has read without understanding. I think it is an important book though----if you want, let's try to find at least some parts of it we can fathom.


As backup explanatory material you might want to bookmark two earlier things by Rovelli:

"Loop Quantum Gravity" in the online series hosted by the Albert Einstein Institute, Berlin, called "Living Reviews in Relativity"

http://www.livingreviews.org/Articles/Volume1/1998-1rovelli


"Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance" (co-author M. Gaul at MPI Muenchen)

http://arxiv.org/gr-qc/9910079

Another thing to remember----the field is new and so far there is no introductory textbook. Rovelli's book is for a grad student seriously considering doing a PhD thesis in the field. this is the most urgent need obviously which he must address. It leaves someone like myself still gasping and groping somewhat. the real introductory textbook isn't here yet

(but an undergrad string theory textbook is due to be published next year by Cambridge u. press, so keep in touch with your string interest no matter what someone tells you. It is not my cup of tea but might be yours and the forthcoming textbook will make it more accessible!)

meanwhile, let's see what we can do. if we fail we fail no big deal and we might get somewhere.

if you print it off you will have the October 16, 2003 draft and my sense is that that is darn near final (except for typos). I think it will go to the publisher next year, just a guess.

 

[selfAdjoint]

Is anyone here saying don't study LQG or are you just interpreting according to emotions wherever they come from? If not I think I deserve to see specific examples of the dissing and defacing you refer to.

The dissing contest died down here pretty quick. But it still goes on, virulently IMHO, at the science.physics.research site. Since I visit both sites, I am exposed to attitudes "out of sequence" on one, that come from the other. I know that Lobos Motl, one of the paricipants over there, occasionally becomes aware of some of what is posted here. Sorry if my "entangled state" gave any offense here.

 

[eigenguy]

I think we can safely forget about these confusions and misunderstandings. Thanks to both you guys.

 

[marcus]

Originally posted by eigenguy
I think we can safely forget about these confusions and misunderstandings. Thanks to both you guys.

if that includes me, you are welcome (tho don't know and don't need to know for what). I had another thought---I think everyone is responsible for teaching himself things here, it is a little like a long distance bicycle race where other people on your team will take the lead from time to time which helps a lot (cuts the wind resistance for the others).

but when I do that, interpret something, it doesn't mean I claim expertize or promise you anything or take on responsibility for your learning

selfAdjoint has somewhat more public spirit and sense of responsibility, I suspect, but even with his help as mentor the scene is largely self-help do-it-yourself

if you want to try rovelli book, tho, I'm game and would like to see if there is anything we can both 'get our minds around' as
I've heard others say here

 

[eigenguy]

Originally posted by marcus
if that includes me, you are welcome (tho don't know and don't need to know for what). I had another thought---I think everyone is responsible for teaching himself things here, it is a little like a long distance bicycle race where other people on your team will take the lead from time to time which helps a lot (cuts the wind resistance for the others).

but when I do that, interpret something, it doesn't mean I claim expertize or promise you anything or take on responsibility for your learning

selfAdjoint has somewhat more public spirit and sense of responsibility, I suspect, but even with his help as mentor the scene is largely self-help do-it-yourself

if you want to try rovelli book, tho, I'm game and would like to see if there is anything we can both 'get our minds around' as
I've heard others say here

Sounds perfectly fine to me.

 

[marcus]

Originally posted by eigenguy
Sounds perfectly fine to me.

do you happen to have the Gaul/Rovelli paper printed out?

we could skim over it first

at first we would just be sampling various things to see
what is understandable and simpatico

BTW several people here at PF have tried Rovelli's book
and find it doesn't work for them, but some of the
less-technical parts work for me. I can't rationally
recommend anyone text (there is no specifically
introductory text in loop gravity) but I can suggest
a kind of wine-tasting expedition to see what works.
So, have you tried the Gaul/Rovelli yet, if so how did
it seem, if not would you like to?
the link is
http://arxiv.org/gr-qc/9910079

 

[selfAdjoint]

I am currently studying Thiemann's Introduction to Modern Canonical Quantum Gravity, http://arxiv.org/PS_cache/gr-qc/pdf/0110/0110034.pdf . He says it is accessible to folks with fairly modest backgrounds, but he lies...

 

[marcus]

Originally posted by selfAdjoint
I am currently studying Thiemann's Introduction to Modern Canonical Quantum Gravity, http://arxiv.org/PS_cache/gr-qc/pdf/0110/0110034.pdf . He says it is accessible to folks with fairly modest backgrounds, but he lies...

I remember you also looked at Thiemann's easier more introductory lecturenotes

"Lectures on Loop Quantum Gravity"
http://arxiv.org/gr-qc/0210094

I don't have the courage or stamina (I suspect) to try what you are reading (Introduction to Modern Canonical Q. G.) but I have printed out these lecture notes of his. So if anybody ever
decides to start on them I can join in.

We should make a bibliograpy:

hard Thiemann (Intro to Modern Canonical)
"easy" Theimann (Lectures on LQG)
Rovelli's draft textbook Quantum Gravity
Gaul and Rovelli 1999 introductory LQG paper
Rovelli's LivingReviews 1998 article
Sahlmann's PhD Thesis 2002 "Coupling Matter to LQG"


I mention Sahlmann's 2002 thesis because I remember thinking
that he did a nice job of summarizing the basic theory in the
first chapters of the thesis, so that this thesis (online at uni-potsdam) could actually provide a relatively painless introduction in just the first 50 pages. Anyway I have that printed out too if anyone wants to sample it and discuss it.

But when Thiemann speaks from his high seat in the cathedral it inspires me with dread

 

[marcus]

Rovelli has a funny (but not, I think, unkind) footnote about Thiemann's Intro to Modern Canonical.

This is in the preface (page x.) of "Quantum Gravity" where he is explaining to the reader under what circumstances one should read his textbook and under what circumstances one should instead read Intro to Modern Canonical. Here is the footnote:

"1. Consider the following two sentences. (i) Let [script] L be the set of all tame subgroupoids of piecewise analytic paths and X_l = Hom(l,G). If (mu_l) for l in [script]L defines a consistent family of regular Borel probability measures on X_l, then there exists a unique regular Borel probability measure mu on X[bar] such that mu * p_l ^-1 = mu_l."

(ii) "The only possibility of locating a point is with respect to the dynamical fields and the dynamical particles in the theory. This is the only basis for the spatial and temporal notions in general relativity. It is precisely a modern implementation of Descartes' notion of contiguity."

If (i) sounds more congenial to you, [Intro to Modern Canonical] is your book. If (ii) does, this is your book."

 

[selfAdjoint]

And my view is that the second one is the high level presentation aimed at somebody who is not likely to want to go much deeper. As such, very worthy. By the way, all the "this is what the theory really says" is in Thiemann too. Just leave out the math. IIRC, that's a strategy you suggested for reading Rovelli. Again perfectly worthy, and of course there just isn't any Brian Greene for LQG (except Baez! Who is wondefully clear, but who is focussed on the path integral approach.)

On the other hand, if you want to see what they are really doing, you have to dig in. If you want to read Homer in the original, you have to master the second aorist. And if you want to keep up with Thiemann, you have to grapple with Borel measures. So far I haven't found to much to complain about. Admittedly I skipped a lot of the ADM presentation, I may go back for that later. And when he gets into symplectic manifolds and the Ω constraint, I don't have a handy reference to run to. But it's refreshing, it really is, to see down to the bottom of a chain of reasoning, to see where those E 'electric fields" really came in in deriving the Ashtekar variables from an "expanded" ADM.

 

[sol1]

Originally posted by selfAdjoint
The dissing contest died down here pretty quick. But it still goes on, virulently IMHO, at the science.physics.research site. Since I visit both sites, I am exposed to attitudes "out of sequence" on one, that come from the other. I know that Lobos Motl, one of the paricipants over there, occasionally becomes aware of some of what is posted here. Sorry if my "entangled state" gave any offense here.

The way I see it is if I was interested in the appication of loop why such entanglement becomes a issue espcially if we are seeing the basis of loop and string relevant in the discussions.

Sorry if my "entangled state" gave any offense here.

I guess even here in the physics forum, the idea of preferiential treatment is okay as long as it comes from certain people?

Not meant to be a radical, but somehow perfection of the pursuate of the basis and undertandings, has forgotten somehow to respect the aspirations for undertanding from those less gifted, in the renditions of loop.

I was fortunate to have been involved in the open atmosphere of Superstringtheory, to have gained in perspective, and at the same time recogized the struggle for the forum's credibilty. Hard to do for a theory But in doing research somehow what was piped through, does go to supporting the framework for discussion no matter how ridiculous. For often post presentation, is sideswiped with a direct reinforcement of the correct knowledge, will not survive long, from a wrong basis of understanding.

That's why better minds should be on guard to correct what might have been illusion in the substance of the topic at hand.

I know I am following the logic here, but one had to understand from its inception, how loop is prepared indeed to handle the information. For introductions and the links indeed, help greatly. Based on the links, the question will reveal how serious or how far the person speaking has moved foward to 2003:). A lot of times one can remain trapped on the foundations of, and not look to current physics for developemental possibilties. I have found by doing generalize concept building that current articles on the topic help greatly to build this formulation of math becuase the generalize concepts prep one for the required basic maths .

The philospohical basis had to recognize that historically the currents math supporting GR had to become evident in the loop model or it cannot survive either? That's a first direct question about the foundation. Background and non background and this difference is a difficult concept for me, yet I know it is the basis of both loop and strings. So how would you attack loop without GR and recognize that loops wil help in our formulation of gravity?

The paradox of the the small with the large and how would we understand curvature? How would Kaluza and Klein ~ become effective in the undertanding of transiton in the feymann model to describe electron positron creation? How is gravity effecting photon creation at this level?

Community development is indeed a good thing, but it retains personalities who like to feel comfortable, and restrict individuals from actually particpating, becuas eit has somhow attck the basis of its group by attaching to other groups?

If we limited this interaction we limit the ability of neuron developmentWhat you guys know, I can know too, and nothing limits this possibility except closed minds. The area of loop needs all the help it can get:)Present articles out there that can be linked raise legite questions as well. Not just pdf files we see so much here. Try "Edge" and from the mouth of these people like Smolin one gets a better perspective. The current article out of PI, and Marcus understands how information can keep us current. How nice the opportunty that people can bring to this forum or any other links(why not other forums?) that will help the public understand what these scientists and phyicists all are talking about. How it is effecting our perception in regards to LIGO. LISA, GRACE and how many more will help to formulate(Thorne, Wheeler Penrose) our current views in loop and strings?

Somehow one has to retain some perspective and not loose themselves in all math structures. All the power to the guy/girl who can help us marry current concepts to real live situations. Dickt you have been instrumental in my development and it did not fall under the umbrella of closed minds. How should I adapt to this community, you knowing full well what I am like? Is there a set rule here on forum particpation or ideals? Some requirement of the partcipators that they have a university degree? I don't, but I can still engage minds.

To much effort you suppose?

http://www.superstringtheory.com/forum/metaboard/messages19/26.html

Speaks direct to the Cognitive style of math that is associated with Platonic formulations and I wonder indeed sometimes how discrete structures have overtaken the mind, without understanding that expansion contraction, had to philospohically answer how we are directlly building on theorectial structures. What is the monte carlo effect in undertanding quantization of grvaity and how is it being formulated?

The Math of Supersymmetry and its formulation also is being spoken to here. I am not proposing any of my theoretcial defintions but the engagement of what is currently held in thought about how we approach strings and loops.

Pascals triangle is much more then just adding numbers but defines indeed the pathways for how we would describe the discrete natures and the building of? It is not difficult for me to see twosides of the coin.:) Superstring explains gravity(dimension) very nicely and loop, well what are structures but holding issues with gravity?

Sol

 

[marcus]

Originally posted by selfAdjoint
...And if you want to keep up with Thiemann, you have to grapple... So far I haven't found to much to complain about.

well your good report of the "hard"Thiemann treatment persuaded me to give it another try yesterday, and in fact it did seem a lot more readable than when I looked at it several months ago----having something like that could prove essential for us even us PF amateurs! And yes, I do personally place a lot of importance on the non-technical exposition that tells you in words (to the extent that is possible) what is happening.

I'm worried by an email circular from Greg about the traffic limit for October being reached. (it is a little like CO2 emissions, should I drive my car less?) Are you economizing on posts these days. I believe I will some.

I read your favorable mention of PF on Usenet SPR---answered by someone's "more-professional-than-thou" scorn for PF amateurishness---and your salad-bar riposte. thanks, from at least one poster here (me).

I feel that someone or several of us should try to lay out an intuitive picture----among other things it would provide orientation for the harder more technical discussion. Later today, unless we have to cut way back on posting, I will try to add something to that intuitive sketch of loop gravity thread.

 

[selfAdjoint]

Since Greg the magician got us a reprieve on the bandwidth thing, I'll add a little. I just read your very good intro to connection on the other thread, and it set me thinking. Should we try to motivate, say a principle bundle, the lie group and lie algebra acting on the manifold - actually on the tangent bundle, and all that? This is basic stuff, and really belongs on the diff manifolds board that is sort of dormant right now. Just a thought, let me know what you think.

Working on the Thiemann intro, I am now trying to conceptualize the term "anti-self-dual". A few more times around the block and I'll have it.

BTW we should retrieve your explanation of covariant and contravariant, and our discussion of pullbacks, that all goes in here too. Build up a chain of posts like a FAQ that people could use in trying to make sense of these papers.


It's late at night and maybe this is just mindfog speaking, but do let me know what you think.

 

[marcus]

Originally posted by selfAdjoint
...Should we try to motivate, say a principle bundle, the lie group and lie algebra acting on the manifold - actually on the tangent bundle, and all that? This is basic stuff, and really belongs on the diff manifolds board that is sort of dormant right now. Just a thought, let me know what you think...

those tools we need----lie group/algebra, diffeomorphism, tangent space, are all differential geometry tools based on
the idea of a manifold. I think having a place for brief
descriptions of them is a good idea. I started a thread in
the differential geometry forum (essentially just quoting
your post here, with my concurrence)

 

[ranyart]

Originally posted by selfAdjoint
Since Greg the magician got us a reprieve on the bandwidth thing, I'll add a little. I just read your very good intro to connection on the other thread, and it set me thinking. Should we try to motivate, say a principle bundle, the lie group and lie algebra acting on the manifold - actually on the tangent bundle, and all that? This is basic stuff, and really belongs on the diff manifolds board that is sort of dormant right now. Just a thought, let me know what you think.

Working on the Thiemann intro, I am now trying to conceptualize the term "anti-self-dual". A few more times around the block and I'll have it.

BTW we should retrieve your explanation of covariant and contravariant, and our discussion of pullbacks, that all goes in here too. Build up a chain of posts like a FAQ that people could use in trying to make sense of these papers.


It's late at night and maybe this is just mindfog speaking, but do let me know what you think.

Dick, I have just read this paper, and It seems to be quite close, but not quite! (thats my limited opinion)


http://uk.arxiv.org/abs/hep-th?hep-th/0310168

 

[selfAdjoint]

Right, this is not on the same wave length with LQG or spin foams. Sigma models are being used a lot in stringy physics, and this looks like an approach to apply known stringy tools to spacetime.

 

[Ambitwistor]

Originally posted by ranyart
Dick, I have just read this paper, and It seems to be quite close, but not quite! (thats my limited opinion) http://uk.arxiv.org/abs/hep-th?hep-th/0310168

I'm not sure of the context of your post, but if you're looking for something that introduces basic differential geometry (bundles, etc.), that perhaps isn't the best choice; it's rather specialized.

There are various books, but as far as online material goes, I don't know of any "easy" introductions to differential geometry at the level of bundles. On the arXiv, for instance, this one is fairly extensive, but does require some background:

http://arXiv.org/abs/math-ph/9902027

(If you want to learn about bundles and Lie groups in a physics context, then you will probably need to look for references on gauge theory.)

There is also,

http://www.cds.caltech.edu/~marsden/bib_src/mta/Book/

but it doesn't discuss principal bundles.

You can also look at various GR-oriented references (which usually don't talk much about bundles or Lie groups, but do talk about tensors and manifolds and geometry and such), like:

http://pancake.uchicago.edu/~carroll/notes/
http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html

 

[marcus]

Originally posted by Ambitwistor
...introductions to differential geometry at the level of bundles. On the arXiv, for instance, this one is fairly extensive, but does require some background:

http://arXiv.org/abs/math-ph/9902027

There is also...[Jerry Marsden]...,

Upon inspection, it appeared that math-ph/9902027 was
written by a person in a state of mathematical grace, and
I printed it out forthwith. Thanks for the link.

Marsden's book is also a very fine one but is more aimed at
understanding dynamical systems IIRC and not quite as
right-on as these lecturenotes of George Svetlichny.

These notes, called "Preparation for Gauge Theory",
from a course he taught in Brazil at the Catholic University of Rio,
seem excellent. I will post the link in Differential Geometry forum

 

[selfAdjoint]

Marcus, in the Svetlichny notes, look especially at page 29, paragraph beginning "Let now G be a Lie group", where he introduces the connection one form, with values in the Lie algebra. Remind you of anything? I ran into this form in my copy of Nash and Sen a while back. It clears up some of what we discussed earlier.

 

[sol1]

Twisting

https://www.physicsforums.com/showthread.php?s=&goto=lastpost&forumid=57

Maybe I am the one confused?

http://www.vislab.usyd.edu.au/gallery/mathematics/sound/maths_index.html

How would you then speak about plasmatic features that are quite intensive in supergravity? Here in the mathematcs of sound it is interesting how we could percieve energy as a analogy, in regards to movement?

In gravitational considerations using "Grace" to show variations in the Earth's graviational field, we would then map accordingly, as we have done here in the mathematics of sound?

Sol

 

[Ambitwistor]

The Svetlichny paper is definitely closer to what is needed to understand the Ashtekar variables or gauge theory, but the Marsden book is also good as a lead-in to Poisson manifolds (which in turn is a foundation for geometric quantization).

 

[marcus]

Originally posted by selfAdjoint
Marcus, in the Svetlichny notes, look especially at page 29, paragraph beginning "Let now G be a Lie group", where he introduces the connection one form, with values in the Lie algebra. Remind you of anything?...

yeah I remember you talking about vertical and horizontal and so on, Svetlichny is what we should have had handy then.

I haven't yet gotten around to putting a link to Svetlichny's "Preparation" in the differential geometry forum, tho I did start an appropriate thread there

 

[marcus]

Originally posted by Ambitwistor
The Svetlichny paper is definitely closer to what is needed to understand the Ashtekar variables...

I would like to, so its the right thing. I think I said thank you already, but if not, thanks.

Maybe we have two different constructive things we could do. One is to compile an annotated bibliograph to post here so that someone like selfAdjoint or me can teach himself efficiently about loop gravity to the point of following current developments with some degree of understanding

The other is a riskier agenda which is to patch together essays by different people to make a kind of online Loop Gravity for the People textbook----actually the obvious style model is John Baez (X for bears of little brain,...many examples) and its not impossible that he will do an intuitive quantum gravity for the people set of webpages at some point. But until that happens there is an obvious niche because people are interested in it and there is no basic entry-level text, not that I know of anyway.

I don't want either of these two agendas to get in the way of good person-to-person conversations you might have with selfAdjoint or nonunitary. So I might start a separate thread to accumulate explanations and ideas for these projects

 

[marcus]

there is something almost obvious about loop gravity, I hope it won't turn people off if i put it in a really dirt-common way. A connection (the way a tangent vector swirves while being transported along a path) is a visual intuitive idea. Likewise the little animated film that shows that starting on the equator and going up to the north pole and so on, precisely because of the curvature it comes back different from how it started.

these are bedrock accessible intuitions you can build on and develop an idea of quantizing geometry

because if the soup of all possible connections is a reasonalble facsimile of the soup of all possible geometries (on the underlying manifold you want to study)

then why not take the soup, sorry i mean "space", of all possible connections as the -------what you build wavefunctions on.

and then if A is configuration space how else can you imagine defining a quantum state

f:A --> C

besides with things like loops and networks? Really. If you want to get a complex number out of a connection A that is how you are going to go about it---with some kind of path to run the connection on. I never bothered ot find out who Wilson was who first proposed taking traces of holonomies and it must be a time-honored practice almost a reflex by now.

Maybe this has already been covered in "Three Roads" or in some past "This Week's Finds". In that case let's cite our sources and paraphrase the gist of it. Anyway one way or another post a rock-bottom conceptual version of loop gravity.

I am trying to figure out what the catch is. What would turn out to be prohibitively difficult? The next thing would have to be the measure on A so you can integrate and actually have a hilbertspace. And then there is the business of modding out morphisms. (so that the network is an abstract knotwork rather than specific thing embedded some particular way). It would be so nice if all this could be said in plain language, conveying a sense of familiarity. Well, enough wishful raving at least for now.