Introducing Loop Quantum Gravity: Differences with String Theory

[marlon]

hello,

can anyone give me some introductory notions of what loop quantum gravity (i hope it is in the right order) and what are the differences with string theory. I know my QFT and i have some introductory notions on strings, so i don't mind a deeply elaborated physical answer.

Feel free to indulge yourselves

thanks
marlon

 

[marcus]

hello,

can anyone give me some introductory notions of what loop quantum gravity (i hope it is in the right order) and what are the differences with string theory. I know my QFT and i have some introductory notions on strings, so i don't mind a deeply elaborated physical answer.

Feel free to indulge yourselves

thanks
marlon

take a quick look at a recent survey by Lee Smolin called
"Invitation to Loop Quantum Gravity"
http://arxiv.org/hep-th/0408048

it is written for grad students, postdocs, researchers with questions about
LQG and who might be considering the field
It has FAQ----questions physicists from other fields frequently ask

It has a list of open problems to work on. It has a listing of results proven so far.

It has a summary of experimental testing planned or in progress (still pretty tentative but some good possibilities coming up near term)

In acknowl. section Smolin thanks string-theorist John Schwarz for giving him the idea to write this type of survey article. And it is meant for publication in the annual reference series "Reviews of Modern Physics".

So this paper seems like a good match with your needs and interests.

I will post this as a start and if I think of other stuff will add it later.

 

[marlon]

thanks, marcus for your answer. I will dig into this article right now...

regards
marlon

 

[marcus]

thanks, marcus for your answer. I will dig into this article right now...

regards
marlon

I'd appreciate having someone to discuss the paper with, if you feel like doing going over parts of it later after having a look.

regards from here too

(btw there are parts I don't get, but let's try to overlook my deficiencies and see if there are some we can tackle )

 

[Mike2]

I'd appreciate having someone to discuss the paper with, if you feel like doing going over parts of it later after having a look.

I certainly like the four key observations that LQG is based on.

1) background independence,
2) duality and diffeomorphism invariance
3) gauge field theory,
4) topological field theory.

It give a sense of deriving it from first principles, or physics from pure mathematics, as opposed to string theory which seems to be a contrivance (more curve fitting fudge factors).
I don't like the concept of quantized space. Or perhaps I don't understand it. I suppose I could except that quantized space is a quantum mechanical superposition of non-quantized space. But I'm not sure that this is a correct interpretation.

 

[marlon]

I'd appreciate having someone to discuss the paper with, if you feel like doing going over parts of it later after having a look.

regards from here too

(btw there are parts I don't get, but let's try to overlook my deficiencies and see if there are some we can tackle )

ok, ok, sounds very nice marcus

Give me a few days to read it thourougly...

regards
marlon

 

[marlon]

ok,marcus, let's get started on the Smolin-article.

Just for the record and the good mutual understanding. I wish to discuss the content of page 8 : The connections in LQG are the gauge fields. I think this has to mean that them gauge fields are covariant right? But isn't that always the case, just like in QFT ?

All possible metrics and connections form the state space. All possible configurations of the gauge fields form the configuration space. But what do we mean by the configuration of a gauge field? ??

In order to describe the dynamics of the gauge fields we perform parallel transport of these gauge fields along some Wilson loop and we study how these gauge fields change during the transport. Now we have a system to study fields independently of the metric, like in GTR. Is this vision right.

Finally I have some difficulty with imagining how excitations (these are the particles) are defined by Wilson loops acting on the vacuum. Is this an analogy to QFT where particles arise as excitations of the QCD-vacuum-state??

regards
marlon

 

[marlon]

And if the gauge field is viewed as a connection over a principal G-bundle, we do the parallel transport of the identity around the loop which would give an element of the Lie group G.

Let's suppose the used identity is a vector. This G-bundle projects this vector onto the tangent-vector which is to be parallell transported. Doing the holonomy means doing the actual transport and looking how the "connection" between the original vektor and the tangent vektor changes. The result gives an element of the Lie group.

WHAT IS THIS ELEMENT ? WHAT DO WE KNOW FROM IT ?

regards
marlon

 

[marcus]

...can anyone give me some introductory notions of what loop quantum gravity (i hope it is in the right order) and what are the differences with string theory...

hi marlon, I am eager to continue the discussion of LQG started by your question.

today I found a good page of Quantum Gravity links assembled by Seth Major, a physicist at Hamilton College (somewhere in NY state, I think)
http://academics.hamilton.edu/physics/smajor/resources.html

It looks like he has assembled this page for his students and has included
some good explanatory and introductory material, as well as surveys.
Also the page is seemingly up-to-date, which can be a big advantage.

You asked also about the physical meaning of a holonomy---the path integral of a connection. I believe it depends very much on the path
and that holonomy on a path going around a loop intuitively tells information about the curvature inside the loop. Also my feeling is that
you are probably better than me about describing these things! Or anyway I am not the best person at PF to try to do it! So I would be happy if you would do some of the exposition. (Or some other knowledgeable person if they wish to step in)

I will make an attempt in the next post but please anyone feel free to augment or correct this preliminary effort

 

[marlon]

Hi, marcus

just have been looking at this site of Seth A Major. It is the best.

There is a nice reference to an article that explains the origin of spin networks, some crazy stuff. Assigning lines and so on to the eigenvalues of the angular momentum operator is freeky yet geniously work out in there.

I can only say : thanx, thanx, thanx
ps : there is still a lot of work to be done in this research. Maybe we will earn our Nobel prize here (lol)


regards
your new collegue
marlon

ps : what do you do marcus, what are you working on, are you a student ?

 

[marcus]

Smolin's "Invitation" http://arxiv.org/hep-th/0408048
is a truly wonderful paper---a landmark in being finally a really good
QG survey boiled down into few pages----FAQ, list of solved problems, list of unsolved problems, thumbnail sketch of experimental situation etc.

But to read the paper one needs to get over an initial barrier, which Marlon has pointed to. What is a connection?

why does this arise? Because at first in 1970s and even earlier when Wheeler and DeWitt (and others) did Quantum Gravity they naturally considered the configuration set to be all possible metrics and then
around 1986 people switched to using the set of all possible connections.

One must have a configuration set representing all possible geometries of the manifold. At first it was clear to everybody that it is the metric or distance function defined on the manifold which tells its geometry (its angles, areas, volumes, distances etc). so the set of all geometries must obvously be the set of all metrics. Then the quantum states were functions defined on the set of all metrics.

Quantum states are somewhat like probability densities defined on a set of possible configurations of the world. Quantum states must be defined on something. Shall it be the set of all possible metrics on our manifold?

they tried this in the 1970s and encountered serious difficulty. Around 1986
Ashtekar and (I think) Sen suggested using the set of connections instead.
(this account is dangerously oversimplified but I need to have some overall perspective)

Using as configurations the set of all connections seems to have worked better. So one must ask "What is a connection and how does it represent essential features of a geometry?"

One should, I believe, picture the manifold and imagine all the possible frames at every point. If one could interconnect a choice of frame at every point then one could say "If I take an infinitesimal step in some direction, how does the frame begin to twist around?"

An infinitesimal step in some direction corresponds to an element of the tangent (or the cotangent) space at that point. An infinitesimal rotation corresponds to an element of the Lie Algebra (one makes some arbitrary choices to equip oneself with a Lie Algebra, and basis elements, at every point and one must pay later by having to factor the arbitrariness out, but at least one gets some good out of it)

So a connection needs to be, at every point, simply a linear map from the tangent (or cotangent) space to the Lie Algebra.
Because of arbitrarily chosing basis elements one can even present this with actual numbers in matrix form.
To remember: it tells how the frame will infinitesimally rotate as one takes an infinitesimal step in some direction.

With my bad memory, I cannot remember if one defines this map on the tangent space or the cotangent space at the point! Perhaps either will work.
Perhaps it is best described as a Lie-algebra-valued differential form.

Well, I am now expected to go to the market to get food for company coming, and must continue this later. But first I just want to mention that
one of the nice things one can do with information about infinitesimal steps at the microscopic level is integrate over a macroscopic journey.

so once we have the connection we can consider traveling along any path
and seeing how the frames twist and turn around! We can break the path down into lots of microscopic steps and do the integral of the corresponding Lie algebra elements and get a Lie group element corresponding to the path from one point to some other.

In particular if we take a path around in a loop, then the frames will twist around and perhaps will be something different when we get back! So the loop tastes something about the geometry inherent in the connection.
Well now i have to go buy meat and vegetables and when I get back I hope my head will still be pointed in the same direction as now. this marketing is also something of a holonomy, but it must be done. til later.

 

[selfAdjoint]

Nice description Marcus! Here is a little addendum. The Lie Algebra as you said provides the differentials of the group actions; if you can stretch your mind this far, think of the group (gauge group) as itself a curved manifold, and somewhere on it is a point representing its group identity, the group element that doesn't change anything. Then the group manifold has its own tangent space, in particular there's a tangent "fiber" at the identity and that tangent fiber is a vector space of those differentials, spanned by some basis vectors. The vector space is made into an algebra, the Lie Algebra of the group, by defining a bracket product, but we don't need to go there. What we do need is a theorem that if you exponentiate the Lie Algebra vectors you get the group elements, and this provides a mapping from the Lie Algebra to the Lie Group.

So now look at Smolin's expression (4):
T[\gamma,A] = Tr Pe^{\int_{\gamma}A}

where \gamma is a loop and the P operator enforces pathwise ordering. We take the frame around the loop, and we INTEGRATE all the differential motions to come up with a total motion, and we EXPONENTIATE to get the group element that equals the final result. The group element is a matrix, and we take its trace. And that map from loops to numbers is the Wilson loop.

 

[marlon]

Nice explanation marcus and selfAdjoint

So these connections are indeed some map from the tangent space to the Lie Algebra in which we have the rotations that the chosen frame undergoes while we perform parallel transport.

Once we went around the loop we see for axample that the original frame has turned 90 degrees. We look for the matrix-representation of a 90-degrees-rotation and we take its trace. Then we have a number that tells us that the frame (which in this case is the actual gauge-field, right) rotates 90 degrees after the loop is completed.

Still one question though : is it ok to say that the Lie-group contains the infinitesimal paths of which we construct the loop by integrating. And given some gauge-field, how do we construct the associated Lie-group ? Isn't the Lie-group the group of transformations that leave the gauge-field invariant, like in QFT ? I guess no because this has something to do with how the frame (here the gauge field) changes when following the loop.


regards
marlon

 

[marlon]

Nice description Marcus! Here is a little addendum. The Lie Algebra as you said provides the differentials of the group actions;

selfAdjoint, do you mean by this that in the Lie Algebra , we find all the possible transformations in order to go from the original frame to the "rotated" frame after completing the loop? So in like in my previous post, this would be the 90-degree-rotation ?

A differential of the group action means : "how does a frame change when we do something with it? In this case, taking it along the loop " Is this correct ?

regards
Marlon

 

[sol2]

It's over in https://www.physicsforums.com/showthread.php?goto=newpost&t=27555.

sorry

 

[marcus]

If I have gone off topic let me know.
...

Yes sol, IMHO, and most thoughtful of you to ask.
Personally I would like it very much if we could keep this one thread as a sort of "working LQG thread"----keep other topics to a minimum and focus on whatever is recent in that particular approach, and hopefully some nuts-and-bolts.

 

[selfAdjoint]

selfAdjoint, do you mean by this that in the Lie Algebra , we find all the possible transformations in order to go from the original frame to the "rotated" frame after completing the loop? So in like in my previous post, this would be the 90-degree-rotation ?

A differential of the group action means : "how does a frame change when we do something with it? In this case, taking it along the loop " Is this correct ?

regards
Marlon

From one physics textbook, I remember this explanation:
The transformations (elements) of the original group are fine for math, but in physics we need a form that goes with the differential equations and integrals of mechanics, hence the differentials of the group elements. So yes, if we transport the frame around the loop, adding up (integrating) the differential transformations we wind up with a group element; instead of all the business with the loop you could have just rotated the frame from its original position to its final one with a single 90^o turn. That single element is what we recover by exponentiating.

One thing in your other post bothered me; you ask if the differentials form pieces of the loop. No, the loop is there in the manifold; the differentials are pieces ("seeds" maybe) of the group transformations that act on the manifold. As you move the frame along some "d(loop)" it experiences some "d(rotation)."

 

[jeff]

...I would like it very much if we could keep this one thread as a sort of "working LQG thread"----keep other topics to a minimum...

What, no more poetry?!

 

[marcus]

What, no more poetry?!

in other threads!

 

[Entropy]

LQG is like the idea that gravity is so weak because it is distrubuted over lots of (or infinite amount) if dimensions right? Or am I thinking of something else?

 

[marlon]

LQG is like the idea that gravity is so weak because it is distrubuted over lots of (or infinite amount) if dimensions right? Or am I thinking of something else?

distrubed over lots of what ?

In my opinion LQG is the idea the quantize the GTR. One takes gauge fields , curved on a manifold (just like in GTR) then quantize them like in QFT. the most important aspect is that we need to have two things

1) diffeomorfism invariance (this is the general covariane of GTR)
2) gauge invariance (like in QFT, invariance of gauge fields under local symmetries)

Basically these things ensure us that we have background independence so that we can choose any metric we want in order to describe the manifold. The different possible frames on that manifold must yield the same eguations at any point on the manifold, that is the covariance (just like in GTR)

Marcus and selfAdjoint have both posted some nice explanations on how to describe a metric and the connections by using the system of Wilson loops, check them out...very interseting...

regards
marlon

 

[marcus]

... Or am I thinking of something else?

I'd say probably thinking of something else.
That idea I don't recall ever coming up in LQG.

Basic idea of LQG is same as basic idea of classical 1915 General Relativity---that concentrations of energy curve spacetime, so that
the gravitational field is realized as shape

In classical GR, the shape is determined with perfect mathematical clarity down to the smallest scale (except at locations where the theory fails, which are called singularities). By contrast, when the theory is quantized, shape becomes a fuzzier, less certain idea----a kind of graininess creeps into the ideas of area and volume----and it becomes possible that geometry at very small scales can be qualitatively different from human-scale geometry. Among other things the classical theory's (black hole and big bang) singularities go away. One loses the ideal mathematical point, which can even be a help because does nature actually have these absolutely perfect infinitely small mathematical points, or is she really rather vaguer about location than that.

The art of quantizing a classical theory seems to involve introducing just enough opportunity for uncertainty, but not too much. One must still be able to define the ideas of area and volume. But operators that measure them must be able to waffle---must have several possible values depending on the quantum state of the geometry.

Frank Wilczek has said that gravity is neither weak nor strong. It is what it is. the question to ask, says he, is not "Why is gravity so weak?" but
instead "Why is the mass of the proton so small?"

He wrote a wonderful series of thee articles about this for Physics Today.

In natural units----with c = hbar = G =1, or at least their values being one----the mass of the proton is one over 13E18
this is 13 quintillion, a big number.
Wilczek explores why it is so large. this is what one must explain, because gravity is what it is. And he arrives at some tentative ideas.

The series of articles is calle "Scaling Mount Planck" and it can be found online.

 

[sol2]

Basic idea of LQG is same as basic idea of classical 1915 General Relativity---that concentrations of energy curve spacetime, so that
the gravitational field is realized as shape

I am speaking to this in another thread called liminocentric structures. If this is understood I am continuing regardless of my particpation here. String theory also addresses this in what is called supersymmetry. It will become apparent in time

 

[selfAdjoint]

LQG is like the idea that gravity is so weak because it is distrubuted over lots of (or infinite amount) if dimensions right? Or am I thinking of something else?

You're thinking of the Randall-Sundrum model in string theory. In it, we live in a brane which is the boundary of another, higher dimensional brane. All the quantum forces are expressed in terms of open strings with their ends tied to the brane, so they can't move out of it. But the graviton is known to be generated by CLOSED strings, which have no endpoints and cannot be pinned down to our brane. They are free to roam into the higher dimensions, and being spread out that way, as you have noted, they cause gravity to be much weaker than the other forces.

 

[marcus]

when I lay out the more interesting LQG-related papers from recent months one thing that is especially noticeable is a convergece of quantum gravity with MOND and with modified versions of Special Relativity.
The modified versions of SR are called things like DSR and TSR for doubly and triply special rel. It looks like LQG might, like an amoeba, engulf MOND.

It is not clear to me where this is going (and i would not expect it to be) the best thing to do for now is probably just take a deep breath, and assemble some links giving general information.

for MOND it would be Stacy McGaugh (acknowledgments to Nereid)

http://www.astro.umd.edu/~ssm/mond/mondvsDM.html

http://www.astro.umd.edu/~ssm/mond/litsub.html

http://www.astro.umd.edu/~ssm/mond/

http://www.astro.umd.edu/~ssm/

---------------------

for N-scale Relativity it would be Etera Livine and Florian Girelli and
Daniele Oriti and Lee Smolin and Jerzy Kowalski-Glikman

http://arxiv.org/gr-qc/0406100
(the prospect of building mond-like effects into a GR-type theory
is considered on the second half of page 15 and in the last 3 or 4 lines of the conclusions paragraph at the end)

http://arxiv.org/hep-th/0406276
(see pages 3 and 4 where mond is again approached from a cosmological constant direction.)
--------------------

for LQG with a positive cosmological constant
(and the long invariant length scale) see Smolin's third lecture at:
http://ws2004.ift.uni.wroc.pl/html.html

 

[marcus]

I've been using this link on an almost daily basis to keep track of the new LQG papers being posted at arxiv.
since this is marlon's LQG thread I will stash it here so I will have it handy and also anyone else who might be interested
http://lanl.arxiv.org/find/nucl-ex,...m+AND+OR+triply+doubly+special/0/1/0/past/0/1

 

[Tom McCurdy]

Ahhh I feel lost in a sea of brilliance I just printed out the first paper and am starting to read it. I hope to catch up to you guys in a few years.

 

[Tom McCurdy]

Ok I made it to page 5 so far but I had a question when it says that Loop quantum gravity implies that the einstein equations are just the low energy limit of a more fundamental theory it means that the einstein equations only work at low energies being "low" as in what we occur in our day to day lives. as opposed to say the big bang. Is this basically like Newton versus einstein equations Newton's being ok for everyday activities but breaking down when you near c

 

[marcus]

Ok I made it to page 5 so far but I had a question when it says that Loop quantum gravity implies that the einstein equations are just the low energy limit of a more fundamental theory it means that the einstein equations only work at low energies being "low" as in what we occur in our day to day lives. as opposed to say the big bang. Is this basically like Newton versus einstein equations Newton's being ok for everyday activities but breaking down when you near c

that's a good analogy.
Tom, sorry, did not see your post here until just now.

 

[marcus]

Ok I made it to page 5 so far but I had a question when it says that Loop quantum gravity implies that the einstein equations are just the low energy limit of a more fundamental theory...

It is nice to have a question referring to something specific from that paper, like page 5.

I am trying to see what you are talking about and I see this on page 5

----quote from Smolin "Invitation"----
The principle of background independence does not imply that the fundamental theory must be based on fields living on a manifold. But it does imply that whenever manifolds appear, whether fundamentally or as part of the low energy effective theory, the dynamics of the fields will be invariant under active diffeomorphisms of the manifold. The reason for this was worked out first in detail by Dirac, and his [24] is still a good source for understanding the connection between background independence and diffeomorphism invariance 3.
------end quote----

this doesn't seem to be what you were talking about.

Whew! you have me guessing! Another time please paste in a quote
from the paper

then I can more easily see what you are talking about.

 

[marcus]

Ok I made it to page 5 so far but I had a question when it says that Loop quantum gravity implies that the einstein equations are just the low energy limit of a more fundamental theory ...

there is nothing wrong or unusual in what you say----completely apart from Smolin's paper.

but let's read the paper.

I am guessing that when you say you had a question
it was about something on page 4:

---quote from page 4---
2. The four basic observations[/size]

While the principles assumed are only those of general relativity and quantummechanics, there are four key observations that make the success of loop quantum gravity possible. These are

I. Classical general relativity is a background independent theory, hence any theory which is to have general relativity as a low energy limit must be background independent. A background independent theory is one whose formulation does not assume or require the existence of any single preferred spacetime metric or connection. ...
---end quote---

He is not saying what you said.
He is saying that ANY theory claiming to have classical Gen Rel as limit must be background independent in his sense (in the sense he explicitly explains on page 5).
One radical implication (to show the strength of this principle) is that any theory which is not background independent in this sense cannot be asserted to have Gen Rel as limit.
What he is nailing to the church door here is a criterion for success.

He observes that LQG meets this criterion, and also one other thing:
that various actions besides the the Einstein action can be accommodated.
If there are higher order terms someone wants to include that is fine with LQG. It can accommodate fancier actions that have classical Einstein as the limit.
( there is a dark rumor among stringers that LQG is wed solely to the Einstein action---seemingly the only basis for this being that they've seen loopers use that action a lot and assumed they couldn't use anything else).

----from page 5---
While many papers in LQG are concerned with the quantization of the Einstein action, we can equally well study other actions, including supergravity and terms of higher powers in curvature. Loop quantum gravity is perfectly compatible with the expectation that the Einstein equations are just the low energy limit of a more fundamental theory.
----end quote---

In other words it can take supergravity or leave it alone if that makes sense to you.

 

[marcus]

I see the confusion now.
You said LQG IMPLIES that classical GR is just the low energy limit of a theory with higher order terms (becoming negligible at low energy).

Smolin says LQG IS COMPATIBLE with that option. so far no one has found a more complicated formula that predicts better than classical Einst. eqn. but if they did it could be plugged in and it would play.
the framework can accept upgrades
(although since so far no one has found an improvement on the Einstein-Hilbert action, this seems of no immediate concern)

 

[Tom McCurdy]

thanks that's what I thought I will continue to read the article, but I am a little busy at the moment so it may take me a few days to finish it

 

[marcus]

thanks that's what I thought I will continue to read the article, but I am a little busy at the moment so it may take me a few days to finish it

I can never finish. when the sliced meat is finished there are still the bones to gnaw.

report anything at any time. if we wait till we both understand it all we will be old men

 

[marcus]

Tom, I've momentarily lost track of where we were discussing
the idea of a forum for QG, and maybe asking Miguel A. to mentor.
I'm very glad you are in touch with him.
He is a good person to know, I think ('pressive: fencing, Go, Baez student, Wiki writer,...) and maybe something will turn out later.

I'm glad he answered you immediately and friendly-wise

I'm also glad he said no---that means he's focusing on finishing his
Loop gravity thesis, hopefully this year or next.

Did you actually set up a QG forum? Most likely it will not need a mentor for quite a while because it will be very quiet-----like an empty stage doesn't need a director. Please give us the link again and I will go glimpse it, if the place exists.

nice to see the old smilies are back (they temporarily changed for a while this morning)

 

[marlon]

Hey, guys, i made an attempt to describe the basics of LQG. I am planning to make a whole new website, dedicated to this subject. Since it is not my field of expertise (that's QFT) I ask you specialists outhere to read and correct my text.

Please, remember it is my intention to write down the structure of LQG in human language, though your corrections can be made in heavy QFT-language if necessary. I will try to understand.

Does anyone have suggestions on what there should be added.


regards
marlon

 

[marlon]

I must admit though, the last sentence I stole from SelfAdjoint.

The rest of the text is based upon my own knowledge together with the cristal clear explanations from marcus and SelfAdjoint. Thanks guys


regards
marlon

 

[humanino]

Nice Marlon ! I propose to give you comments according to the fact that I don't know anything about those... loops
Kidding. I mean : Since I am very new to the subject, and won't ever become an expert, I could play the ignorant student discovering LQG through your texts, if you want.

 

[marlon]

Nice Marlon ! I propose to give you comments according to the fact that I don't know anything about those... loops
Kidding. I mean : Since I am very new to the subject, and won't ever become an expert, I could play the ignorant student discovering LQG through your texts, if you want.

Hi Humanino, still not asleep ?

I ain't no specialist myself, yet i try to understand the subject. I had some classes at college on this matter, yet the main intention of this text is to make LQG understandable for the interested reader.

So by all means, give my all your constructive critisim. it is only by that way, the text will be improved.


regards
marlon

 

[humanino]

No Marlon, I'm not home remember I could not use my notes on the YM mass gap problem to sum up my "informations" ? That's because I'm in the US. In campaign for Georges' next election. :
No way... Doing physics as usual.

Maybe you need another thread for yourself, or do you want to receive comments by mails ? Just suggestions to organize things.

 

[marlon]

No Marlon, I'm not home remember I could not use my notes on the YM mass gap problem to sum up my "informations" ? That's because I'm in the US. In campaign for Georges' next election. :
No way... Doing physics as usual.

Maybe you need another thread for yourself, or do you want to receive comments by mails ? Just suggestions to organize things.

Well if you want to you can mail me at nikolaas.vanderheyden@ugent.be

The Ugent stands for university Gent.

PS : good luck on getting Bush onto his next term. To be honest I think you are going to succeed. I think Bush is better for fysicists than Kerry would be. Why ? Well, eeuuuhhhhh

regards
marlon

 

[marlon]

Hi, guys,

I made some corrections to the introductory LQG-text. Does anyone have more suggestions or corrections.

if you want to mail, the address is

Nikolaas.Vanderheyden@Ugent.be

 

[Tom McCurdy]

QG Forum

Tom, I've momentarily lost track of where we were discussing
the idea of a forum for QG, and maybe asking Miguel A. to mentor.
I'm very glad you are in touch with him.
He is a good person to know, I think ('pressive: fencing, Go, Baez student, Wiki writer,...) and maybe something will turn out later.

I'm glad he answered you immediately and friendly-wise

I'm also glad he said no---that means he's focusing on finishing his
Loop gravity thesis, hopefully this year or next.

Did you actually set up a QG forum? Most likely it will not need a mentor for quite a while because it will be very quiet-----like an empty stage doesn't need a director. Please give us the link again and I will go glimpse it, if the place exists.

nice to see the old smilies are back (they temporarily changed for a while this morning)

Good- glad to find this convo again

umm I really need his email again -- I would like to thank him an keep in contact with him

Although I am slightly partial to invision boards in order for laTEx typesetting to work I need the forums to be made with phpbb

to see waht invision is
www.quantumgravity.tk[/URL] should do the trick

to see what forum I will be using
[url]www.quantumninja.com/QuantumGravity[/url]

keep in mine i have not really gone public because I am still working on the php with a friend in order to get the latex to actually work but you will see if you were to respond the option is already tehre

ahh soo much work
i hate college apps

 

[marcus]

Hi Marlon,
Your introduction to LQG has grown to over two pages.
One reason I like it is that it is direct, concrete, and brief
(not ever using more words than necessary)

so it is a good introduction for the practical working physicist.

I can not think of any intelligent suggestion to change what you have
written. I only hope you will sometime write a second chapter
when you see a clear way to continue

(the quantum states of gravity, how they form a Hilbert space?)

Some English-speakers may wish that you would spell vector as is normal
in English and also that you would write diffeomorphism as they are used
to see it. But I am happy to see words spelled as in German (I like the language).

I agree with you that the tangent space of a Lie group, at the identity, has a Lie algebra structure. I visualize a connection as being (at every point of the manifold) a linear map from the tangent space to a Lie algebra (which I think of as infinitesimal rotations).

So when I read your second paragraph on page 2, I feel mostly OK but a little confused because the language does not seem as clear as it is other places----you say: "When we start in A we actually take a tangent vektor. This is an element of the tangent space of the manifold at point A. The transformation that is used to go from a point A on the manifold to the tangential space is called a projection. This tangent space can be turned into a socalled the Lie-Algebra,.." this part might need some work.

In third paragraph of page 2 you say "paragraphe" with an e at the end. This spelling is too French for my taste. You should either say paragraph as in English or else paragraf.

You see my comments are mostly trivial----about spelling! I regret not having more serious comments, but cannot think of any right now.

In the last complete paragraph on page 1 you say "fysical" instead of normal english spelling physical.

thanks so much for contributing this essay! I hope you will be content, at least for now, with only these minor comments.

 

[Tom McCurdy]

Hey, guys, i made an attempt to describe the basics of LQG. I am planning to make a whole new website, dedicated to this subject. Since it is not my field of expertise (that's QFT) I ask you specialists outhere to read and correct my text.

Please, remember it is my intention to write down the structure of LQG in human language, though your corrections can be made in heavy QFT-language if necessary. I will try to understand.

Does anyone have suggestions on what there should be added.


regards
marlon

With the completion of the forum it would make sense for us to work together rather than appart--- I already have a Theory of Everythign site that I will be restarting when I can get some time-- I have to focus on college apps for a little while

however I am almost done with the QG forum

we should work on a way to combine the lqg site with the forum with the toe site
or maybe just have the toe site include lqg

or i could HAVE easily made a member site with the forum for lqG
but it may be a little more difficult to now

I could still do ti though

I will need some input quickly though

Do we want just a forum
or a site with forum dedicated to LQG

if you want the membership area for the site to work for the forum i need answer ASAP

or if you want to incorperate teh toe site with teh forum
however it will require separate names

 

[marlon]

Hi Marlon,
Your introduction to LQG has grown to over two pages.
One reason I like it is that it is direct, concrete, and brief
(not ever using more words than necessary)

so it is a good introduction for the practical working physicist.

I can not think of any intelligent suggestion to change what you have
written. I only hope you will sometime write a second chapter
when you see a clear way to continue

(the quantum states of gravity, how they form a Hilbert space?)

Some English-speakers may wish that you would spell vector as is normal
in English and also that you would write diffeomorphism as they are used
to see it. But I am happy to see words spelled as in German (I like the language).

I agree with you that the tangent space of a Lie group, at the identity, has a Lie algebra structure. I visualize a connection as being (at every point of the manifold) a linear map from the tangent space to a Lie algebra (which I think of as infinitesimal rotations).

So when I read your second paragraph on page 2, I feel mostly OK but a little confused because the language does not seem as clear as it is other places----you say: "When we start in A we actually take a tangent vektor. This is an element of the tangent space of the manifold at point A. The transformation that is used to go from a point A on the manifold to the tangential space is called a projection. This tangent space can be turned into a socalled the Lie-Algebra,.." this part might need some work.

In third paragraph of page 2 you say "paragraphe" with an e at the end. This spelling is too French for my taste. You should either say paragraph as in English or else paragraf.

You see my comments are mostly trivial----about spelling! I regret not having more serious comments, but cannot think of any right now.

In the last complete paragraph on page 1 you say "fysical" instead of normal english spelling physical.

thanks so much for contributing this essay! I hope you will be content, at least for now, with only these minor comments.

Thanks Marcus for your ever sharp analisis. Sorry for my english, that is sometimes too ,eeuuhh let's say, "continental"

I will be starting on the follow up using the Seth Major article, which I Like very much...
regards
marlon

 

[marcus]

..- I have to focus on college apps for a little while

however I am almost done with the QG forum

we should work on a way to combine the lqg site with the forum with the toe site
or maybe just have the toe site include lqg

...

Tom, it looks like those college applications really deserve the highest priority. I wouldn't want to think that talking websites was distracting from the main agenda. Will be glad to offer advice (for what it's worth) about
a QG forum or subforum later when you have ample time.

 

[marlon]

With the completion of the forum it would make sense for us to work together rather than appart--- I already have a Theory of Everythign site that I will be restarting when I can get some time-- I have to focus on college apps for a little while

however I am almost done with the QG forum

we should work on a way to combine the lqg site with the forum with the toe site
or maybe just have the toe site include lqg

or i could HAVE easily made a member site with the forum for lqG
but it may be a little more difficult to now

I could still do ti though

I will need some input quickly though

Do we want just a forum
or a site with forum dedicated to LQG

if you want the membership area for the site to work for the forum i need answer ASAP

or if you want to incorperate teh toe site with teh forum
however it will require separate names

Tom,
you are an angel.
I think we should work together on a site contributed to LQG, let's get famous on this subject.

As a matter of fact, now university will start in 2 weeks, I still have some time. I also just started an evening-course in order to learn how to make nice websites and my girl is a professional web-designer for over 5 years now.

Yaeh, I feel the potential...

regards
marlon

 

[Tom McCurdy]

Thats awesome-- I will continue to work on developing the forum for now and if time the site... I am very excited about this

Plus I am really hauling through applications so that's good as well
of course I am only doing the easy stuff
and I still ahve a lot to do

btw I am not sure what kind of class you are taking
but
I am pretty good in
photoshop
frontpage
flash

I also have ennough web design friends for everything
I have been designing web sites since I was comming out of elemntary school unfortuently photoshop ones are last 2 years but I know some useful tricks

this should work out great

 

[marlon]

Hi guys,

i am still completing my quest for knowledge on LQG.
I have written a new text that talks about loops and spin networks.

Please, check it out.

Any comments or suggetions are more then welcome. Especially from Marcus...

If anyone is interested, i can also mail it to you...
I am sorry, but the two used figures were to big to send.

regards
marlon