Introducing Loop Quantum Gravity: Differences with String Theory

[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

 

[marlon]

Besides, you just got to imagine the figures (the first one) as dots (nodes) that are connected with lines (links).

 

[marlon]

I have a question though. In LQG gravitons should be viewed at as excitations of the quatized gravitational field. Following this quantization, space has somekind of granular-structure. Now how exactly are the gravitons generated. Should they be seen as excitations of the loops that describe the space or do they come out of the nodes ?

And once generated, do they travek via links from node to node or what ? I mean how do particles travel through space in LQG? Or is that just the same as in QFT where we can see the space as a continuum when particle-motions are described ?



regards
marlon

 

[marlon]

Hello where is everybody ?

regards
marlon

 

[marcus]

I have a question though. In LQG gravitons should be viewed at as excitations of the quantized gravitational field. ...

Hi marlon,
right now I can't think how to respond to your question about gravitons.
I may need more time, or help from someone else. In my reading of LQG, I don't remember a discussion of gravitons.

(such a discussion would come come up naturally in a perturbative approach to QG where one has a fixed flat background and a small perturbation superimposed on it---coming from QFT, that is exactly what one would expect to see in quantum gravity)

Is it possible that in LQG, because the approach is non-perturbative, the concept of a graviton is not essential? I regret to say I don't have a satisfactory response.

regards

 

[Chronos]

In some respects, gravitational attraction under LQG reminds me of surface tension in a fluid. I get a little lost after that, the mathematics involved get rather complicated in 3 dimensions. For more confusion, see this
http://science.nasa.gov/headlines/y2003/25feb_nosoap.htm

 

[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

Hi,
anybody got any comments on the text on LQG that I posted sometime ago ?

Or may I say that no correction is needed. I think there are no mistakes inthere, but i can never be sure though

regards
marlon

 

[marlon]

A new day in LQG space...
Hi, guys,

Right now i am studiyng on spin networks and how to implement them in QM. I refer to this article by Seth A Major : http://academics.hamilton.edu/physics/smajor/Papers/AJP00972.pdf

I am having some difficulties with the content though. Can anyone help me out with page 4 (page 975 in the text). We need to show in the first exercise that a two-line is a projector using the skein-relations (they are also given in the text). How do we do that ? I think i have a solution but i really don't need these relations...

Then what about this n-loop. I don't grasp the explanation on the indices and the sum of the indices having a+1 possible values. Well I understand why, but what i don't get is this : For an edge with a strands the sum of the indices A,B,C,... is 0,1,2,...,a. Why oooh why is that ?


regards
marlon (i suggest this text to veryone, it is real fun )

 

[marcus]

Hi marlon,

you say Seth Major's spin network tutorial is "real fun ".
I tried it some months ago and could not make progress with it.
Maybe if I try again.

In this passage you mention he refers to "Reference 13". There is no bibliography with a reference 13 but there is a footnote. One sees he has footnote 13 which is a recursion relation

\Delta_{n+2} = -2\Delta_{n+1} - \Delta_n

\Delta_0 = 1, \Delta_1 = -2

after that must come 3 = -2x-2 - 1

after that must come -4 = -2x3 - (-2)

after that must come 5 = -2x-4 -3

so his footnote 13 is relevant, because it suggests a recursive proof of what he is saying in the main text between equation (7) and (8):

"Making the simplest closed diagram out of these lines gives the loop value often denoted as \Delta_n

\Delta_n = (-1)^n(n+1)

His style of writing english is a little too casual for me. He uses expressions in quotes that he does not define. The next sentence is this:
---quote---
The factor n+1 expresses the ‘‘multiplicity’’ of the number of possible ‘‘A values’’ on an edge with n strands.
---end quote---

HE DOES NOT EXPLAIN WHAT THESE EXPRESSIONS IN QUOTES MEAN! What is "multiplicity" or what is "A values"?

 

[marcus]

hi marlon, I had to be away from the computer so I took
an introduction to LQG with me on the train to read
Marcus Gaul and Carlo Rovelli
http://arxiv.org/gr-qc/9910079

I still do not know a better introduction. I re-read it with pleasure.

I should not be so critical of Seth Major, but I think he would be
a talented teacher if you could get him in person in a classroom
with a blackboard so that he could demonstrate with pictures and
gesture. By contrast I found his writing overburdens my intuition. I dont
have good enough intuition to follow him.

 

[marlon]

Marcus,
your reference seems very clear. i will look into it and drop Seth A Major for a while...

see you next time

regards
marlon