Introducing Loop Quantum Gravity: Differences with String Theory

[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

 

[marcus]

Marlon, I have taken up reading a more recent pedagogical
treatment of LQG. It is clear but a bit heavy.
Ashtekar and Lewandowski
Background Independent Quantum Gravity: A Status Report
http://arxiv.org/gr-qc/0404018

come to think of it, it is very heavy, not just a bit heavy
but they explain
maybe they explain too much
I am frustrated, not having the perfect introductory textbook
why don't you write one

 

[marcus]

I'm trying to get a little better idea of the Immirzi parameter.

this is is a sore point right now

Ashtekar and Lewandowski (Penn State and Warsaw) think it is 1/4.21 (roughly a quarter)

and Smolin thinks it is 1/8.088
(around an eighth, roughly half as big as Ashtekar wants it to be)
He explains his side of the argument in
http://arxiv.org/hep-th/0409056

they don't really have enough physical evidence to decide,
just some classical and some semiclassical calculations about
black holes-----since no-one has seen one up close that shouldn't
really count as evidence should it?


A place the Immirzi parameter comes up is in the area spectrum.
the quantum operator that measures the area of some given surface
has a discrete spectrum----it is the same for any surface: area can only take on certain discrete values.

these turn out to be multiples of the Planck unit of area
$$\inline{l_P^2}$$

but instead of just being nice algebraic multiples of the Planck area it turns out to be multiples of this messy Immirzi number times times Planck area
so it is as if the real unit of area is not $$\inline{l_P^2}$$
but is instead
$$\inline{\frac{1}{8.088}l_P^2}$$
or
$$\inline{\frac{1}{4.21}l_P^2}$$

 

[Tom McCurdy]

Good news: Supposidly we got what we needed to do for the forum to be cusomized to my sever

Bad news: The host doesn't allow for what i need. I will have to figure out what i need to adjust to get it to work

If anyone has any help on how to intall latex typesetting with cpanel
I am hosted through surpasshosting
that would be great

 

[marcus]

Marlon,
you have shown strong interest in making an
introductory text-book level explanation of LQG.
This is as we both know a real lack, and a big challenge.

Probably it needs to be taken up and tried by several
people---gradually the best way to explain and discuss
will be found.

A hopeful sign: today A. Perez (a long-time postdoc with Ashtekar
at Penn State who has now also with Rovelli at Marseille)
has posted his attempt at the desired "beginning Loop Gravity textbook"


Introduction to Loop Quantum Gravity and Spin Foams
http://arxiv.org/abs/gr-qc/0409061

His specialty is spin foams, so he makes a short treatment of
regular LQG and then more than half of the time he spends
discussing spin foams.
I am hoping that some part of this paper can be useful to us!

 

[marlon]

Marlon,
you have shown strong interest in making an
introductory text-book level explanation of LQG.
This is as we both know a real lack, and a big challenge.

Probably it needs to be taken up and tried by several
people---gradually the best way to explain and discuss
will be found.

A hopeful sign: today A. Perez (a long-time postdoc with Ashtekar
at Penn State who has now also with Rovelli at Marseille)
has posted his attempt at the desired "beginning Loop Gravity textbook"


Introduction to Loop Quantum Gravity and Spin Foams
http://arxiv.org/abs/gr-qc/0409061

His specialty is spin foams, so he makes a short treatment of
regular LQG and then more than half of the time he spends
discussing spin foams.
I am hoping that some part of this paper can be useful to us!

Hi marcus

this is indeed a great link and i will study this one thoroughly. I have had a lot a difficulties with finding info on the fundaments of LQG, this is the reason why i am writing this introductory text...

Thanks for providing me with info on such a regular basis...


regards
marlon

 

[marcus]

Hi Marlon,

there is a high-risk paper out
that argues a fragile line of inference
from LQG to a (to me very surprising) conclusion
that there is a limit of on-the-order one Planck mass (22 micrograms)
to the size of a BoseEinstein condensate

even tho this is very tenuous
I thought you might be interested.
Two of the three co-authors
(Matt Visser and Stefano Liberati)
are somewhat familiar to me from their
earlier work.

Look at the bottom paragraph of page 11.
they give the example that one Planck mass is about 10¹⁷
Rubidium atoms
and B-E condensates made until now have only involved roughly around 10⁶ atoms, they say------so we are roughly ten orders of magnitude away from the presumed possible limit.

gr-qc/0410113

 

[marlon]

Thanks for the info Marcus
I will certainly check it out. The introduction on LQG has been postponed a bit becausei have a lot of work at college right now...

to be continued

marlon

 

[marcus]

Thanks for the info Marcus
I will certainly check it out. The introduction on LQG has been postponed a bit becausei have a lot of work at college right now...

to be continued

marlon

realworld studies should come first!
this gr-qc/0410113 reference is potentially just causing us problems and confusion because it concerns an actual split among LQG theorists

if we narrow it down to the small group well-known who have been working in the field a long time then it reflects this division:
Ashtekar and Rovelli both say that DSR is not necessary and one can keep simple Lorentz invariance

(one could say "Lorentz bleibt Lorentz" to describe their attitude)

But on the other hand Smolin seems to be very interested in possibilities for modifying Lorentz invariance. Note that DSR (deformed special rel) is high risk. It would actually be a relief if one could experimentally falsify DSR and settle the matter.
I have to go, but let me first quote the thing on page 11

---quote---
In this sense, our proposal simply implies that it should be impossible to find a coherent quantum system whose overall mass is larger than the Planck mass. Indeed, we note that the most extensive Bose-Einstein condensates experimentally created to date contain about 10^6 atoms [23], corresponding to a mass of about 10^8 GeV. If the DSRs in fact represent the correct way of doing quantum gravity phenomenology, and if our interpretation of the DSRs as a modified theory of measurement is the correct one, then the "saturation problem” may be viewed as predicting a maximum attainable mass for a Bose-Einstein condensate, of order one Planck mass, corresponding to about 10^17 Rb atoms. This is a robust qualitative prediction of the DSR framework, which is in principle testable (though technically challenging). Furthermore, since in this framework the limitation alluded to above is actually a limitation on the maximum mass of a coherent quantum system we can (more boldly and more speculatively) also tie this back to Penrose’s speculations on the gravitationally-induced collapse of the wave-function [24].
---end quote---

notice that the Planck mass is 22 micrograms
you probably know better than I do that it is majorly impossible to test this with current technology----so this "in principle" testability gives only a little comfort. But they are saying that if one could make a coherent quantum system like a BE condensate which mass more than 22 micrograms then one could refute all types of DSR.

this would presumably make Ashtekar and Rovelli happy and it might disappoint Smolin----but one can only speculate. In my present frame of mind I can say that personally I would be glad but I must remember the issue is not settled and could go either way, so my personal feelings are irrelevant.

Maybe later I will fetch the quotes from Ashtekar and others indicating why they tend to ignore DSR an unnecessary complication.

 

[marcus]

Against all the papers from Smolin, Magueijo, Kowalski-Glikman and others about DSR (doubly special, or deformed special) and further extensions like TSR, one can cite these three from a different point of view:

Rovelli and Speziale Reconcile Planck-scale discretization and the Lorentz-Fitzgerald contraction
http://arxiv.org/gr-qc/0205108

Livine and Oriti About Lorentz invariance in a discrete quantum setting
http://arxiv.org/gr-qc/0405085
See especially page 2 end of introduction section:
---quote---
Does a quantum gravity theory with an invariant length and a discrete spectrum for geometric observables necessarily break Lorentz symmetry or necessarily require some sort of modification/deformation of it? The answer, as we will see, is simply “no”.
---end quote---

Ashtekar Gravity and the Quantum
http://arxiv.org/gr-qc/0410054
See especially page 28, end of first paragraph
"As was recently emphasized by Rovelli, there is no tension whatsoever..."

So Olympian is Ashtekar's perspective in his review paper that he barely mentions the controversy and devotes only a couple of sentences to it.

 

[marlon]

I wrote a little introduction on LQG because i have seen that many people ask similar questions on this topic...anyone that is interested can read it in my journal...

regards
marlon
corrections are always welcome...