# Loop quantum gravity

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

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

Hello where is everybody ???

regards
marlon

marcus
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marlon said:
I have a question though. In LQG gravitons should be viewed at as excitations of the quantized gravitational field. ...
Hi marlon,
right now I cant 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 dont have a satisfactory response.

regards

Chronos
Gold Member
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

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marlon said:
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.

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

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
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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"?

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marcus
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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 [Broken]

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.

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

see you next time

regards
marlon

marcus
Gold Member
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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 [Broken]

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 dont you write one

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marcus
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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 [Broken]

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 $$\inline{l_P^2}$$
$$\inline{\frac{1}{8.088}l_P^2}$$
or
$$\inline{\frac{1}{4.21}l_P^2}$$

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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
Gold Member
Dearly Missed
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!

marcus said:
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
Gold Member
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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

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
Gold Member
Dearly Missed
marlon said:
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
Gold Member
Dearly Missed
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 [Broken]

Livine and Oriti About Lorentz invariance in a discrete quantum setting
http://arxiv.org/gr-qc/0405085 [Broken]
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 [Broken]
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.

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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...

marcus
Gold Member
Dearly Missed
marlon said:
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...
marlon,

that is a really good use of the PF Journal resource. it makes me think that I should write an essay on something in my journal, or assemble some information.

you put real thought----including your intuition as a particle physicist---into your essay.

I hope that it was not only for other people but that it also was valuable for you---you worked on it and thought through what happens step by step in building LQG. thanks for a good contribution.

=====
there are some non-standard English expressions. Actually I like european or germanic-style English quite a lot. sometimes it sounds better or more interesting than standard does.

I will mention only one. the word "fundament"

It is a very well established fact that gravitation and quantummechanics both have totally different fundaments, which makes it very difficult to unify them at “first sight”.
In English the word "fundamental" can be either adjective or noun.

Adjective: "harmonic analysis is fundamental to this theory"

Noun: "the two theories are based on different foundations."
"the two theories have different fundamentals"

But one does not say "the two theories have different fundaments"

It sounds slightly wrong, although interesting.

Actually instead of criticizing I should compliment you on your writing, because you do a fundamentally good job at explaining the fundamentals of Loop Quantum Gravity!

Marcus as always i need to thank you for instructing me...
please feel free to make more comments on the text, this is the best way to learn it and gradually move on to more advanced material. I prefer to have a simple and clear understanding of what i wanna learn before to move on to more "exotic" texts (which i wanna write to here in the near future...). This is the way i learned QFT in college and this is the best way to understand LQG...

thanks again and regards

marlon