Gravitons in Loop Quantum Gravity

[Haelfix]

I've been trying to read the two papers for half hour already but I can't seem to get the essence. The reasons we created all those Calabi-Yau is to simulate the ricci-flatness so that the particle physics approximation of flat spacetime + spin-2 field = curved spacetime can work. But in cosmology like inflation and FRW model... it doesn't support those approximation at all.

You have gotten it all mixed up (here and pretty much everywhere)! First of all, the reason none of this material makes any sense to you (when explained by multiple parties) is b/c you haven't heeded my advice to start from the beginning. For instance, chapter 1 of Misner, Thorne, Wheeler or some other undergraduate level book on general relativity.

What's happening is you are confusing several different english words, that are utilized in different physical and mathematical contexts. Unfortunately its often the case that these things have multiple meanings in quite different situations. Worse, you are doing this with posts on physicsforum and other places on the internet where the word choices/phrasing aren't necessarily as polished as a textbook.

When a physicist reads a paragraph written in english about some physics subject, what he has in mind is a sort of substition (this is referring to a calculation that is done on page xx of book/paper or blackboard yy). Even there it can be a little bit ambigous and another reader will ask for clarification in a very particular way where it is clear that both parties are on the same wavelength.

What you are doing is grouping together words and concepts and trying to develop an abstract intuition about the physics. Well, believe me, you can stop right there b/c it won't work. It has not worked for the greatest geniuses of our time. The only way to learn this material is the hard way. ok?

Now.. If you really, really want to talk about in what sense and how linearized gravity works, I will be happy to explain. But only if I know you have done some groundwork first (this means knowing what a metric is, what gravitational waves are, what initial value formulations of GR are, and so forth aka a mastery of the first 18 chapters of the aforementioned MTW)

 

[waterfall]

Now.. If you really, really want to talk about in what sense and how linearized gravity works, I will be happy to explain. But only if I know you have done some groundwork first (this means knowing what a metric is, what gravitational waves are, what initial value formulations of GR are, and so forth aka a mastery of the first 18 chapters of the aforementioned MTW)

I agree with you of course. As the details are what can make me comprehend 100%. But laymen just want to get a general feel of it all. And thanks to an interesting old thread where you participated intimately. I got the superficial grasp. Above I was asking about how GR came from strings, not about linearized gravity. After 3 weeks of discussing linearized gravity that spans many threads and more than a dozen people. Of course I got the basic of it. Basically the idea is that the correspondence between GR's curved manifold and a model using a flat manifold plus a spin-2 interaction has only been shown for weak gravity in a region small enough that the two manifolds can be put into 1-to-1 correspondence. This doesn't work for FRW. And I've been wondering for two days how strings can handle FRW. I'm also reading Tong paper you shared in the classic old thread:

https://www.physicsforums.com/showthread.php?t=495351
"General Relativity from String Theory"

I have read the thread twice and will do it again and again for the next few days.

You mentioned in #7 there:

After compactification, and integrating out the matter modes and taking the hbar --> 0 limit, the result is 4 dimensional Einstein Hilbert lagrangian. Solving the Euler-Lagrange equations yields Einsteins field equations in vacuum exactly.

This is completely analogous to the derivation in MTW where a spin 2 field and a weak field expansion is shown to reproduce the EFE exactly. Here though, the consisteny criteria are already staring at you in the face on the worldsheet. There is nothing else that string theory can limit too, it always must have the EFE's in the IR exactly!

And you detailed it in #9:

Tong explains it perfectly. You start by fixing a background on the worldsheet, and demanding that the quantum theory be conformally invariant (eg that the beta functions vanish). After a calculation you find a set of equations or requirements that must vanish.

Up to this point, everything is perturbative to a given order and fixed.

Now you switch perspectives, and ask, what is the low energy effective lagrangian over spacetime (as opposed to the worldsheet) that gives those beta functions as equations of motion.

And you are led to the EH lagrangian. This last step is decidedly not perturbative, it is not fixed, it is simply a statement that in the hbar --> 0 limit (which takes care of all the 2+ loop corrections from the worldsheet), that the EFE's are the only possible equations of motion that reproduces that lagrangian classically. All you then need to do is show that it is unique. Which is a classical theorem by Hilbert, and you are done.

The bottomline is that there is no controversy that string theory gives GR in the low energy limit. It is basic textbook material!

(edit: The action here is indeed 26 dimensional, and strictly speaking this is the Bosonic string. The real calculation would involve compactification on the Superstring (eg 10 dimensional), and obviously it is a little more subtle with a lot more notation. But the actual proof goes through in a completely analogous manner, except there you won't derive pure GR, but rather supergravity (and then you have to worry about how to break supersymmetry))

Brilliant! Later in the thread, in msg# 50. Finbar mentioned thus:

qsa makes a good point. If we go by Tong's calculation string theory is only consistent in strictly Ricci flat space-times. Since evidence(accelerated expansion) points to us living in de-sitter space we must need to find some degrees of freedom(modes of the string), other than gravitons, which form a coherent state corresponding to de-sitter space.

Anyone know if this has been achieved??

You didn't comment on it. So maybe you agreed on the statement that something besides the gravitons modes of the string can form a coherent state corresponding to de-sitter space? This is my only question to you for this year before I started MTW for the next 2 years.

tom.stoer replied to Finbar statements above:

I guess this is a fundamental problem, namely that in a certain sense background independenca means something different in string theory. One has to prove for a certain background that a consistent quantization can be achieved. And this has to be done for each background separately. Therefore the background (or let's say the class of backgrounds) changes the d.o.f.

I mentioned this because I can't figure the acronym "d.o.f.", what is d.o.f.? Depth of Field? I really need to know this because that old thread is a classic and it would be on my mind a lot.

tom.stoer ended it thus:

The problem is that one should somehow categorize backgrounds in terms of something like "classes" or "superselection sectors". Different sectors may or may not be "connected" by dynamics. In string theory the specific background can affect the details of the degrees of freedom living on it.

I see the following problems:
- one has to identify the correct d.o.f. for each background (sector)
- there may be backgrounds (sectors) which cannot be equipped with a viable string theory
- dynamically connected backgrounds (sectors) cannot be studied coherently if they have different string d.o.f.

Now the question is how to construct viable string theories for certain classes of backgrounds relevant in GR, especially
- dynamical collaps, e.g. pre-Schwarzschild and pre-Kerr
- FRW, dS, ...

So the question in my message previous to this was answered by tom last year. That we may need to to "construct viable string theories for certain classes of backgrounds relevant in GR, especially
- dynamical collaps, e.g. pre-Schwarzschild and pre-Kerr
- FRW, dS"

Now. Haelfix. I don't disagree with you that I read MTW book for the next one year. And I'm not looking or asking for any more details now if you don't want to ask more. I just want to know if you agree with Finbar and Tom above because in that old classic thread. You didn't respond to them. So you agreed with them? This is all I need to know at this point in time and I know I won't ask more questions before I mastered MTW book.

And Tom or others. Don't forget to tell me what is d.o.f. Many Thanks to all.

 

[tom.stoer]

d.o.f. = degree of freedom ;-)