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Gravitons in Loop Quantum Gravity 
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#19
Feb2912, 08:22 PM

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#20
Mar112, 12:57 AM

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P: 5,366

In the standard formulation in ST one introduces a spacetime metric. Some decades ago this was typically "4dim. Minkowski spacetime" * "6dim. compactified CalabiYau space"; in the meantime other geometries have been discovered and are studied extensively.
From ST one can derive a consistency condition for the spacetime on which strings are propagating. This consistency conditions requires Ricciflatness and forbids arbitrary spacetimes and arbitrary compactified dimensions; Minkowski spacetime * CalabiYau is a typical solution, but as I said, others are possible, and in the meantime string theorists were able to relax these conditions. The problem I see with string theory is that "spin2 fields plus flat spacetime = curved spacetime" does not really work; you have to chose are curved spacetime in the very beginning and study propagation of strings as "weak distortions" on top of it". But these strings do never change the whole spacetime dynamically, it always stays in some fixed subsector which does not change dynamically. This holds afaik for other approaches (e.g. branes, fluxes, ...) as well. This is what is called background dependence and is basically due to the approach "fix a background and then quantize small distortions". LQG tries to get rid of this problem and avoids to fix a classical background. But as suprised explained, one still has to introduce some kind of boundary condition or background when doing physics; it's not required for the definition of the theory (and that's a major step forward), but it's required for detailed calculations (e.g. when studying black holes in LQG one has to define an isolated horizon classically; a full dynamical setup w/o any input like boundary conditions or background is not possible). 


#21
Mar112, 01:05 AM

P: 381




#22
Mar412, 12:27 AM

P: 381

1. Particle Physics approach 2. String Theory 3. Canonical Quantization or LQG The Particle Physics approach is the one that treats spin2 field in flat spacetime = curved spacetime. Not String Theory. For 5 years. I thought String Theory was about it. According to the above mentioned book: "The perturbative superstrings programme involves quantizing a classical system; but the system concerned is not general relativity, but rather a system in which a onedimensional closed string propagates in a spacetime M (whose dimension is in general not 4). More precisely, the propagation of the string is viewed as a map X : W → M from a twodimensional ‘worldsheet’ W to spacetime M (the ‘target spacetime’). The quantization procedure quantizes X, but not the metric γ on M, which remains classical." The above suggests string theory is not about spin2 on flat spacetime. Can anyone confirm this (or is there any objections?). The above says string theory is about quantizing the map X : W → M. Does anyone have other ways of saying it that can make it clearer? Or web site links that specifically details this particular aspect? How do you connect it to Spin2? Could it be possible that this worldsheet and dimensions not 4 somehow produce the predictions of spin2 over flat spacetime. Is that what the above is saying or suggesting? Thanks. 


#23
Mar412, 03:24 AM

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P: 5,366

String theory is about quantization of strings; but one finds one oscillation of a closed string that corresponds to a massless spin2 particle which is then identified with the graviton. There is a limit in which string theories reduce to quantum field theoirs of poiintlike particles; this limit is a supergravity theory containing gravitons, gravitinos (and a lot of other stuff). In that sense ST contains gravitons.
The consistency condition is Ricciflatness. CY are Ricciflat and are in that sense not arbitrary. 


#24
Mar412, 03:55 AM

P: 381

http://motls.blogspot.com/2007/05/wh...instring.html "If the worldsheet theory is consistent as a string theory, it must be scaleinvariant, and the spacetime geometry must thus be Ricciflat! We have just derived Einstein's equations from scale invariance of a twodimensional theory." It didn't mention about CalabiYau. But these are supposed to be 6 dimensional. I wonder how they could be Ricciflat. It's like one has spike balls, how can it be flat.. unless you are saying since they are so tiny, they look flat at larger scale even though they are like spike balls? If someone can explain too. Please do so. Thanks. 


#25
Mar412, 04:01 AM

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P: 5,366

look at a twotorus T²; the embedding in R³ doesn't seem to be flat, but mathematically it's possible (w/o considering an embedding) to a define an atlas consisting of flat metrics on T².



#26
Mar412, 04:28 AM

P: 381

Is the above an example of a twotorus? How does "one define an atlas consisting of flat metrics on T²"? In CalabiYau, there are 6 dimensions with 6 different axis.. how do you make it flat, maybe from looking at a distance very far? Thanks. 


#27
Mar412, 07:49 AM

P: 381

http://universereview.ca/R1526CalabiYau.htm Thanks for pointing out that manifolds that is not flat can really be flat. It's counterintuitive that was why I missed the concept in all the years I read Brian Greene books. I guess the reason they make it ricciflat is so that it can satisfy the condition "ricciflat plus spin 2 graviton field = General Relativity. But then. Since it can't even describe the FRW Universe. What good is it I'm wondering?? 


#28
Mar412, 08:37 AM

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P: 8,394

The curved spacetime of a Schwarzschild black hole is Ricci flat.
String cosmology doesn't seem that well developed, but here are some recent reviews. McAllister, Silverstein String Cosmology: A Review Burgess, McAllister Challenges for String Cosmology 


#29
Mar412, 08:38 AM

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P: 5,366

unfortunately that's not a twotorus but a twofold or double torus; in T² the "2" means twodimensional ;)
a twotorus T² can be defined as tupels (x,y) in an interval ]0,L_{x}[ * ]0,L_{y}[, i.e. R² with a grid where all points (x+mL_{x},y+nL_{y}) etc. (with integers m, n) are identified; the flat metric is nothing else but the standard metric on R² 


#30
Mar412, 06:07 PM

P: 381




#31
Mar512, 03:25 AM

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P: 1,677

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) 


#32
Mar512, 05:00 AM

P: 381

http://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: tom.stoer replied to Finbar statements above: tom.stoer ended it thus:  dynamical collaps, e.g. preSchwarzschild and preKerr  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. 


#33
Mar512, 06:27 AM

Sci Advisor
P: 5,366

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



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