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Whatever was said in popular media doesn't matter. LQG was shown to be Lorentz covariant in a technical paper by Rovelli&Speziale in around 2009.kye said:...4. In one of the Sci-Am article about Loop Quantum Gravity. It is said if different wavelength photons from far away in space are measured to arrive differently, it can support the discreteness of space. Isn't it this experiment has been done already? Is the result null or non-null?
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It was never proven rigorously that LQG predicts different arrival times (dispersion). So if they ever observe energydependent speed of light this will, unfortunatelyNOT support Loop or spin foam gravity. There was speculation that Loop might imply dispersion up to around 2006 but then people tried very hard to prove it mathematically and failed. So there is this free-floating popular misconception...
3. Does Loop Quantum Gravity use the principle of Shape Dynamics or are they independent GR theories?
There are several versions of Loop gravity being worked on by the community. SD people including Barbour and Koslowski were all over the opening day program of Loops 2011 at Madrid. They had a less prominent role at the next Loops conference. I have seen papers by SD people about what SD can give Loop, what can be put in, how to do SD in a Loop way etc etc. Loop people have a lot of experience QUANTIZING theory of spacetime geometry. And SD is still basically a classical theory--it still has not gotten very far in the quantum direction. So SD people get invited to present and Loop people listen and there is room for collaboration.
But if you want my private opinion I think SD was to some extent a FAD, which peaked around 2011. I see diminished activity. IT HAS THINGS TO TELL US though. So you should notice what I said about the ILQGS talk by Koslowski on November 12, in about one week from now. It is basically about "What can Loop learn from SD?" This is the online International LQG Seminar hookup, like a big conference call with various places in US Canada Europe. Listen to the presentation, the questions, the answers, the discussion. If the connection is good and everybody joins in you can get a feel for how it is going with SD.
The short answer is that Loop is several things and they are separate from SD. Loop has about 10 times the research activity and might eventually cannibalize SD---we can't tell the future of research, it is almost by definition impossible to predict the future evolution of human understanding. Anything can happen. BTW Loop has its own "in house" study of global time called "Tomita Time" or "thermal time hypothesis". We've had thread about that. My feeling is that it is more interesting than SD, but also in preliminary growth stage so one cannot tell much.
1. Besides Unimodular, what other GR proposed replacements have global time...?
Well a world-famous GR expert named Ted Jacobson has something called Einstein-Aether which has a timelike unit-vector field. And Petr Horava at UC Berkeley (pronounced Ho-zha-va) has proposed GR replacement that I believe somebody has gotten a preferred foliation out of. I don't keep track of all the proposed GR replacements. You know about CDT, i guess. Ambjorn and Loll's Causal Dynamical Triangulation. That is built on a preferred foliation. That is slicing spacetime into space like slices so you get layers---essentially a preferred time.
And of course there is Tomita Time that some Loop people have been working on.
And as I told you you get a preferred time in Cosmology as soon as you fill the early universe with hot gas and look at the CMB. Or even if you just have ordinary Friedman model expansion.
I told you I think there was a lot of excitement about it which I think peaked a year or two ago. And it is one of SEVERAL proposed replacements that have global time. I wouldn't get excited. Another world-famous GR expert George Ellis just posted on arxiv about Unimodular. I think Unimodular has considerably more legs than SD so if I was going to be interested in one of these i think it might be Tomita Time or Unimodular. Ellis co-authored the classic book on spacetime geometry ("the largescale structure of space time") I have very high regard for his intuition and sense of what matters and where things are going. Unimodular is cool but you couldn't necessarily explain why it is cool to a lay audience in a short popular article or in a book like "Time Reborn". Smolin made an excellent choice in what to use as an example.2. What do you think about Shape Dynamics?
I think it is time to LEARN WHAT WE CAN from SD and move on. So I will definitely listen to the Seminar talk by Koslowski when he talks to the Loop people (and not for the first time!) on ILQGS. I'm not an expert or a researcher, but I watch the research scene with interest, and I'm always prepared to be surprised. So we'll see.
Unimodular solves the main Cosmological Constant problem which is a huge plus. If SD would turn out to solve the CC problem that would be significant. Maybe Koslowski will report something on that score. I'm prepared to learn something new from his talk--smart young guy. Maybe you should listen.