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Conformal Nature of the Universe (at PI) Is nothing sacred? 
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#1
May712, 09:32 PM

Astronomy
Sci Advisor
PF Gold
P: 23,270

Starting Wedesday 9 May at PI will be an unusual conference at Perimeter.
Some topics of talks include: Shape Dynamics (Barbour, Koslowski, Gryb, Gomes...) Relationalism (Edw. Anderson...) Horavaism 't Hooftism Magueijoism These talks will presumably be online (a wonderful practice of PI) and some of them will probably be extremely interesting. Here's the schedule: http://www.perimeterinstitute.ca/en/...erse/Schedule/ 


#2
May712, 09:56 PM

Astronomy
Sci Advisor
PF Gold
P: 23,270

Here are the abstracts for the conference talks:
http://www.perimeterinstitute.ca/Eve...rse/Abstracts/ I really like Joao Magueijo's title. I think it's funny: Is Nothing Sacred? The Cosmological Pay Off from Breaking Lorentz and Diffeormorphism Invariance Shape dynamics is an example where you give up diffeo invariance, you agree to be tied down to a fixed foliation into simultaneous timeslices (thus sacrificing diffeo invariance.) And in exchange you get CONFORMAL invariance. Is that good? Some people think so. With conformal invariance things have no definite size they are just in a definite angular relation to each other. Other theories are exploring conformal invariance as wellhence the conference. So here we have these sacrosanct principles of Lorentz and Diffeo invariance and suddenly it is fashionable to devise and study theories which break them. Julian Barbour is giving the COLLOQUIUM talk connected with the conference. Colloquia are generally aimed at a wider audience and held in a larger auditorium. http://pirsa.org/12050050 One of the other speakers, Edward Anderson, just posted a paper called Relationalism on the arxiv, and will be giving a talk by the same title at the conference. Here's the talk's abstract. ==quote== Edward Anderson, Université Paris Diderot Relationalism I shall describe Relationalism, especially in the LeibnizMachBarbour sense of the word and my variations on that theme. My presentation shall give five extensions to Barbour's work: (more or less) phase space, categorization, subsystems analysis, quantization, and physics as a propositional logic (`questions about physical systems'). I shall also briefly explain how some of Crane and Rovelli's ideas do fit within this scheme, whilst others are at odds with the LMB scheme, leaving one choosing options rather thanjust considering unions. I shall also present how scaleinvariant and scaled relational particle models (the latter originally discovered by Barbour and Bertotti in 1982) can, in dimension 1 and 2, which suffice to toymodel many midisuperspace aspects of GR, be very generally solved at the following levels. 1) configuration space geometry following my fortuitous connection with Kendall's work in the statistical theory of shape involving the selfsame space of shapes, and then the cone over this in the scaled case. 2) Conserved quantities and classical equations of motion. 3) Quantum equations of motion and their solutions. 4) Parallels of many Problem of Time strategies. I view this second paragraph as relevant not only by 4) but more widely by how it is a model of quantum background independence (BI), with BI being argued to be the other half to 'relativistic gravitation' in that gestalt entity known as General Relativity. ==endquote== Here's the arxiv paper's abstract: http://arxiv.org/abs/1205.1256 


#3
Nov1412, 06:49 AM

P: 5

If you are referring to three dimensional diffeomorphism invariance, then SD certainly doesn't get rid of that, but in addition to it, we have the additional conformal constraint.



#4
Mar3013, 11:07 AM

Astronomy
Sci Advisor
PF Gold
P: 23,270

Conformal Nature of the Universe (at PI) Is nothing sacred?
so glad to see comment from one evidently knowledgeable about some QG matters in particular SD. I didn't see your post earlier. Actually I was referring to 4D diffeo invariance as being given up. I realize one still has 3D. I'm not an expert however and welcome others checking for errors and misconceptions. As I understand it, one accepts a fixed foliation (spacelike slicing) and so one "trades" full 4D diffinvariance for the conformal invariance one gains. I was glad to see that you picked out the paper by Sean Gryb et al in the current poll. http://www.physicsforums.com/showthread.php?t=681598 I was interested to see that the authors did not CALL what they were doing by the name "Shape Dynamics". Could you explain in what sense it is SD and in what sense it may have evolved slightly into something else, requiring a different name? http://arxiv.org/abs/1303.7139 Symmetry and Evolution in Quantum Gravity Sean Gryb, Karim Thebault 


#5
Mar3013, 11:41 AM

P: 5

Greetings Marcus,
You are right in saying that one gives up the full, four dimensional diffeomorphism group in Shape Dynamics, but in order to better phrase it, one need note that Shape dynamics employs what's called "symmetry trading" in it's construction, this means that in order to attain the (parameterized) SD phase space, which at the unconstrained level is indistinguishable from that of ADM general relativity, we need to gauge fix a certain second class constraint of what's called the "Linking Theory" (interesting construction) and this can be done in two ways, one which leads to a physical scale and a reparameterization constraint (ADM gravity) or, in order to get Shape Dynamics we fix the reparameterizations by choosing a foliation (here, CMC) and we are left with unphysical scale (hence the confromal constraint) and a global scalar Hamiltonian constraint, which is but the Lichnerowicz York equation which can be solved and the more modern framework of SD is what is thus attained. But here's the thing, the consequence of symmetry trading is that it would be as meaningless, in SD to talk about reparameterizations as it would be to talk about the local anisotrpoic Weyl transformations generated by the volumepreservingconformal constraint in canonical ADM gravity. That aside, I am not sure why Sean Gryb and Karim Thebault do not explicitly call what they were doing SD. It 'is' SD in the sense that they are essentially using SD in the section where they deal with the goemetrodynamics that is, the manner in which the true Hamiltonian is derived from deparameterization of the linear FCC and so on. They also use Best Matching which is very much in the spirit of old SD but perhaps as they are basing this work on their older work on Relational Quantization, but here for the geometrodynamic part of SD, they may not have wantted to mention explcitly that it is SD. So I dont think I could give you an answer as to why it 'isn't' SD, nonetheless, I hope that this was satisfactory. 


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