Workshop on tests of gravity in Case Western – day 2 and Arkani-Hamed’s talk
ASTRO, COND-MAT, HEP-TH/PH, Various — By Dmitry Podolsky on May 28, 2009 at 10:24 pm
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The second day of the Workshop on Tests of Gravity (and here is my blog post about the first day) was mostly devoted to analog models (Bill Unruh, Michael Uhlmann, George Pickett) and models of modified gravity (Nima Arkani-Hamed, Justin Khoury, Stacy McGaugh, Ted Jacobson, Levon Pogosyan and Mark Wyman).
Regarding analog models I don’t have too much to report – since I am located here at relatively close vicinity to Grigory Volovik (he works in Espoo, while I work in Helsinki), I think I know the agenda quite well, and my overall impression that no so many exciting things happen on the field was confirmed on the workshop. Basically, it proves to be relatively easy to construct models of relativistic chiral fermions and vectors from non-relativistic condensed matter systems (for example, He-3). However, it seems to be impossible to construct relativistic dynamical gravity (that is, effective theory with Einstein-Hilbert action) starting from these systems – recent attempt by Horava seemed to be promising, but the ultimate answer is still the same. What we can do at most is to model a “relativistic” field theory on a curved background (such as Painleve-Gullstrand BH), but this background is static and backreaction of our field theoretic degrees of freedom on it is zero. That’s what activities on the field of analog models of gravity revolve around for almost decade.
So, let me turn to modified gravity and Nima’s talk. Since nobody in the physics blogosphere seems to really discuss the content of his talk (see Mark Trodden’s report – he attended the workshop, too), let me proudly do it for you 
As you may already know, the title of the talk is “Don’t modify gravity – understand it“. Nima started by saying that he spent too much time inventing models of modified gravity and now wants to officially confess his sins.
Why? First (but not the most important as you’ll see below), because modified gravity is boring – in all (or most all) it can be reduced to usual GR + scalar field. More accurately, he has introduced the following classification: all modified gravity models can be divided into two classes -
- boring, with subclasses a) very boring (and not excluded) and b) moderately boring (and excluded by experiments) – because of the name of the class he did not want to talk about those models at all
- exciting. This class, according to Nima, includes only deeply flawed models such as DGP (where aforementioned scalar field possesses “Galilean invariance”) and Higgs phases of gravity (where scalar fields are essentially Goldstone modes of spontaneously broken spacetime symmetries).
So, why exciting models are deeply flawed from Nima’s point of view? The reason is the fact that, according to well-known theorem quantum gravity (based on usual GR) can not have local observables. The physical reason for that is simple. Quantum mechanics in principle allows us to measure positions of quantum particles with infinite precision (not both position and momentum though). However, measuring position with infinite precision assumes that we have an infinitely heavy apparatus to measure it. Quantum gravity in turn does not allow us to have an infinitely heavy apparatus (sufficiently heavy one would trivially turn into black hole).
A correct language for describing gravitational degrees of freedom should look more like holography. Basically, holography means non-local degrees of freedom, and non-local degrees of freedom mean holography.
Yet, non-locality of gravity will only be noticeable only if we take into account non-perturbative effects, suppressed by
,
where 
is Newton constant, that is, gravity is non-local but in a very subtle way.
Now, why exciting models are deeply flawed according to Nima? Well, Higgs phases of gravity violate “non-local” part in the statement above – they are manifestly local. On the other hand, DGP violates “subtle” part of the statement above, since it allows for superluminal propagation.
Basically, a general effective scalar field theory featuring CP violation looks like
.
DGP is a rather special CP violating theory, where the last term before the dots is canceled due to a special symmetry, and this allows theory to feature superluminal propagation.
He concluded by explaining what questions should one study to understand non-local nature of gravity better. Basically, since non-locality is suppressed by a factor 
, it should become important again in situations where some kind of 
enhancement is present – such as questions related to BH information paradox and eternal inflation (in the latter case, enhancement comes from the fact that you are never able to measure more than models in dS universe, where 
is de Sitter entropy).
I’ll try to cover remaining talks of the second day tomorrow.
7 Comments
Certainly you mean “deeply flawed” and not “deeply flowed”?
“Deeply flowed” could be a technical term in renormalization group theory. If it’s not, maybe it should be. (-:
So what’s Nima’s comment on Horava’s modified gravity?
Isn’t it obvious from Dmitry’s text? The Horava-Lifshitz theory is neither “subtle”, because it has even more generic superluminal signals than DGP that Nima took as his bad enough but still much better example.
And despite this superluminality, it is not really “nonlocal”, and it has arbitrarily short spatial distances that can’t be measured because in proper gravity, the heavy gadgets needed to see them should collapse into a black hole which is again larger. So the theory violates pretty much every rule that Nima has listed, doesn’t it?
“Deeply flowed” is cute. If you were Chinese, you could also write “deeply fraud”.
I just spoke to God about the possibility to forgive Nima’s sins because what he says about the “subtle” “nonlocality” finally makes sense.
You are all little buggers making fun of old poor fellow who does not know how to talk properly (but at least tries hard) LOL Thanks for the correction anyway, fixed.
Surprisingly, Horava’s gravity wasn’t mentioned a single time during the workshop, not even by analog people. (And those people I talked to were not aware of it.) Nima didn’t mention it either.
My personal opinion is the same as Lubos’ one he presented above, Horava’s gravity is not subtle since it features superluminal propagation of signals.
By the way, Nima has admitted that the point of view “screw holography and BH entropy, gravity is effective theory, and locality should win in the end” is perfectly legitimate, so whether you accept holographic philosophy or not is a question of taste. My impression is that holography is a good taste, and analog gravity is a bad taste: theory itself tells you something (and this something is very deep), while you prefer to ignore it saying that the theory is approximate anyway.
The second thing is that it wasn’t really proven that the action of Horava theory is reduced to Einstein-Hilbert action in the IR.
Cheers,
Dmitry.
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