今天我自己没有什么好写的，最近忙于非物理的事情比较多（假如这也包括很多论文答辩的话），arXiv也没有什么令人特别感兴趣的东西。本来我约好宋伟和庞毅继续批评Horava理论的，但网上并没有值得批评的文章。Horava理论短暂降温了两个礼拜，现在又开始回温了，但多数还是应用，例如今天出现的蔡一夫同学的文章。向大家推荐一个很好的理论物理专业博客，NEQNET: Non-equilibrium Phenomena，话题主要是理论物理，也有些其他话题，例如最近关于哈佛大学面临破产的可能。抄一下这个消息：

Just wanted to finally end my day and go to sleep (way too much work today), but heard some news and cannot help sharing it with you.

According to Boston Magazine Harvard University is to face some very serious problems. The University currently spends about 1.5 billion USD/year, it has lost several billion during crisis - including 500 million thanks to Larry Summers, super feminist fighter (essentially, he presented those 500 million as a gift for GS). If only Dr. Summers spent more time thinking about what he was supposed to think about… but he is clearly not the person to blame as they want him to be.

11 billion of Harvard’s money are currently to be repaid to private investors as capital commitments in the next 10 years, Harvard currently has 13 billion in various assets - and what if the crisis did not reach its bottom yet? What if Harvard is to expect more endowment losses? And all this does not include construction of the new campus in Allston which will be surely put on hold.

Sad, saaad news.

另一个有趣的帖子是谈Arkani-Hamed警告大家不要随便修改爱因斯坦引力理论的。Arkani在他的演讲中并没有提到Horava理论。我还是转贴一下这一段：

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

Nima Arkani-Hamed

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 -

1. 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

2. 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 G_N 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 S is de Sitter entropy).

I’ll try to cover remaining talks of the second day tomorrow.