SidneyFest!

By now, the readers of physics blogs will be familiar with the concept of Sidneyfest, the two day extravaganza meant to celebrate and pay tribute to the retirement and career of the incomparable Sidney Coleman. There are good postings about it at Lubos' blog and Serkan's blog. It being held just down the block, most of us MIT-CTPer's couldn't resist.

A brief look at the speaker list might tell you why. Out of eight speakers, there were six Nobel Laureates, one Fields medalist (who, as is oft repeated, may be the smartest man alive), and two other very well known and prominent physicists. Even the people who were slated to introduce the speakers were incredibly famous.

It was a first year graduate student's wet dream. Had a giant bomb exploded on the lecture hall where this conference was, at least thirty years in theoretical physics would have been lost. Most of the particle physics talent east of the Mississippi was there. Oh yeah, and I got to watch. Larry Summers said it best when he said that "there had not been so much talent gathered around the snack table since Einstein snacked alone." We tried to act cool and not to ogle, but we failed. It really was like the Oscars of theoretical physics, with me and some CTP friends playing the roles of Joan and Melissa Rivers (and every other graduate student doing the same, I imagine). Statements like "Is that 't Hooft chatting with Weinberg? Awesome!", "Has Witten arrived yet?", "What does Ken Wilson look like?", and "Do you think Wilczek will finally wear a tie?", were bandied about (Frank went with the usual trendsetting get-up of a t-shirt and blazer). So, acting cool and collected kind of failed. It was kind of like the time Natalie Portman came to my senior prom, and I tried to act cool: hopeless. Oh yeah, and our buddy David brought a digital camera, and so, lacking the courage to introduce ourselves to so many famous Nobel Laureates, we tried to take pictures of them when they weren't noticing (pictures to be posted as soon as I get them from Dave).

But on to the actual conference! David Gross was the first speaker, and gave his talk on The Future of Physics. This was the same Hilbert-like 25-most-pressing-questions lecture that he had given earlier this year, as blogged by Sean Caroll here. He made the interesting statement that string theory was continuously connected to the Standard Model, and so we could never get rid of it (a dig to someone in particular? We speculated.) It was a very good talk, but went over the alloted time, and provided fuel for jokes of subsequent speakers.

Next, Frank Wilczek kept it real for MIT by giving his Nobel asymptotic freedom talk. According to the other MIT students, it was the same talk he had given earlier this year at MIT. It was excellent, chronicling the discovery of asymptotic freedom and what it has taught us about physics. Next, we took a coffee break, during which time, my friends and I ogled some more, and took more pictures. When we came back, Larry Summers gave a brief talk/dedication to Sidney. At any other conference he would have been the controversial superstar, but I think we all just wanted him to get out of the way so more of our idols could talk. His speech was short and fine, and he made some semi-humorous jokes about how he had learned much about physics recently: there is turbulence, strange interactions, etc.

Next up to bat was Paul Steinhart who talked about Cosmology in a False Vaccum and his oscillating universe. I think it was a pretty good talk, but by this time, the coffee in my veins was running out, and Harvard's delicious snacks were hitting me pretty hard. For some reason, I get the impression that his oscillating universe is not received so well in the physics world. Anybody know why?

Next, Murray Gell-Mann was up! This guy should go on the road, cause he worked the crowd like nobody else. He, of course, talked about working out the eight-fold way, and Sidney's influence, and in between cracked hilarious jokes. At several points during the talk, his cell phone rang (Murray Gell-Mann has a cell phone!) and he played the confused old man who doesn't know how to turn off his cell phone. It was a delightfully funny talk, and just what I needed to get over the sleepiness that those snacks were inducing.

To top the day off, Sheldon Glashow got up and talked about some more recollections of Sidney. These guys spent their early careers working together, and Sheldon told some other funny stories about them traveling around the world. At the end of the talk, he got serious, and started talking about exactly what Sidney meant to him. It underscored a bittersweet feeling that permeated the entire conference. Sidney's health is not good--apparently he has some form of Parkinson's--it also prevented him from attending the conference. Sheldon gave a very heartfelt tribute to his good friend and I must say I got a bit verklempt. It was a beautiful note for the first day of the conference to end on.

Saturday I got up early (that's how good this conference was), and took the T to Harvard. We met up with another CTP student and ended up searching for the correct entrance to the Jefferson Labs with Steven Weinberg. There was a deliciously awkward moment where we were all trying to hold the door for him. Ultimately, though, I think we accidentally ended up closing the door on him (which led me to joke to a friend that his career was now over). Erick Weinberg gave the first talk on vacuum tunneling in DeSitter space. I remember an interesting post over at Peter Woit's blog where he mentioned that Weinberg had the calculation of the QCD beta function assigned to him, but he didn't do it because he had too much other work. Ouch. Well, its not exactly as if he's been a slouch since them. His talk was very interesting even though I knew very little about the subject.

Steven Weinberg gave the next talk, and discussed calculating diagrams for quantized GR. The best part was that he was talking about work in progress, and at the end he said "I don't know what to do now, does anybody else?" This was the place to ask! He also said "in happier times, I would have gone straight to Sidney Coleman," which caused me to tear up again. I'm a softy.

Next there was a lunch break, and I gorged myself at an Indian buffet. After sprinting back to get a seat (I spent half of the next talk catching my breath), Gerard 't Hooft--with the coolest beginning of a last name, ever-talked (he started with advice on how to pronounce his last name). It was an amazing talk (of course) about the history of the development of QCD, etc. He also seemed to be (jokingly) complaining that he did not get a second Nobel. The funniest part occurred when he recollected how Veltmann introduced him to two American "gangsters," that ended up being Coleman and Glashow. Immediately they asked 't Hooft to show them around the "darker side of Amsterdam." These are my kind of physicists! He ended by discussing some calculations he had been doing with black holes, and how what seemed to pop out of this calculation was a string scattering amplitude. This seemed remarkable to me, as he claimed not to be using any string theory. It also seemed to be remarkable to Witten who asked something like "you don't actually mean that it's a string amplitude?". He did.

Rounding out the talk was Witten, whose title Emergent Phenomena in Condensed Matter and Particle Physics had started much gossip about how the talk might be indicative of Witten turning a way from string theory a bit. It wasn't. He ended up mostly talking about AdS/CFT, and how space and time need to be emergent phenomena if there is going to be any quantum theory of gravity. It was a nice talk to top things off, and the conference ended. All in all, I'd say it was the best thing. Ever. Easily a major highlight of my first year in Cambridge.

Other famous people (not necessarily) physicists who showed up at the conference included Stephen Wolfram. I had half a mind to go up to him and give him a piece of my mind about how Mathematica never does the integrals I want it to do. Also, apparently Serkan Cabi got to go to lunch with Gross, Wilczek and Wolfram- that lucky bastard-and hear Wolfram argue about why he thought his crazy theories were true. Paul Ginsparg, the inventor of the physics arXiv was also there. According to Ed Farhi he "changed academia". Ed said that they used to have to go to some sort of place called a "library," to look at papers. I did not understand what he was talking about. Also, apparently Peter Woit was at the conference (although I couldn't confirm as I don't know what he looks like). Lubos and Woit at a conference together? Inflatable sumo suit wrestling anybody?

David Guarrera, Pizza Czar

I have mysterously inherited the responsibility of ordering pizzas for the CTP's friday lunch club. On any given friday you might find nobel lauretes, discoverers of supergravity, namers of bosons, and discoverers of anomalies eating my pizza. I've taken on the self appointed title "Pizza Czar," but my girlfriend likes to call me the "grad student bitch." I know my role is a litle bit more important than that. As Danny Aiello said (roughly) in "Do The RIght Thing": "What I do is special. I've watched these kids grow up, eating my pizza."

Everytime I watch that scene from henceforth, a tear will roll down my cheek.

The Levi-Civita Connection and Torsion Gravity

One of the most interesting concepts in mathematics and modern physics is the concept of a connection on a vector bundle. In this beautiful language, for example, the gauge fields of particle physics and the covariant derivative of GR are just different manifestations of the same geometric object. I hope to talk more in the future about connections on general bundles, but now I'll talk about gravity and the usual connection on the tangent bundle.

In (pseudo) Riemannian geometry, there is an infinite number of choices for a covariant derivative, or connection. This connection determines how we take derivatives of vector fields along curves on the manifold. All that is required is a family of functions \Lamda^k_{ij}, the Christoffel symbols, that have the correct transformation law between coordinate patches. In most cases (and usually in relativity) we choose a specific connection, known as the Levi-Civita connection, to work with. The two defining properties of this connection are

1. It is metric compatible. That is to say \nabla_i g_{jk}=0, where \nabla is the covariant derivative.

2. It is symmetric. That is to say, \Lambda^k_{ij}=\Lambda^k_{ji}.

This connection is unique and always exists. The obvious question is: why the Levi-Civita connection?

The question can be answered from both a mathematical and physical perspective. Requirement #1 is sort of straightforward: we would like our metric to somehow be related to the way we take derivatives of vector fields along curves. Requirement #2 is more mysterious.

Let's deal strictly Riemannianly (though I'm almost sure, that the following generalizes to the pseudo-Riemannian case). Let's embed S^2 in R^3 in the usual way, with its usual induced (pull back) metric from R^3. What would be our best guess as a way to take a directional derivative of vector fields on the sphere? Well, we would take the directional derivative in the usual way in R^3, and project that result onto the tangent space of the sphere. This is just the most logical thing to do. It turns out that this connection is metric compatible, and also that it is symmetric. As the Levi-Civita connection is unique and has these properties, it must be the Levi-Civita connection!

This leads us to ask if this can be done more generally, and indeed it can be. You may be familiar with the Whitney Embedding Theorem, which states that any manifold can be embedded in R^n for some high enough n. There is a stronger theorem, the so called Nash Embedding Theorem, that says that any manifold with Riemmanian metric g may be embedded in R^m for high enough m such that the inherited or "pullback" metric from R^m is exactly g. More concisely, you can always put a Riemmanian manifold in Euclidean space such that it "looks like" what its metric is. We can then take directional derivatives intuitively as above and without surprise it is exactly the L.C. connection!

In geometry courses, it is often emphasized that a manifold need not be embedded in R^n, has an existence and topology of it's own, etc. But the above, at least for me, provides a very nice picture of why we use the Levi-Civita connection. Just "look" at the surface (you may have to be an m dimensional being), and take directional derivatives as is most obvious, using calculus. You've been doing this all along by using the L.C. connection, without even knowing it. I'm pretty sure that the above also holds when you embed a pseudo-Riemmanian manifold in flat Minkowski space.

Let's look at it from a relativity standpoint. In the standard formulation, we use the Levi-Civita connection. The following result:

A. Geodesics are locally minimizing.

B. At any point, normal coordinates can be constructed where the Christoffel symbols are zero and gravity and locally be "transformed away". This is the content of the equivalence principle.

In so called "torsion" theories of gravity, Requirement #2 does not hold: the connection is not symmetric. The amount by which the connection differs from the L.C. connection is characterized by the torsion tensor at each point.

In any theory of gravity, it seems to be that we would like to keep both A and B. A seems in line with the basic principles of minimization in physics, whereas B is a definite physical constraint.

In a torsion theory of gravity A is, in general, no longer true. I am told by my office-mate (but I haven't checked) that A still holds if the torsion is anti-symmetric everywhere. That seems a reasonable constraint to me. It's also not clear to me that B is true, and it would be a disaster if it weren't. Any time I have proved that \Lambda^k_{ij}=0 at the origin of normal coordinates, it seems I have invoked the symmetry of the connection. Does anybody know how this problem is handled for torsion gravity? Will the anti-symmetry of the torsion also let B hold? I'm hoping you know the answer, Serkan. Another reason torsion gravity seems a bit contrived to me is that we will also need an equation governing the dynamics of the torsion. How to determine the torsion? Does anybody know what is used?