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Archive for the ‘gravity’ Category

The Gravity Research Foundation announced the results of the 2010 competition. Here are the results. At UCSB we discussed the prize-winning paper by Mark van Raamsdonk today. It was a very lively discussion and we thought it was a great paper to read. Mark’s paper provided some very tantalyzing evidence that entanglement seems to play a very important role in building up geometry.

On another note, a paper by Daniel Green, Zohar Komargodski, Nathan Seiberg,
Yuji Tachikawa, and Brian Wecht
appeared today. They solve a problem in four dimensional supersymmetric conformal field theories on counting how many marginal deformations there are. As a byproduct, they also solve the problem in 3-d field theories with N=2 Supersymmetry. The paper is beautiful and it is a huge improvement on the work by Leigh and Strassler on the subject many years ago. After reading it I was kicking myself because ‘I could have done it’ (I was interested in the problem and I knew many of the facts. I just didn’t put them together. But if I had thought hard about it I probably could have, although the paper would read rather differently). It’s not surprising that these authors at the Institute for Advanced Study found the solution and that it is written in the particular way that it is written since they have been studying very carefully the superfield formulation of supersymmetric theories in four dimensions. Lubos also commented on the paper.

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We now have a few working examples of a microscopic theory of quantum gravity, all come with specific boundary conditions (like any other equation in physics or mathematics), but otherwise full background independence. In particular, all those theories include quantum black holes, and we can ask all kinds of puzzling questions about those fascinating objects. Starting with, what is exactly a black hole?

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Comments by Giotis on my previous post, about emergent gravity, reminded me about one of the tricky points in gauge-gravity dualities such as the AdS/CFT correspondence. This is the understanding of them as dualities between one theory that lives in the “bulk” spacetime (say quantum gravity on five dimensional AdS space) and another that lives on the boundary of that spacetime (four dimensional supersymmetric gauge theory in that case). This is kind of correct, if you know precisely what you mean, but it can also lead you to scratching your head if you don’t.

The tricky part in thinking about dualities is internalizing the idea that the two sides are actually two descriptions of one and the same object.  So, the gauge theory has the same properties as quantum gravity in five dimensional space, it is a five dimensional quantum gravity theory. Like any other description of this quantum theory, it has a bulk and a boundary, it has gravitational forces and propagating gravitons, it has black holes forming and evaporating, etc., etc. … All of those are realized in a somewhat unfamiliar language, more suited for the quantum rather than the classical theory, but all the same they are still there.  It’s a good mental exercise to phrase gravitational properties of the theory in terms of the gauge theory variables, it forces you to distinguish physics from language. So, I’ll do that here by discussing bulk and boundary of spacetime in the gauge theory language.

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Alright, time to discuss some physics again. A while back I outlined the basic dichotomy of quantum gravity. In brief: we have classical general relativity as an excellent description of all observed gravitational phenomena, but when we go to extremely short distances we need to have a good description of quantum gravity. There are two possibilities: either the description of gravitational phenomena by the machinery of general relativity (metric, the principle of equivalence, etc.) holds all the way down to those extremely short distances, or it doesn’t. If it doesn’t, which is my own prejudice, classical general relativity and its variables are never to be quantized, there is no range of energies (or distance scales) which is described by quantum metrics obeying a quantum version of Einstein’s equations.

This situation is similar to the hydrodynamical description of fluid motion: it is a classical effective field theory, which breaks down long before quantum mechanics is needed. We can observe granularity in the fluid on distance scales much larger than those relevant to quantum mechanics. From that perspective, quantizing Einstein’s equations makes as much sense as quantizing the Navier-Stokes equations, which is to say not too much sense.

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So I have been pondering about Newton lately. Mostly because I heard various stories that might be apocryphal. I could not find a reference to them, but they strike me as being true. There is a legend about apples falling on Isaac Newton’s head as a story of how he discovered the law of gravitation…

 

Alas, Newton discovers too late that one should not exchange apples and moons.

Alas, Newton discovers too late that one should not exchange apples and moons.

Of course, this is probably just a fancy legend concocted after the facts to paint a more romantic picture of the discovery. What is true however, is that Newton had some hint of using a central force to explain the motion of the planets from Hooke. However Hooke could not solve the problem, and Newton had to invent calculus and differential equations to really solve this problem.

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