Tuesday, December 31, 2013
Einstein's equations from first law of thermodynamics in AdS
Happy New Year!
First, Nima Arkani-Hamed (IAS) and Jaroslav Trnka (Caltech) have released another amplituhedron preprint, Into the Amplituhedron, in which they expose the amplituhedron origin of various QFT rules applied to cuts – the unitarity double cut, the multicollinear limit (which explains why the amplitude is sometimes the exponential of something simpler), and other cuts (whose properties emerge from the shape of \(d\)-dimensional faces of the amplituhedron).
But there's another intriguing hep-th paper published on the last day of 2013 (even if we overlook the remaining dozens of papers): Thomas Faulkner, Monica Guica, Thomas Hartman, Robert C. Myers, and Mark Van Raamsdonk wrote
Event horizons and thermodynamics: more than analogy, TRF 2010).
These five authors try to reformulate the first law of thermodynamics (with not only \(dE\) but also the entropy-related \(T\cdot dS\) term!) that holds within the CFT in terms of the gravitational AdS bulk variables. What they find are nothing else than Einstein's equations – well, they reach these equations in their linearized form expanded around the zeroth approximation, the empty anti de Sitter spacetime geometry.
The old heuristic picture of Jacobson should be considered to be just a localized (i.e. region-by-region attributed) version of Bekenstein's and Hawking's original intuition relating geometric properties of black holes with the thermodynamic quantities. Neither Bekenstein or Hawking in the 1970s nor Jacobson in the 1990s actually had any good idea about the microscopic degrees of freedom representing the entropy.
This paper brings the ideas to a new level. By being rooted in AdS/CFT, it has a well-defined and controllable microscopic description of the entropy built into the whole game – in this sense, it is adding all the visibility that Strominger and Vafa brought into the research of the black hole entropy. Moreover, the new AdS approach seems to work for higher-derivative curvature terms, too: they also show how Wald's formula (calculated from a Noether's current) arises from their derivation.
So far, the analysis has some drawbacks relatively to Jacobson's heuristic analysis: they quantify the properties of global Rindler horizons and not local ones which is what Jacobson did, and that's why they can only derive the linearized approximation of Einstein's equations.
At any rate, Einstein's equations – dynamical laws determining the spacetime curvature – may indeed be derived from the laws of thermodynamics (they are pretty much the same thing!) as long as we also substitute some basic geometric formula for the entanglement entropy. For the simplest, Bekenstein-Hawking form of the entanglement entropy \(S=A/4G\) proposed by Ryu and Takayanagi, they may derive the original, minimal Einstein's equations in their basic linearized form.
I would say that this paper is the newest paper in one of several interacting branches of the modern research that indicates that the "entanglement's being the glue that may attach the surfaces" is perhaps the most fundamental principle that implies many properties of quantum gravity – black hole thermodynamics and even the original classical Einstein's equations of the general theory of relativity.
2013 and 2014
Your humble correspondent doesn't plan to write extensive summaries of the year 2013 in physics and what to expect in 2014. Just a few words. We saw some interesting experiments in 2013 – hints of the dark matter signal that were killed by the super-powerful negative result from LUX. I think that theoretically, the amplituhedron and the entanglement-related research in quantum gravity (ER-EPR correspondence and the Papadodimas-Raju Ansatz for the black hole interior) belonged among the most interesting advances in theoretical physics.
2014 has been declared by the United Nations as the "International Year of Family Farming and Crystallography" because diamonds and organic feces are among the cleanest and most beautiful objects that the apparatchiks know. I may write a text on crystallography later.
It will be the final complete year of the Two Years' Vacation at the LHC. The machine is being revitalized and upgraded and around April 2015, it should start proton-proton collisions at a higher energy \(13\TeV\), much higher than the \(8\TeV\) center-of-mass energy in 2012. Because of this "quantum leap" in the energy, the exclusion limits from 2012 won't mean much: lots of new particles may be discovered almost immediately (within weeks) despite the null results from the previous collisions. It's also possible that the Standard Model will continue to work for these collisions, too.