Workshop on Emergence of Spacetime

Olaf Dreyer, Imperial College
On the weekend of November 18 the Perimeter Institute hosted a workshop on the emergence of spacetime. The workshop was organized by B. G. Sidharth from the Birla Science Centre in Hyderabad, Lee Smolin from the Perimeter Institute, and Olaf Dreyer, now at Imperial College London.

The aim of the workshop was to discuss a problem that all quantum theories have in common: How does a classical spacetime emerge? This problem of emergence has a technical and a conceptual component. The technical part is that it is usually very hard to infer details of the dynamics for a given large quantum system. The conceptual problem is the added difficulty that arises when a basic concept such as time is to emerge, as is widely expected to be the case in quantum gravity. The workshop was conceived to address both these issues.

To shed light on the technical problem we invited solid state physicists to the workshop. The solid state community has always dealt with large quantum systems and has developed techniques to describe their dynamics. This community has in particular stressed the importance of emergence. Large quantum systems can have properties that emerge on the level of the whole system but do not make sense on the level of the constituents. In recent years, members of the solid state community have started to see this emergent point of view as a paradigm for all of physics including gravity. Their views then also provide a new take on the conceptual problem.

In order to allow for in depth discussions the workshop limited the number of formal talks. All formal presentations were given on Friday. The speakers were Grigori Volovik, Renate Loll, Xiao-Gang Wen, Fotini Markopoulou, Peter Horava, and Seth Lloyd. These presentations set the stage for the weekend where the atmosphere was much more informal. The presentation can be found on the website of the Perimeter Institute

The in-depth discussions on the weekend lasted one to two hours and consisted of a short presentation on the black board followed by a long set of questions. This format allowed the participants to really familiarize themselves with the different approaches and see their advantages as well as their shortcomings. The final overview on Sunday was unique in that it reviewed all the approaches and listed their pros and cons. I think this last part was a first in a workshop on quantum gravity.

The point of view presented by Grigori Volovik posits that the physics we see around us is described by the ground state of a fermionic many body system. Such ground states are characterized by the topology in momentum space. The relevant momentum space topology for us is that of a Fermi point. These are points on the Fermi surface where the excitations become gapless. The physics near such a Fermi point is remarkable in that it looks a lot like current high energy physics. Lorentz invariance, gauge symmetries and also a dynamic metric are all emerging.

Renate Loll presented exciting new results in causal dynamical triangulations. Having worked their way up from two and three dimensions they have now arrived at four dimensions. The results so far are promising in that they show the correct dimensionality of four emerging at large scales. A very curious feature of the approach seems to be that at Planck scale the dimensionality becomes effectively two. The significance of this observation is not yet clear.

A presenter that stayed clear of quantum gravity proper was Xiao-Gang Wen. His presentation focused on the other pillars of our current understanding of fundamental physics: fermions and gauge interactions. Wen showed how these objects could emerge from a fundamental theory made up of simple quantum spins. A ground state of the system called spin-net condensate has excitations that are fermionic and have interactions described by a gauge theory.

Fotini Markopoulou described her attempt to deal with the conceptual problems of quantum gravity. For her the spacetime should emerge from the interactions of persistent degrees of freedom. To define such degrees of freedom she introduced noiseless subsystems, a notion borrowed from quantum information. The persistent degrees of freedom are noiseless with respect to the evolution of the system.

A connection between solid state physics and string theory was shown by Peter Horava. The Fermi points introduced by Grigori Volovik also appear in the physics of D-branes. The formulae describing the behavior near a Fermi point used by G. Volovik turn out to be a special case of the Atiyah-Bott-Shapiro construction in K-theory. Peter Horava proceeded to use these constructions for a new kind of emergent spacetime in string theory.

A completely new approach to quantum gravity was presented by Seth Lloyd. His model is based on a quantum computer. He showed how every quantum computation can be viewed as a superposition of histories and how every such history can be viewed as a spacetime with matter. The quantum computation is thus a quantum superposition of spacetimes.

The most interesting outcome of the workshop is the path that a number of participants have chosen to address the conceptual part of the emergence problem. They have made progress by assuming a fiducial time. The interesting question is: Does this step invalidate the progress that has been made? The final discussion showed that it is still too early to decide. Crucial steps still remain to be taken. In the approach presented by Renate Loll recent results have shown that the dimensionality of the emergent spacetime is correct but it is still not clear whether gravity is correctly described.

Another thing that became clear during the workshop is that the time frame for quantum gravity is beginning to change. Quantum gravity research has been going on for more then sixty years and has not had much success. With such a time frame the expectations tend to erode and nobody seems to be rushed. With the results presented by Renate Loll and Seth Lloyd though this situation seems to change. These programs might be able to produce quantum theories of gravity in a time frame of a couple of years rather then decades.

The situation we would be facing then would be a new and welcome one. Instead of having no theory of quantum gravity we would have several competing ones. One would then have to decide which one of these is the correct theory. A task that will require the competing theories to make observable predictions. What a thrilling prospect.

Jorge Pullin 2006-02-28