It all went well, except that my co-organizer cancelled two days before the start of the workshop, so I had to be the sole entertainer of a group of 27 people. A group that, to my own shame, was almost entirely male except for one student, which however I only realized when I was standing in front of them. I have a public speaking anxiety, one of the most common anxieties there is, but really somewhat unfortunate for a scientist. People tell me my talks are okay, but the more ancient parts of my brain still think the smart thing to do when a group of guys stares at me is to run really fast, and the Scandinavians are a particularly scary audience. Anyway, I think I managed to pull it off, minus the usual projector glitches.
My interest in non-locality comes about because it shows up in different approaches to understand the quantum structure of space time, and it plays a role in many attempts to resolve the black hole information loss problem too. It is, in that, comparable to the minimal length that I've been working on for, ah, a hundred years or so, at least in somebody's reference frame. Nonlocality and the minimal length both seem to be properties of nature deeply connected to quantum gravity, even though we don't yet really understand the details, and they're also related to each other.
Nonlocality comes in many different variants and the purpose of the workshop was to shed some light on the differences and features. The most common forms of nonlocality are
- Quantum mechanical entanglement. The type of nonlocality that we find in standard quantum mechanics, no information exchange over space-like distances though.
- Quantum field theory, non-commuting operators on space-like separated points. This can ruin the causal structure of your theory and should be approached with great caution.
- Quantum field theory, higher-order Lagrangians which show up in many models and approaches but bring a lot of problems with them too. Gariy Efimov and Leonardo Modesto spoke about realizations of this, and how these problems might be remedied. A certain book by Gariy Efimov that was published the year I was born, in Russian, and was never translated into English, plays a central role here. It's so much a clichee I couldn't not mention it - I'll probably end up having to dig out the damned book and learn Russian or at least pipe it into Google (as Leonardo apparently did).
- Quantum mechanics and quantum field theory, non-commuting operators for space and time themselves, ie non-commutative space time in its many variants. This might or might not be related to the previous two points. The problem is that many approaches towards such a quantum space time are not yet at a point where they can deal with quantum fields, so the relation is not clear. Klaus Fredenhagen gave a very interesting talk about the spectrum of area and volume operators in a non-commutative space-time. Michael Wohlgenannt, Michele Arzano, Jerzy Kowalski-Glikman and his student Tomasz Trzesniewski spoke about other versions of this idea.
- The whole AdS/CFT bulk-brane stuff, black hole complementarity and so on. Larus Thorlacius spoke about that. Unfortunately, Samir Mathur who had intended to come to the workshop couldn't make it, so the topic was very underrepresented.
- It might have passed you by, but Giovanni Amelino-Camelia, Lee Smolin and Kowalski-Glikmann, together with a steadily increasing number of co-workers have cooked up something they call "the principle of relative locality," essentially to cure the problems with nonlocality in DSR (see this earlier post for details). The idea is, roughly, that the notion of what constitutes a point depends on the location of the observer. I've tried and failed to make sense of this - it seems to me just DSR in disguise - but who knows, I might be wrong, and maybe they're onto something big. They too can't do quantum field theory on that space (yet), so it's not well understood how this notion of nonlocality relates to the above ones. Lee went so far to claim relative locality solves the black hole information loss problem, but I think at this point they don't even have a proper definition of what constitutes a black hole in this scenario to begin with, so it seems a little premature to claim victory.
- A failure to reproduce a local space-time that occurs in lattice or network approaches, that runs under the name of "disordered locality." You can imagine it like tiny wormholes distributed over a nicely smooth space-time, except that the wormholes have no geometry themselves because, fundamentaly, space-time isn't a manifold. Fotini has been on to this for a while, but since she couldn't come the topic only came up once or twice in the discussion.
- As Ingemar Bengtsson reminded us, trapped surfaces in General Relativity have some non-local features already.
Lastly, I should mention we had two discussion sessions that picked up the topics from the talks, one moderated by George Musser, one by Olaf Dreyer.
It was an interesting group of people that mixed better than I had expected. I had been a little afraid they would just talk past each other, but it seems they found some overlap on many different points. I certainly learned a lot from this meeting, and it has given me food for more thought.
There are some slides of talks on the website; we hope to receive some more during the next week.