A strange but satisfying aspect of my time here (I’m at the Aspen Center for Physics, recall) has been the fact that due to some odd serendipity, there’s a ton of people from the “old days”. Which ones? My Princeton years, in the early 90s, as a postdoc at the Institute for Advanced Study (and later at Princeton University). These are not all people doing what I do, but in a wide range of fields such as high energy physics, astrophysics, condensed matter physics. Several of us were postdocs together. I’ve been chatting with people I’ve not seen for a while, sometimes not since those days, or they are people I met back then, and with whom I have a pool of shared memories from those days. So it has put me in mind of those times somewhat.
A quick example. Soon after I arrived last week, I was walking along, chatting with Petr HoÅ™ava (Berkeley) about various things, and we got on to reminiscing a bit about our time together as postdocs in Princeton. And then minutes later, as though conjured from the very substance of our conversation, who should walk by but one of the Gods/Legends of the field (then and now), Princeton’s Alexander Polyakov. He walked by in exactly the same sort of way he would back then, either coming from or going to a walk along the river or canal, perhaps to give us a lecture. Petr and I looked at each other, and continued our walk and talk.
The great news for me last week was that Polyakov then gave a talk. I’ll admit to being a big fan of his physics. When he gives a talk nearby, I show up, no matter how confused I might end up at the end. There’s going to be good stuff in there – it’s only a matter of time before it sorts itself out in your head. Often years. Decades. Several of us sat in on his graduate class back in Princeton in the early 90s just to try to catch the pearls of wisdom which we’d pick up as he lectured on….. Well, I’ve no idea to this day what the class was really about. He would show up (probably fresh from a walk), with no notes or anything, and just pick up a piece of chalk, stare out the window for a few seconds, and then start writing stuff. Essentially, he was randomly jumping around the subject matter in his widely under-read book “Gauge Fields and Strings”. He was all over the book. It was not always a simple and coherent path through the subject matter, and it seemed that he was largely exploring whatever took his mood in the moment, but I suspect that was largely my ignorant young mind’s impression.
Sadly, it is the type of course that these days would score close to zero in most universities in (especially undergraduate) teaching evaluations, but in which -if you cared about the physics and took the time to think through what he said after and let the seeds that were planted grow in time- you could learn more physics in one or two lectures than from an entire semester’s course given by someone teaching a highly structured user-friendly course that required no effort on the part of the audience. Not surprisingly it is the latter sort of lecture that we are expected to give these days at all levels -forcing out this unstructured sort of style- because today’s students (undergraduate and increasingly graduate) seem to have much less of the patience, time, (or whatever) to fill in the gaps themselves, do voluntary extra reading, or to take the long view of some of the things they’ll hear and not immediately understand. We really seem to have to spoon-feed the material and baby-sit more than ever. I do not mean to offend here. In my opinion, this is nothing to do with how smart the students are (they are as smart as they ever were, I’m sure), but more with how the system has become more tilted toward the expectation on the part of the students that the spoon-feeding and baby-sitting will be there. So give open-ended or loosely structured lectures (where you hope students will make connections and explore more on their own) at your peril. On the other hand, for every Polyakov there’s several hundred people who, if they lectured in his style, the content would simply be zero (or less)…. They simply don’t have his knowledge or insight into the material. So while I believe more structure by default is the way to go, we must leave room for the Polyakovs of this world.
Ok, back to Aspen. My ignorant older mind of last week found him much more understandable, partly as a result of having learned more about how to listen to him from back then, and partly because I know a trifle more about things than I did back then. It was my highlight of the visit to Aspen so far this year, in terms of talks that were given. Some of the reason for this is nostalgia, I will grant. I was sitting there like a kid in a candy store just enjoying the style of physics, his turns of phrase (he’s got a funny but understated sense of humour – his curious ways of saying things are not accidental, I think), and the feeling that I’d been transported back in time 14 years.
Most of all, however, it was just great to hear from one of the old masters on a subject of great interest to me – He was talking about aspects of doing quantum theory in de Sitter spacetimes, presenting a new proposal for how to do this, and exploring some of the consequences. For those of you who don’t know what that means, don’t worry. Briefly, de Sitter spacetime is one of the prototype spaces you study as a model of positive cosmological constant. A cosmological constant can be thought of as an intrinsic energy density that space itself has. A positive energy density turns out to mean that it is energetically favourable to increase the volume of space (more volume, more energy…. its a density you see), the space obligingly expands as a result of this positive energy density. So in physics terms, you’d say this was an outward or “negative” pressure of the vacuum. It is believed (after the spectacular supernova observations announced in 1998 that show that our universe’s expansion is accelerating) that our universe may have a positive cosmological constant (it is one of the simplest effects consistent with the observations). This is the “Dark Energy” issue that you hear a lot about from time to time. (Search the archive of posts for earlier discussions.) One of the biggest problems in physics is that nobody has a good theory of how to do quantum physics completely reliably in the context of positive cosmological constant. So people spend time studying model spacetimes that allow you to focus on the technical issues. de Sitter is one of them, and this is what Polyakov was doing, although much of what he was saying pertained to other issues as well, such as (technical aside:) defining propagators in the quantum theory, Ã¡ la Feynman, in various kinds of spacetimes you can put into two categories, “eternal” or “non-eternal”. His working definition of “eternal” was that there were no instabilities that would arise that would destroy the background metric. “It is a very limited definition of eternity”, he remarked, not without humour and irony. I was in theoretical physics heaven.
Well, I’ll end with an amusing (to me story). I suspect that only people working in the field will really get it, so I apologize. Near the end of the talk, Polyakov was talking about the implications of some of the things he’d presented, and he prefaced his main point (which he never got to – I took it upon myself to organize an informal follow-up presentation from him so that he could tell his main point to those who wanted to hear it) with a preamble. The gist of the preamble was that he keeps being surprised to hear from people to day that the AdS/CFT correspondence is the realization of ‘t Hooft’s original idea from the 70’s. The AdS/CFT correspondence, I remind you, tells you that the physics of a large class of four dimensional gauge theories (the theories at the foundations of particle physics) in a certain limit called the “large N” limit, is the same as the physics of string theories and the quantum gravity they contain, in higher dimensions. This is a central piece of the physics many of us work on in one way or another, whether it be in applications to cosmology and higher energy particle physics, or to understanding aspects of the nuclear interactions. It was ‘t Hooft who pointed out a long time ago that gauge theories may well be re-written as string theories in certain limits, which might be extremely useful for computations, but the idea never really took hold fully in all its glory (for four dimensional gauge theories you might want to think about since we know that the real world uses them) until the AdS/CFT came along (proposed in its simplest form by Maldacena) in 1997. “I remember t’Hooft’s idea well”, Polyakov said (which is sort of funny, of course), and he went on to say that what people are saying is wrong. AdS/CFT is not what ‘t Hooft was saying back then1.
Murmurs and a bit of in-seat-shifting from the audience, since the connection of this new and marvellous piece of physics with what ‘t Hooft was saying long ago is one of the things we love to point to. I suspect ‘t Hooft does too. (1999 Physics Nobel Prize winner Gerardus ‘t Hooft is another God/Legend of the field who still walks the earth, but more about him some other time).
Well, before he could explain what he meant, his mobile phone rang. Of course, the joke sat up and begged and so I had to feed it: “It’s ‘t Hooft!”, I called out.
- Ok. Semi-technical words follow: For those of you who work on this stuff and whose world is shattered by Polyakov’s remarks, don’t worry. I understand what he is saying and it is rather nice, and strictly it is true in a sense. Taking N large in an SU(N) gauge theory is not by itself enough to ensure that the diagrams that are dual to the resulting Feynman diagrams actually fill up densely enough to become the smooth string world sheets of the dual string theory. This is not really what happens in AdS/CFT at all. The string world sheets are swept out by flux tubes. They don’t really arise as dual Feynman diagrams, as suggested by ‘t Hooft. This is Polyakov’s point. To get ‘t Hooft to work, you need to also tune the theory to a point where while N goes large, the diagrams fill out the world sheets. How? You tune a coupling in the theory too. This is familiar from the “double scaling limit” of the late 80s and early 90s, in the context of matrix models of string theory, but that was for zero and one dimensional gauge theories, which gave rise to one and two dimensional dual strings (which we now think of as early examples of holography too). So AdS/CFT is strictly not ‘t Hooft, while matrix models are. He was saying all this for a reason to do with his new work, but I think I’ll leave it there.[return]