Since I was going to be down here anyway to sign books at the World Science Festival Street Fair, Kate and I decided to catch one of the Saturday events at the Festival. It was hard to choose, but we opted for the program on Hidden Dimensions: Exploring Hyperspace (Live coverage was here, but the video is off), because it was a physics-based topic, and because I wrote a guest-blog post on the topic for them.
(No, we didn't go to the controversial "Science and Faith" panel, opting instead to have a very nice Caribbean dinner at Negril Village, just around the corner. I'll take excellent Caribbean food over science-and-faith discussions any day...)
The panel consisted of three theoretical physicists (Lawrence Krauss, Brian Greene, and Shamit Kachru) and an art historian, Linda Dalrymple Henderson, plus a string quartet. I was a little uneasy about this going in, because it seemed like the science-and-art connection could get a little gimmicky. I was pleasantly surprised at how well it came together, though. It was a really good program, and a fun evening.
OK, to be fair, I thought the string quartet was a little gimmicky. They came on to play one short Beethoven piece after Brian Greene did a very showy multimedia introduction to the Kaluza-Klein notion of extra dimensions. Classical music in general does very little for me, and while it was fairly obvious what the point was supposed to be (it was a fugue, with simple themes elaborated and expanded through many repetitions), I could've done without it.
The art history part of it, though, was brought in very well. Henderson is apparently an expert on artistic uses of the idea of a fourth spatial dimension, and she did a nice job of explaining how the notion of an additional dimension was in the air in the late 19th century (Flatland and all that), and how it was picked up and used by artists. This was then related to the way ideas of extra dimensions float around in math and science, and get picked up for various purposes. I was very glad that she didn't attribute the whole fourth dimension thing to Einstein (the lazy cultural commentator's shorthand for everything), and she did a nice job commenting on how Einstein's arrival on the stage shifted a lot of thought about the fourth dimension from space to time.
The more scientific portion of the panel consisted of Kachru and Greene waxing rhapsodic about string theory, while Krauss tried to keep things somewhat grounded in reality. He was only partly successful, but he was a good sport about the whole thing, and didn't insist on dragging the whole panel into a debate about the status of string theory. If anything, he worked hard to connect everything back to the artistic side, and was really the best of the three scientists about that. He also busted out a Plato reference, which was a nice display of the benefits of a Classical education.
It's easy to nitpick what was said, which I will proceed to do in the next few paragraphs, but on the whole this was a really good event. John Hockenberry, the moderator, did a great job of keeping the discussion moving, and got in a few sharp quips that brought the house down. All of the panelists were very sharp and quick on their feet, and the audience-- which completely filled the lower level of the Skirball Center at NYU (fire capacity 880), and part of the upper level-- was really into the whole thing. We had a great time.
But, of course, there are nitpicks. There are always nitpicks...
On the art side, when she started to talk about the transition to thinking of the fourth dimension as time, and incorporating time into art, I was expecting something about film which seems to me to be the most obvious example of time in art. She went on to say something about kinetic sculpture, which was surprising to me, because my impression is that kinetic sculpture has always been a very niche thing. But then, all I know about art I learned from spending this afternoon at the Met, so maybe it was critically important to mid-20th Century art, but doesn't exhibit well, or something.
On the science side, the whole thing was pretty much a constant drumbeat about the greatness of string theory, with occasional "Wait a minute, now..." interjections from Krauss. This is probably inevitable in a panel on extra dimensions, as I think string-y theories are the only real area of physics using the notion of extra dimensions these days. There were a few things said and left uncorrected that seemed a little dodgy to me, though, that I'll mention here.
The first, relatively minor one, is that Greene's potted history of extra dimensions makes it sound like string theory exploded out of nowhere in the 1980's (coincidentally, when he was a grad student and got involved with it). While that's when it really took off, the string idea had been rattling around for at least ten years before then, so he's chopping a decade off the timeline. Krauss did mention this at one point, but I think people got a slightly misleading idea of the history.
Kachru was the least polished of the panelists (though he had visual aids, unlike Krauss), and had a couple of minor mis-steps. His description of the origin of the cosmological constant was a little garbled, and made it seem like something very natural, that Einstein had unnaturally set to zero, when in fact, as I understand it, there's no particular reason why you should expect it to be there (other than that you're allowed to put it in mathematically). Certainly, when I took "General Relativity for Idiots" nigh on twenty years ago, it was mentioned as more or less a historical curiosity, something you could stick in, but didn't need.
Obviously, the discovery of dark energy changed that, but again, I thought Kachru was a little misleading. He talked about dark energy as a really exciting development for string theory, when again, my understanding is that it's kind of a problem. People were happily constructing string models without any kind of cosmological constant for years, and when dark energy turned up, had to scramble a bit to make it work. You can make it work (a little too well, in fact-- there are a nearly infinite number of equally good theories with very slightly different parameters that could work, and no obvious way to choose between them), but it's not something that falls naturally out of the theory.
The other thing that was slightly infuriating was the (very brief) discussion of possible testability, which was the usual LHC hype, followed by an admission by all of the scientists that they don't expect the LHC to be able to say anything about extra dimensions within their lifetimes. There are a number of other ways to look for new physics, though, and it would've been nice to hear some mention of them. Likewise, a little more about the other possible theoretical approaches would've been nice, though again, I don't know that there are non-string models using extra dimensions.
I also would've liked to see an experimental physicist up there, to provide a little more grounding about what the actual problems are, and how you might hope to look for something. But then, I always think there should be more experimental physicists involved in everything.
As I said, though, those are mostly nitpicks, minor wrong notes in what was otherwise a very enjoyable evening. And the size and enthusiasm of the crowd was great to see.
As we were coming in and leaving, we could see preparations under way for the Street Fair, which looks like quite the undertaking. It should be fun.
From the point of GR, there's no reason for the cosmological constant to be there. On the other hand, under the quantum mechanical idea that anything not forbidden is mandatory, it ought to be there. It's a free parameter in the theory. It's sometimes said that it's a prediction of quantum field theory that the cosmological constant is very large, but that's not really true. What is true is that it is unnatural for it to be small because you are canceling a large amount of quantum corrections against to very high accuracy.
Really, the reason people were constructing string models without cosmological constants for years was because they were horribly unrealistic. Even before you break supersymmetry, lots of models have cosmological constants (albeit negative), and once you do end up breaking supersymmetry, all hell breaks looses as always. And that's not even getting to the contribution to the cosmological constant from ordinary symmetry breaking.
Of course, the models we currently have are still embarrassingly unrealistic, but they're realistic enough to have cosmological constants. I suppose one could view it as a success of string theory that it may have enough discrete vacua such that a few of them might have a cosmological constant close to the observed value, but it seems just a tad haphazard to me.
I'll agree that most extra-dimensional models are stringy-motivated, but you have neglected the host of phenomenological models that sprung up over the past ten years or so - the ADD and RS models (and modifications thereof) in particular. A number of these models have distinct collider signatures well within the realms of the LHC (KK modes tend to be rather distinct ;-)), so it's not entirely implausible for extra dimensions to show up sometime within our lifetimes.
A panel on extra/hidden dimensions with three physicists and... an art historian? How about a mathematician? Who do these people think came up with the language of extra dimensions anyway? And way before Einstein, if I may add.
Greene is a professor of Physics & Math; and the art historian actually talked quite a bit about the history of extra dimensions in math as inspiration for the artists.
Sorry, this is lengthy, but I think it's worth writing down accurate statements.
String theory did explode in the 80s. It was briefly popular in the 70s in its earlier incarnation as the dual resonance model of hadrons, but people gave up on that and only a handful of people remained interested in string theory. 1984 is when it became a mainstream research topic aimed at explaining both particle physics and gravity.
General relativity, like hydrodynamics, is a derivative expansion. If there's a zero-derivative term, like the cosmological constant, that affects the physics, it doesn't make sense to leave it out without a good reason. As Anon said, quantum mechanics will almost always generate it. (Experimentally, we have a good reason to mostly ignore it: it's really tiny, which is why people were able to think for so long that it might be exactly zero. But that's a mystery. From a theoretical point of view, it should have been there from the beginning.)
It's not true that string theorists could happily construct models without a cosmological constant. A lot of them worked on toy theories that had zero cosmological constant, but it was always clear that the only reason for this was supersymmetry, and that these were toy theories that were not our world. (In fact supersymmetry, again as Anon said, often predicts a negative cosmological constant, but is sometimes okay with it being zero when there is a "moduli space" of infinitely many vacua. Again, nothing like our world.)
We live in a world without supersymmetry, and any theory in such a world will predict a cosmological constant, almost always tens of orders of magnitude larger than the one we see. This problem didn't suddenly arise recently; it's always been there.
Almost every model of extra dimensions that the LHC could see is non-stringy, although often motivated by string theory. Also, they're almost all deeply flawed models. Essentially, we know from precision measurements at existing colliders that there's a limit to how weird things can be at the TeV scale. In the unlikely event that extra dimensions are detectable at these scales, they're not going to look much like extra dimensions.
For instance, you sometimes hear people say that given large, ADD-type extra dimensions, the LHC can make black holes. But "black hole" implies a semiclassical object with certain properties, and it's almost definitely true that if the LHC could make such a thing, it would be in some intermediate quantum regime that isn't much like a black hole at all. Similarly, Randall-Sundrum models are just a different language for talking about new strong interactions, and wouldn't really be in a regime where they look much like an extra dimension at all.
There was an interval when these ideas were new and it seemed reasonable to say that there might be a good chance of seeing extra dimensions. But we understand things much better now, and I think selling this idea to the public is a real stretch. Any reasonable theorist will tell you there are basically two good ideas about what the LHC might see: supersymmetry or new strong dynamics. The latter is only an "extra dimension" if you squint. We all hope for something unexpected, of course....