What size did physicists normally consider for the extra dimensions of, say, string theory?

Normally you think they must be really tiny, 10^-33 centimeters. If you just extrapolate Newton's inverse square law for gravity, and ask at what distance does gravity become comparable to all the other forces, you get 10^-33 centimeters, which is an incredibly miniscule distance. So people thought that since that seemed to be a natural scale associated with gravity, if we do have extra dimensions, they should be curled up at that miniscule size. But every now and then people floated the idea that these dimensions might be bigger, as big as 10^-17 centimeters. This still wasn’t incredibly brave, because you're still putting them just out of reach of experiment. Nevertheless, this idea was suggested most forcefully by Ignatius Antoniadis, one of the co-authors on these two highly papers. In the early 1990s, he started talking about this idea. In fact, Savas and Gia and Ignatius had just written a paper about some properties of these theories, should they make sense, and I looked at this paper and I thought it seemed pretty intriguing.

When I arrived at SLAC and hooked up with Savas, I asked him about this and he said he didn't even know if these theories made any sense, even though they had written this paper about them. So we set out to see if they did. Neither one of us was an expert on extra dimensions, and so we very slowly started learning all kinds of simple things just to understand whether these theories really made any sense. We did this for quite a number of months and basically concluded that it was inconclusive. In the meantime, we had learned enough about extra dimensions that we could start having ideas of our own. Then when Gia Dvali was visiting Stanford in March 1998, we were just sitting around and we realized that there were some incredibly simple properties of these extra dimensions, which were very well known to any experts on the subject, but not to us. One of these very simple things is that the extra dimensions dilute any force that goes there. There's just a lot more room to spread out and so the forces appear to be weaker. And the second we realized that this could happen, it was extremely natural to wonder why we can't make the dimensions so big that we make gravity appear to be very, very weak, which is one thing any successful theory has to be able to do.

  Even if it solved that problem, wouldn't it introduce other problems, like properties of matter that might not match what we see in reality?

That was the next question. If these extra dimensions are there and relatively large, why haven't we seen them yet? The very natural answer was because we're confined to living on a wall in this higher dimensional space. So everything we're made out of, except gravity, actually sticks to this three-dimensional sub-surface in this higher-dimensional space where only gravity can go. These ideas came very, very quickly. We did some very simple estimates and realized that the size of these extra dimensions would have to be huge compared to the size people had been talking about—maybe as large as a millimeter, in the case of two extra dimensions. But we couldn't immediately find any contradiction with having this crazy idea. This was all in the course of an afternoon, and I think we all thought this was crazy and very amusing but surely there most be something wrong with it. The remarkable thing was that the more we thought about it, and the more different ways we tried to kill it off, we couldn’t do it. It survived and was consistent in a pretty non-trivial way with all the experimental results we could imagine. So after four or five months of trying to kill it off every day, we started to become convinced that it wasn't kill-off-able and was a viable idea.

  So there were three papers, two of which make our highly cited list. Tell us about the significance of each paper.

Our very first paper was written by me and Savas and Gia Dvali and looked at how these large dimensions solved the hierarchy problem. The next paper was with Antoniadis, "New dimensions at a millimeter to a fermi and superstrings at a TeV", and this was the paper in which we showed how these ideas could be embedded into string theory, which is the only known framework for making a sensible theory of gravity valid to arbitrarily short distances. And so both of these papers were basically at the level of discussing the main idea and then some quick sketches for why it wasn’t ruled out by anything.

The third paper—"Phenomenology, astrophysics, and cosmology of theories with sub millimeter dimensions and TeV scale quantum gravity"—is not the most cited of the lot, but was really crucial. This was the paper where we systematically analyzed anything that could possibly kill this theory off and demonstrated that it managed to escape everything. We had to think about all kinds of strange things that could happen in cosmology, the collapse of supernovae, astrophysics, lots of different phenomena that we already know a lot about in nature and that could have been drastically affected by these large dimensions. It was not immediately obvious that you could get away with doing this without screwing up any number of things we know about already. All kinds of things could have gone wrong. And the point of this paper was to systematically go through everything we could think of and show that the theory escaped. It occasionally ended up being very constrained by nature, but was nonetheless viable over the entire range of known phenomena.

  That it is highly constrained suggests that it can be tested by experiment. Is that the case?

That’s right. The most exciting aspect of this stuff is that once we demonstrated that we had a viable theory, we could start talking about predictions. If this picture is realized in the world, and it certainly may not be, then there's just a plethora of experimental predictions that it makes. And the really exciting thing is you could perhaps test these both at accelerators and maybe even tabletop experiments. If what we're saying is true, then all the effects of gravity that we don't understand—of quantum theory, of string theory, etc—would all be probed right at the next generation of accelerators. It means you will be able to make strings at the Large Hadron Collider at CERN in the next five to ten years. You might make little black holes. Because all the strange things associated with gravity go from completely inaccessible, down at this miniscule distance, to just above our heads and maybe showing up in the next decade.

  Were you surprised by the impact of your papers?

I think we all realized pretty quickly that if this held up it was very important. And so I was extremely excited about it. I really thought this was a big enough shake-up to the usual picture, that people would have to find it interesting. Of course, for the first six months, at least, the basic reaction was disbelief. People found it interesting but they all thought that surely it was wrong. It took some convincing, and the third paper was critical for that. So for those first six months, it was a little bit frustrating. But I did feel it was a very important piece of work. And that wasn’t immodesty. It was just a very different picture of the universe and it's not very often those come along and are consistent.

  How has the picture developed since you originally published?

There have been more and more refinements and some more constraints have been discovered, although not many more than the ones we originally outlined. There's been a lot of extra work done on yet other aspects of physics that you can fit into this picture—some quite different and very interesting additions to this set of ideas.

  If you were an odds-maker in Vegas, what odds would you give that your ideas are right?

I don't know. I think it's about as likely as anything else we've thought of so far. What I would bet most on is that there's something very strange going on that maybe we haven't even dreamed of yet. After that I would put equal odds on our theory and supersymmetry.

  Now your work has evolved into a mature and crowded field. Are you looking to find something new and different again? Or are you pushing ahead with the large dimension research?

I'm doing something new for precisely the reason you say. Also because I do believe we will find out something new in experiments pretty soon, I don’t see any point in spending lot of time doing detailed work on any one model. So I prefer to think of new possibilities. For the last six or eight months, I've been going back and trying to understand whether there's anything all that special about extra dimensions to begin with. Together with some colleagues here at Harvard, we've come up with what I think is a pretty exciting set of ideas to show that extra dimensions can actually be generated from completely four-dimensional physics. We call this deconstructing dimensions, because it is taking the extra dimensions and taking them down to completely four-dimensional building blocks. It also gives a new slant on the meaning of space. Space isn't something you have to take for granted, but something you can actually generate from the dynamics of completely four-dimensional models. We're busily exploring the consequences of this idea. The idea that space might not be fundamental is pretty well accepted by a lot of people. Before we were thinking about adding extra dimensions and using them to do different things. Now I'm going back and hacking away at the extra dimensions to see what we can do with what's left.

Dr. Nima Arkani-Hamed
Department of Physics
Harvard University
Cambridge, Massachusetts, USA