Different from the warp factor of "Star Trek"?

Randall: Yes. This warp factor basically tells us the strength of gravity as you go out in the extra dimension. To be precise, it is telling us the amplitude of the graviton, or the probability of finding a graviton at any given location at any given time. The idea is that if you live at some distance away from this brane we talked about, you would effectively find that particles look lighter than what you would have very naively anticipated. And the reason is that gravity is weaker because the graviton is strongly attracted to the brane itself and doesn’t venture out from it. 

What does that get you?

Randall: It addresses a problem which to particle physicists is known as the hierarchy problem. That is the fact that gravity is a very weak force compared to the other forces, and it only starts to look strong in the realm of quantum gravity, and that only happens at a scale of distance or mass known as the Planck Scale, which is a huge number. This should be compared to the other scales in particle physics that we know about, like the masses of the W and Z bosons that mediate the electro-weak force. The ratio of the Planck Scale to the electro-weak scale is 16 orders of magnitude.

Why is this hierarchy a problem?

Randall: It’s just something we don’t understand. Why should these things be so different? As physicists we think we should be able to explain it, but it’s difficult to write a consistent theory where these scales are so far apart. In principle it could happen, but it’s very unlikely. You can, in principle, drop a dime and have it land on its edge, but it won’t do it that often. So we think this should be something that’s likely to happen, and there should be a deeper explanation for why it does. The problem is even worse than this, because the theory tries to force the scales to be the same. So we have to solve this more-technical problem as well. The first large extra dimension evoked the large extra dimensions to explain the weakness of gravity. But in that theory you had to write in the fact that the dimensions are so large. You got rid of one big number but you did it by putting in another one.
   In our theory, it turns out that the ratio of masses is very naturally generated because it is actually just the exponential of a number. So we replaced a number that was 10⁶ with a number that’s 30. Its not hard to get extra dimensions that are of size 30 in the units of the Planck Scale. This theory has two branes. There is one brane that is trapping gravity and another brane where gravity is not trapped. On that second brane gravity is weak, and that’s the brane we live on.

And the branes are separated from each other in the extra dimensional space? They’re not in contact?

Randall: Exactly.

How far apart are they?

Randall: Thirty.

Thirty what?

Randall: What’s trapping gravity is the energy on the brane, and that energy sets the scale of all this. It is 30 in terms of that energy scale.

Okay. we’ll let it go at that. How was your theory accepted by your colleagues?

Randall: It took a while for people to be convinced of the significance, or even to believe infinite-dimensional theory. It was actually quite a radical idea that you don’t have to compactify space. There was some skepticism, but now it’s accepted as a possible alternative. A lot of theorists, especially those interested in gravity, have been studying the theory and its consequences. Interesting things happen in the presence of this warp factor.

What, if any, are the implications for experiment?

Randall: On the one hand, if you ask what are the experimental tests in terms of gravity, this theory really looks as if it’s a four-dimensional theory, which is a shocking statement. That’s saying that you look around and measure anything you want—Newton’s laws, for instance—and you’d normally say that it proves that the universe has only three space dimensions. We’re saying, no, this doesn’t prove that, because we have this other theory that gives the exact same predictions. Because of the warp factor, this theory is perfectly consistent and might well be the world we live in.
   On the other hand, with the second brane you naturally have this low energy scale in the theory—namely the scale of particles we see. Because of this physics will change very radically once we get to an energy scale of one trillion electron volts. That, fortuitously, is the scale at which accelerators at Fermilab and CERN will soon be working. At the TeV scale, we predict new particles, coupled somewhat like gravity, but much stronger.

How obvious would such particles be?

Randall: These particles should be very obvious. You produce particles that decay in the detector and you actually see particles that look like a heavy version of the graviton. There is a variant of this theory in which there is an infinite extra dimension, with a second brane in it where we live. In this case, the heavy gravitons decay immediately so you don't see them as particles but as missing energy. That is, something has gone through the detector and taken energy with it. You could then reconstruct this missing energy and see if it corresponds with the existence of an extra dimension.

You started your career as a phenomenologist and now your ideas are being taken seriously by string theorists. Do you consider yourself a string theorist?

Randall: Well, it is not even clear what precisely either of these terms mean. Phenomenologists try to describe the results of experiments. However, calling someone a phenomenologist can be almost derogatory these days. But you can say the same for string theory in some circles. I just don’t like labels in general, but I certainly don’t object to being called a string theorist if it’s said in a nice way.
    Basically, I’m just a theoretical physicist who, like all the rest of us, would like to figure out how the world works. If that involves some string theory, great, but ultimately I think we should be able to connect it to what we see in the world and be able to test it. I’m just trying to put those things together.

June 2002: read an interview with Lisa Randall discussing the Special Topic of Brane in ESI Special Topics.