More on the 5th dimension, before Darth Rumsfeld classifies it, from a very smart woman indeed, Lisa Randall, physics professor at MIT:
SW There are several different theories floating around that evoke large extra dimensions. Could you explain what they are and what makes Randall-Sundrum theory special?
Randall: I’ll start by telling you about the theories that aren’t ours. In the simplest type of theory there are extra dimensions, but the extra dimensions are finite in size. Why finite? Well, at long-distance scales we see strong evidence for the existence of only four dimensions: three of space and one of time. One way of explaining the fact that we only see four dimensions is that other dimensions exist but they’re so tiny that we just don’t feel any effect from them. That was the idea in string theory—that these extra dimensions get compactified on some consistent manifold, and the manifold is very tiny. A lot of people still probably believe that.
SW How does your theory differ?
Randall: One of our ideas is that you don’t actually have to compactify the extra dimensions. In other words, instead of saying gravity is forbidden to go beyond a certain length in the extra dimension, suppose instead there was a strong force—I’ll explain why there should be in a moment—such that gravity was sort of attracted to a specific location in space-time. In principle, it could wander far out in the extra dimension, but this external force centers gravity in one place and it looks effectively four dimensional.
What’s interesting is that this precise theory involves something called a brane, which is a lower-dimensional subspace of the higher-dimensional space. Brane is short for "membrane." So, for example, in our theories we imagine that the brane is only four dimensional, even though it lives in this five-dimensional space. There are three space dimensions and one time dimension that we see and one extra dimension that we don’t. We’re not very sensitive to it. Because the brane itself carries energy, it basically applies an attraction acting on gravity so that gravity stays very localized near the brane. Even though there is an infinite extra dimension, gravity extends so little into that dimension that it is almost as if space were compactified and you only see four dimensions. This is really very different from the compactified theory, however, because it says you can consistently have an infinite extra dimension, but still see gravity as only four dimensional.
SW So what exactly does this extra dimension give you?
Randall: According to what I've said so far, it's not giving us anything. It's simply telling us that we don't necessarily have to compactify and we can still have a consistent theory as far as gravity goes. However, there are problems associated with conventional compactification. When you have these compactified scenarios, you don't know what size or shape those manifolds should be. You have too many parameters. It means you have lots of possible theories. If you could avoid all that it would be great. We think we're on the road to accomplishing that.
SW But the idea is eventually to come up with a testable theory? We don’t seem to be there yet.
Randall: Okay. Now I’ll tell you what happens if you have a second brane in the theory. One of the very interesting things about this theory, called warped geometry, is that they have something called a warp factor...
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.
SW 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.
SW And the branes are separated from each other in the extra dimensional space? They’re not in contact?
SW How far apart are they?
SW 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.
SW 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.
SW 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.
SW 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.
SW 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...
A more mathematical discussion of the Braneworld model is discussed here if you can get past the Science magazine wall. Or here, for those not intimidated by raw differential equations from Wikipedia. If there was a math error, I'd never know it.
Why are an ex-CIA, ex-CSC/Dyncorp CEO Head of NASA and Chancellor Rumsfeld so interested they're putting up satellites to look for local mini-black holes?
It's one thing for Darth Griffin to want to build a hyperspace drive. It's a very different thing if Sith Lord Rumsfeld wants a black hole weapon. That would be a Big Mistake indeed.