See Inside October 2005

The Beauty of Branes

Lisa Randall's thinking on higher dimensions, warped space and membranes catalyzed ideas in cosmology and physics. It might even unify all four forces of nature

It was the summer of 1998, recalls Harvard University physicist Lisa Randall, when extra dimensions finally pulled her in. Extra dimensions--beyond the four we encounter every day (three of space plus one of time)--have been an ingredient of theoretical physics for decades: mathematician Theodor Kaluza proposed a fifth in 1919, string theory requires 10 of them, M-theory needs 11. But Randall hadn't much use for them, she says, until that summer when she decided they might be helpful to supersymmetry, one of the conundrums she was pondering.

Randall contacted Raman Sundrum, a Boston University postdoctoral student with whom she had previously collaborated, and asked him if he would like to brainstorm about extra dimensions and membranes--"branes," as they are called for short. Branes are domains or swaths of several spatial dimensions within a higher-dimensional space. The everyday world we live in could be a three-brane, for example, and it is anyone's guess as to what dimension brane it might be embedded in. "Raman had already thought about branes and extra dimensions, and he was an obvious person to join forces with," Randall explains.

But Sundrum was a little worried. He was on his third postdoc, didn't have a job lined up and was considering leaving physics for finance. But he liked the way Randall thought and decided to set off on what might be his final physics adventure. The fruits of that collaboration, as fueled by caffeine and ice cream as by heady equations, were papers known as RS-1 and RS-2, two of the most cited in physics for the past five years.

The papers, which appeared in 1999, offered novel ways to think about gravity, branes and extra dimensions, and they suggested that the universe might have evolved differently in the beginning than it did later. "For me and a lot of people interested in cosmology and particle physics, it meant that there was this whole new set of possibilities of what could be going on in the early universe," says James Cline of McGill University. For Sundrum, now a professor at Johns Hopkins University, it meant seven job offers. "She is somebody with a marvelous instinct," he laughs.

This instinct often draws Randall to problems she knows little about. While at the renowned Stuyvesant High School in New York City, Randall decided to work on perfect versions of complex numbers called Gaussian integers for the then Westinghouse science talent search. (In perfect numbers such as 6, the factors--in this case, 1, 2 and 3--add up to the number itself.) "The project was looking for and seeing if there were any patterns. And there aren't very many. Basically, I always do this. I don't know anything and take on a big project," she says. Nevertheless, Randall's musings on these numbers tied for first place--a fitting precedent for her subsequent mathematical forays into a host of arcane physics fields: technicolor, charged parity symmetry violation, flavor structure and baryogenesis, to mention a few.

Although they did not intend to, Randall and Sundrum ended up using extra dimensions to offer a solution to what is called the hierarchy problem. It can be framed in several ways, but the problem is essentially this: Why is gravity so puny, so many billion on billions of times weaker compared with the other forces--electromagnetism and the weak and strong nuclear forces? Discrepancy in strength makes it impossible to combine gravity with the other three forces, a unification thought to have existed during the early phase of the big bang.

But rather than invoking supersymmetry--a popular solution that argues for the existence of as yet undetected partners to all the known particles--Randall and Sundrum posited that gravity could reside on a different brane than ours, one separated from us by a five-dimensional spacetime in which the extra dimension is 10-31 centimeter wide. In this RS-1 model, all forces and particles stick to our three-brane except gravity, which is concentrated on the other brane and is free to travel between them across spacetime, which is warped in a negative fashion called anti-De Sitter space. By the time it gets to us, gravity is weak; in the other brane it is strong, on a par with the three other forces.

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