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And then there is "duality." Theories of the unity of opposites are not new, but string theory found a unique application for the concept of duality. And it is in this sphere that Shenker has made some of his largest scientific contributions.
The fact that human life evolved in four large dimensions prohibits humans from directly investigating the universe of the very small. Until now, physicists have extracted clues about subatomic particles by accelerating them to great speeds, running them into one another, and looking at the resulting debris. But strings are so incomprehensibly small that a particle-colliding machine capable of probing their realm would have to be at least the size of the Milky Way galaxy.
So indirect methods of detecting the unfathomable have been invented. Physi-cists have been forced to resort to "thought experiments."
A duality thought experiment might define the behavior of one object in terms of another. For instance, if water poured into a bowl collects first at the lowest point of the bowl, one can reasonably infer -- from this very small model -- that the Earth's vast oceans filled up the deepest valleys first.
String theory reaches back to 19th-century physics, when James Clerk Maxwell showed that electricity and magnetism are dual aspects of the same force -- electromagnetism. Using the precepts of duality, weak natural forces can be shown to mirror strong forces, and visible forces can be related to invisible forces. Seeming opposites can be shown to have the same cause.
The concept of duality led Edward Witten, a physics professor at the world-famous Institute for Advanced Study in Princeton, N.J., and a pivotal figure in modern physics, to invent the first mathematically consistent theory of quantum gravity. This spectacular leap, made public in March 1995, linked the five ugly -- asymmetrical -- string theories into one unified theory, called M-theory. (Michael Duff of Texas A&M University and Paul Townsend of Cambridge University independently made similar discoveries.)
"M" has been variously described as standing for magic, mystery, mother, membrane, and matrix. In other words, it doesn't have a real name because nobody knows what it is named after, but gravity fits M-theory. And so do the equations of quantum mechanics.
M-theory is the most likely candidate for a Theory of Everything, although some stringies seem embarrassed to be making such a grand claim. They qualify their braggadocio with a disclaimer: M is a Theory of Everything That We Already Know. They cannot, however, hide their excitement, and ambitions. Nobody knows what the equations that rule the behavior of the universe will yield in the way of practical application. But there is no doubt whatsoever that lots of fame and money await the anointed discoverers of The Answer.
The nasty particle in the ointment, however, is that M-theory is only a thought experiment. It cannot be proved in the real world. And -- even though it unites gravity and quantum mechanics on paper -- it cannot yet define the basic principles that govern the universe. Nevertheless, it appears to be an amazing achievement of the human mind -- even if the nitty-gritty of the mathematics is veiled from most people's comprehension.
The 11th Dimension
Witten et al. solved the problem of uniting five unruly, 10-dimensional theories by peeping into a higher dimension: the 11th dimension. This was the mathematical equivalent of stepping inside the forest to see the trees. Or, peeling open the tennis ball to reveal the space inside.
When Witten et al. mentally stepped into the 11th dimension, they saw that each of the five previously incompatible string theories share the 11th dimension: a measurement 1 billion trillion times smaller than the atomic nucleus. It had previously been hidden from mental perception because strings wrap themselves around it like a tennis ball -- or inner tube -- wraps around empty space.
When viewing string theory from four-, five-, or 10-dimensional perspectives, it appears to be fragmented. When looked at from inside the littlest, 11th dimension, all the string theories become a whole: M-theory.
Physicists around the world gasped when Witten posted M-theory on the Los Alamos Web site four years ago. The discovery of the 11th dimension unleashed hundreds of new ideas and revelations.
Steve Shenker, Leonard Susskind, Tom Banks, and Willy Fischler were inspired to invent an offshoot of M-theory -- what they call Matrix Theory -- in 1996. Shenker simplifies the discovery by comparing it to a chart in which cities are listed in relation to mileage. To find the miles between two cities you follow the lines inside the matrix to a coordinate. Only, in this case, there are multiple coordinates, because there are multiple dimensions, or multiple ways to measure where and when a string is.
(The theorists carry these matrices around in their heads -- massaging the numbers without benefit of computers. For purposes of discovery, they tend not to use the powerful computers at their command, because machines are stupid; they have no intuition, no art.)
For a short while, Shenker and his collaborators were the toast of the high-energy physics world. Then, a new theory of "p-branes" burst upon the scene. The physicists gasped again.