The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [64]
For many years, physicists had relied on perturbative methods to analyze each of the string theories. When working with the Type I string theory, they assumed its coupling was small, and pressed on with multi-pass calculations similar to what Ralph and Alice did in the lottery analysis. When working with the Heterotic-O, or any of the other string theories, they did the same. But outside of this restricted domain of small string couplings, researchers could do nothing more than shrug, throw up their hands, and admit that the math they were using was too feeble to provide any reliable insight.
Until, that is, the spring of 1995, when Edward Witten rocked the string theory community with a series of stunning results. Drawing on the insights of scientists including Joe Polchinski, Michael Duff, Paul Townsend, Chris Hull, John Schwarz, Ashoke Sen, and many others, Witten provided strong evidence that string theorists could safely navigate beyond the shores of small couplings. The central idea was simple and powerful. Witten argued that when the coupling constant in any one formulation of string theory is dialed ever larger, the theory—remarkably—steadily morphs into something thoroughly familiar: one of the other formulations of string theory, but with a coupling constant that’s dialed ever smaller. For example, when the Type I string coupling is large, it transforms into the Heterotic-O string theory with a coupling that’s small. Which means that the five string theories are not different after all. Each appears different when examined in a limited context—small values of its particular coupling constant—but when this restriction is lifted, each string theory transforms into the others.
I recently encountered a splendid graphic that from close up looks like Albert Einstein, with a bit more distance becomes ambiguous, and from far away resolves into Marilyn Monroe (Figure 5.2). If you saw only the images that come into focus at the two extremes, you’d have every reason to think you were looking at two separate pictures. But if you steadily examine the image through the range of intermediate distances, you unexpectedly find that Einstein and Monroe are aspects of a single portrait. Similarly, an examination of two string theories, in the extreme case when each has a small coupling, reveals that they’re as different as Albert and Marilyn. If you stopped there, as for years string theorists did, you’d conclude that you were studying two separate theories. But if you examine the theories as their couplings are varied over the range of intermediate values, you find that, like Albert turning into Marilyn, each gradually morphs into the other.
The morphing from Einstein to Monroe is amusing. The morphing of one string theory into another is transformative. It implies that if perturbative calculations in one string theory can’t be undertaken because that theory’s coupling is too large, the calculations can be faithfully translated into the language of another formulation of string theory, one in which a perturbative approach succeeds because the coupling is small. Physicists call the transition between naïvely distinct theories duality. It has become one of the most pervasive themes in modern string theory research. By providing two mathematical descriptions of one and the same physics, duality doubles our calculational arsenal. Calculations that are impossibly difficult from one perspective become perfectly doable from another.*
Figure 5.2 From close up, the image looks like Albert Einstein. From farther away, it looks like Marilyn Monroe. (The image was created by Aude Oliva of the Massachusetts Institute of