Preposterous Universe

Monday, December 06, 2004
Why three dimensions of space just aren't enough

The second issue of symmetry has just come out. symmetry is a magazine about particle physics and related fields, jointly published by Fermilab and SLAC. It takes the place of their individual house magazines, and looks like a significant upgrade. The editor is David Harris, who hopefully will get back to blogging once things are running smoothly! This issue includes a good article about the status of inflation, including its connection to string theory.

Another interesting little note was the histogram of citations to the original paper by Oskar Klein on the idea of extra dimensions (Kaluza-Klein theory), reproduced at right. The data are from the SPIRES literature database at SLAC, a fanastic service that makes it a cinch to see who cites what papers in high-energy physics and related fields. (Kind of like google scholar, but years ahead of their time.) You can see that there is a peak in the early 80's, and another one that we're in the middle of right now. These reflect well-defined movements in high-energy theory. In the early 80's, the idea of grand unification of the three forces of particle physics (strong, weak, and electromagnetic) had been pretty well investigated, and people were eager to get gravity into the game. In this spirit, KK theory was resurrected, but now in the context of supersymmetry, which has a natural home in eleven dimensions of spacetime.

The movement toward KK theory was squelched by the rise of string theory; the string bandwagon was launched in 1984 when Michael Green and John Schwarz showed that you could cancel certain annoying "anomalies" (quantum-mechanical effects that can destroy classical symmetries), and (almost) everyone dropped 11-dimensional supergravity to work on string theory. Of course, string theory naturally lives in ten dimensions, so the compactification of the extra dimensions is just as important in string theory as it ever was in KK theory; but there are so many other things going on that it made sense to think of strings as a new beginning, and references to the original Kaluza-Klein papers dropped off.

More recently, the string duality revolution showed that there really wasn't a big difference between ten-dimensional superstring theory and 11-dimensional supergravity; they are each versions of one more comprehensive (and still ill-understood) theory, M-theory. But that's not the reason for the uptick in citations to Klein in the late Nineties; it's because of the phenomenological idea of brane worlds and large extra dimensions, led by the papers from Arkani-Hamed, Dimopoulos and Dvali and Randall and Sundrum. These were inspired by work on D-branes in string theory, since it was in that context that people took seriously that we might live on a brane and be unable to escape into the "bulk" in which it was embedded. But the details of string theory aren't intimately connected to those models (and the idea of being stuck to a brane goes back to earlier work by Rubakov and Shaposhnikov).

The idea that modern theories of quantum gravity imply the existence of extra dimensions was the subject of my talk at the Philosophy of Science Association meeting last month. I've finally turned my slides into a pdf file, for anyone who'd like to check them out. Unfortunately the figures didn't always convert smoothly, so at times you will have to imagine the presence of a string or quark where no image is present. All part of the challenge of modern physics.

Ideas on culture, science, politics.
Sean Carroll

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