Lawrence Krauss of Case Western Reserve University admits that he finds both Randall's and Susskind's arguments seductive. Yet at the end of Hiding in the Mirror, his masterly survey of higher-dimensional theorizing, he remains a skeptic--even though, like the X-Files's Fox Mulder, he "wants to believe."
Each of these books is superb in its own way, but reading them together is especially rewarding, as subtle tensions emerge that illustrate the dilemmas faced by theoretical physicists today. Take the anthropic principle. Susskind almost rejoices in it. "Given a megaverse, endlessly filled with pocket universes," he writes, "the Anthropic Principle is an effective tool to weed out and eliminate most of them as candidates for our universe." Both Randall and Krauss, in contrast, find the anthropic approach rather a letdown. Edward Witten agrees. "I'd be happy if it is not right," he has commented. "I would be happy to have a more unique understanding of the universe."
It is easy to sympathize. Suppose you want to explain why the observable world has three spatial dimensions. You might approach the matter anthropically, arguing that if there were some other number of dimensions, we would not be here to wonder about it. In a world with more than three dimensions, there would be no stable orbits for electrons--hence no chemistry, hence no chemically based life-forms, hence no us. In a two-dimensional world, signals would not propagate cleanly--hence no information processing, hence no intelligence, hence no us. (Proving the impossibility of intelligent life in a one-dimensional world is left as an exercise for the reader.) But by falling back on such anthropic reasoning we might be giving up too early. Indeed, string theorists have come up with more fundamental explanations for why only three of the nine spatial dimensions the theory posits should have expanded to observably large size--explanations that make no reference to the possibility or impossibility of creatures like us being around. The anthropic explanation looks embarrassingly lightweight in comparison, not to say parochial.
Even if the current generation of theoretical physicists can sort out such differences among themselves, they will still have to contend with those who deny that their enterprise is meaningful at all. Susskind writes that "no serious theoretical physicist today is content with two apparently incompatible theories," by which he means quantum mechanics and general relativity. But Freeman Dyson, who decades ago played an important role in tidying up the mathematics of the Standard Model, has declared that he, for one, is happy with the status quo. General relativity explains big things, quantum mechanics explains little things, he points out, and if the twain meet, it is on a scale that is physically undetectable and hence empirically irrelevant.
The question of testability raised by Dyson clearly vexes all three authors. Krauss, in particular, writes that unless the theorizing about extra dimensions and megaverse landscapes ultimately helps to "resolve fundamental physical questions, it is all just mathematics." But that hardly means it will have been a waste of time. Even if Witten's string-theoretical investigations never yield testable consequences, they have nonetheless greatly advanced the area of pure mathematics called knot theory--which is why Witten has been awarded the most prestigious of mathematical prizes, the Fields Medal. No one expects mathematics to be testable.
Still, a little humility on the part of theoretical physicists might be advisable, especially toward their experimental colleagues. "Most really good theoretical physicists don't pay much attention to what experimenters think," Susskind writes. "They build their theories based on their own instincts and go where intuition leads them." Hardworking experimental physicists, for their part, have been known to grumble about the leisurely life of their theorizing counterparts. The experimenters say--facetiously, for all I know--that theoretical physicists will never schedule a meeting on Wednesday, because that would spoil two weekends.
This article was originally published with the title Beyond the Standard Model.