Warped Passages: Unraveling The Mysteries of the Universe's Hidden Dimensions
by Lisa Randall
Ecco (HarperCollins), 2005

The Cosmic Landscape: String Theory and the Illusion of Intelligent Design
by Leonard Susskind
Little, Brown and Company, 2005

Hiding In the Mirror: The Mysterious Allure of Extra Dimensions, From Plato to String Theory and Beyond
by Lawrence M. Krauss
Viking, 2005
What are theoretical physicists up to these days? Judging from the titles of the popularizations they are turning out, one might be forgiven for thinking that they are eating psychedelic mushrooms or chewing on lotus leaves. Warped Passages, Hiding in the Mirror, The Cosmic Landscape--sounds like a trilogy by Carlos Castaneda.

Well, what should theoretical physicists be up to? It's been three decades since the so-called Standard Model was hammered out. Thanks to this remarkable achievement, the behavior of all known particles can be described with exquisite precision, right down to the 11th decimal place. The only force the Standard Model leaves out is gravity, and that is handled very nicely by Einstein's theory of general relativity. Considering that the Standard Model and general relativity together account for any conceivable observation we might make, further theorizing can, without prejudice, be dismissed as metaphysics--which, of course, literally means "after physics."

Needless to say, the authors of these books--accomplished theoretical physicists, all three--don't buy this characterization. Theory has a future, they think, and it will probably involve a fairly extravagant addition to what we think of as reality. Beyond that, however, they don't see eye to eye.

Lisa Randall of Harvard University takes a cautious "bottom-up" approach: she wants to keep her theorizing firmly rooted in the actual observation of elementary particles. And what worries her most is a rather specific flaw in the theoretical status quo: our inability to explain why gravity is so absurdly weak compared with the other forces of nature. To solve this "hierarchy problem," she and her collaborator, Raman Sundrum, have posited the existence of a hitherto unnoticed dimension of space--not a little curled-up dimension, like those of string theory, but a large, possibly infinite dimension. As she explains in Warped Passages, our 3-D world may inhabit this 4-D space the way a shower curtain inhabits a bathroom. The particles in our world are like the water droplets running over the surface of the shower curtain. Only gravitons can escape the curtain into the larger space, and such leakage may account for the observed weakness of gravity compared with the other forces.

Leonard Susskind of Stanford University is very much a "top-down" fellow. In fact, he is one of the creators of string theory. In the four decades of its existence, string theory has not generated any novel predictions that can be tested. Nor have the legions of physicists who pursue string theory been able to find a mathematically unique version of it. At present, there is an enormous "landscape" of theoretical possibilities, numbering something like 1 followed by 500 zeros. Each version corresponds to a different universe with what might be called its own local weather: vacuum energy, number of dimensions, elementary particle masses, coupling constants, and so on. In The Cosmic Landscape, Susskind tries to make a virtue of this seeming embarrassment. Invoking inflationary cosmology, he submits that each of these theoretical possibilities has actually bubbled into existence as a "pocket universe." Together all these pocket universes make up what he calls the "megaverse" (other physicists prefer "multiverse"). Among this enormous multiplicity of pocket universes, Susskind further contends, there is bound to be one with just the right vacuum energy to permit the emergence of intelligent beings. No wonder we observe ourselves to be living in such a miraculously fine-tuned universe, he concludes, unabashedly embracing the notorious anthropic principle.

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.