In the late 1960s the renowned University of Oxford physicist and mathematician Roger Penrose came up with a radically new way to develop a unified theory of physics. Instead of seeking to explain how particles move and interact within space and time, he proposed that space and time themselves are secondary constructs that emerge out of a deeper level of reality. But his so-called twistor theory never caught on, and conceptual problems stymied its few proponents. Like so many other attempts to unify physics, twistors were left for dead.

In October 2003 Penrose dropped by the Institute for Advanced Study in Princeton, N.J., to visit Edward Witten, the doyen of today’s leading approach to unification, string theory. Expecting Witten to chastise him for having criticized string theory as a fad, Penrose was surprised to find that Witten wanted to talk about his forgotten brainchild.

A few months later Witten posted a dense 97-page paper that tied together twistors and strings—bringing twistors back to life and impressing even the harshest critics of string theory. In the past few years theorists have built on Witten’s work and rethought what space and time are. They have already spun off calculational techniques that make child’s play of the toughest problems in ordinary particle physics. “I have never been more excited about physics in my life,” says string theorist Nima Arkani-Hamed, who recently moved to the institute from Harvard University to immerse himself in the emerging field. “It is developing at a blistering pace right now, with a group of roughly 15 people in the world working on it day and night.”

Prior to Witten’s work, twistorians and string theorists moved in separate circles and spoke what might as well have been different languages. Whereas Penrose and his colleagues have made their names studying Einstein’s general theory of relativity, string theorists trace their descent to particle physics. Lionel Mason of Oxford says that when he and Penrose visited Syracuse University in 1987, they blew off a talk on string theory that, in hindsight, would have given them the clues they needed. “We didn’t go to a particle physics seminar—we were relativists,” he says.

Penrose’s original goal was to reconsider how quantum principles apply to space and time. Conventional wisdom held that spacetime geometry should fluctuate on quantum scales, altering how events relate to one another. But in that case, an event that was supposed to cause another may no longer do so, creating paradoxes such as those found in time-travel stories. In twistor theory, causal sequences are primary and do not fluctuate. (The theory gets its name from what causal relations look like around a spinning particle, as shown at the left.) Instead the location and timing of events fluctuate. But twistorians could not make this idea precise—until string theorists showed that an event of ambiguous location and time is nothing more or less than a string.

String theorists, for their part, had a promising idea for the creation of space that they could not get to work. In 1997 they conjectured that particles zipping around in four dimensions can behave just like strings interacting in five dimensions. The new dimension materializes like a figure in a pop-up book. Yet this conjuring trick produced only a single dimension of highly warped space. Using twistor concepts, theorists have now shown how all the dimensions of ordinary space—and even time—can pop out.

Many theorists find it quite natural that spacetime would be derivative. Andrew Hodges of Oxford points out that we do not perceive spacetime directly; we infer that events happen in specific locations at specific times from the information that comes to us. “This idea of points of spacetime as being primary objects is artificial,” he says. Indeed, the concept of distinct positions and times breaks down because of the gravitational warping of spacetime and the notoriously spooky connections between quantum particles.

Whether or not they succeed in remaking space and time, twistorians and string theorists have already endeared themselves to particle physicists. Even fairly simple particle collisions demand equations containing tens of thousands of terms, which are written using a strategy devised by the famous physicist Richard Feynman in the 1940s. Almost all of those terms end up canceling out, but you don’t know in advance which will cancel, so you have to slog through all of them. An alternative strategy inspired by twistors and strings captures symmetries that Feynman’s approach does not, so it sheds the excess mathematical baggage from the outset. Calculations that math whizzes once gave up on now take just a couple of weeks. “I’m pretty sure Feynman would be quite pleased if he saw what we can do,” says Zvi Bern of the University of California, Los Angeles.

The emerging theory of spacetime is still very tentative and so mathematically dense that even those physicists directly involved admit they can barely follow what is going on. Theorists have yet to explain why, if spacetime is merely a construct, it nonetheless seems so real to us. It must somehow take shape much as life springs from inanimate matter. Whatever the process is, it cannot occur only on subatomic scales, because the concept of size must itself emerge. It should be evident on all scales, everywhere around us, if only we know how to look.