Behind the Shadows

Kids often enjoy creating shadow animals against the wall, with the help of a flashlight. Through these simple two-dimensional silhouettes, generated by limited hand gestures, a whole three-dimensional menagerie can be brought to life. Now Joe Polchinski, a physicist at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, wants to take this childhood game one giant cosmological step forward.

Armed with a $54,329 grant from the Foundational Questions Institute, Polchinski is investigating the fate of a shadowy version of an infamous quantum cat hiding behind the horizon of a black hole. If successful, the picture that emerges from his musings could provide physicists with a glimpse at the ultimate structure of spacetime. In turn, that may point them toward the long-sought theory of quantum gravity, which would unify the two pillars of modern physics: quantum mechanics, which deals with the physics of the very small, and general relativity, which describes how very massive objects warp spacetime.

A Hole Lot of Problems

Those hoping to construct a theory of quantum gravity often look to black holes as the perfect theoretical laboratory for pondering what happens when quantum mechanics and relativity meet because they contain huge masses confined within a very small region. In particular, in the 1970s, Stephen Hawking at Cambridge University and Hebrew University physicist Jacob Bekenstein showed that a black hole’s entropy—classically, the number of possible configurations of particles in a system—is proportional to its surface area. This was surprising because every other object in the universe has an entropy that is proportional to its volume. Physicists describe this property as "holographic" because it encodes three-dimensional information into a two-dimensional equation. "The ultimate unification of quantum mechanics and gravity will almost certainly be based on the holographic principle," says Polchinski.

Another famous black-hole paradox posed by Hawking highlights the clash between classical theories (such as general relativity) and quantum mechanics: On the one hand, physicists expect that a quantum particle falling into a black hole should have any information about its original state destroyed—but, on the other hand, this stands in clear violation of the quantum tenet that information is always preserved. The conflict has led Hawking and others to conclude that, to marry the two extremes, there must be profound changes either to quantum theory or to our understanding of spacetime. Polchinski is among the camp that believes we must dispense with the latter, repainting spacetime as a consequence of a deeper underlying structure. "The paradoxes point to a radical picture in which spacetime is not fundamental, but rather emerges from a projection in a lower dimensional space," Polchinski explains.

In an effort to find out how spacetime might emerge—just as our mental images of three-dimensional animals are generated by the movement of two-dimensional shadow puppets—Polchinski and others are now working on a model that views the entire universe as a giant hologram of information. "Polchinski’s work has led to deep insights into the quantum structure of space-time," says physicist Alex Maloney, at McGill University in Montreal, who works on a similar FQXi-funded project.

The question is whether such a counterintuitive beginning can yield a viable theory. "This is so different from the way that physics has always worked that we have no intuition for how it happens," admits Polchinski.

The Hows and Whys of Spacetime

It’s an intellectual challenge he seems to have spent his whole life preparing for. As a child growing up in Tucson, Arizona, Polchinski was fascinated by his illustrated "How and Why Wonder Books," which introduced him to different areas of science, such as atomic energy and electricity. Later, in high school, he recalls wondering a lot about gravity: how strong it was and how fast it traveled. But things really clicked for Polchinski when he went to Caltech as a undergraduate and stumbled across Feynman’s famous lectures. After that, there was no holding him back.

Polchinski’s doctoral research at the University of California, Berkeley, involved trying to explain how the elementary particles known as quarks are confined together within atomic nuclei. His advisor, Stanley Mandelstam, made a seemingly odd suggestion: that the young graduate student should try to mathematically interchange the electric fields in his questions with magnetic fields and the electric charges with magnetic charges. This was Polchinski’s first brush with the concept of duality—the idea that two seemingly disparate quantum theories may actually be mathematically interchangeable. Today, the trick lies at the heart of the holographic principle, allowing physicists to swap sticky calculations that are hard to solve in 3-dimensions, for instance, for easier ones involving different constituents, in 4-dimensions—and vice versa. The strategy also works for interchanging abstract equations that relate descriptions of physics with larger numbers of dimensions, making it very useful for handling multiple dimensions that can appear in string theory—a discipline that Polchinski has helped to pioneer.

"Mandelstam was way ahead of his time and many of the problems he gave me are only now being solved," Polchinski says.

Such calculations are helping Polchinski build up a theory. His earlier work on string theory, for instance, was instrumental in the first mathematical model of such a duality, formulated by Juan Maldacena in 1997, which defined a model universe (containing strings and gravity) in terms of the behavior on its boundary (where the equations described the behavior of elementary particles in the absence of gravity). This is now regarded as one of the key conceptual breakthroughs of the last twenty years, thanks to its ability to bring together gravity and the other forces. Unfortunately, this relationship only holds for a special type of spacetime (Anti de Sitter) with a closed defined boundary; in contrast, our universe is expanding and has no fixed boundary. Part of Polchinski’s work is focused, therefore, on how to apply holography to smaller patches of spacetime—an important step towards understanding our own universe.

Maldacena, now at the Institute for Advanced Study at Princeton, believes that Polchinski has the right credentials to tackle these issues. "Joe has been a leader in this field and has had many important conceptual insights during his career," he says.

Hidden Cats

Holography also implies that the information contained within everything that ever fell into a black hole is entirely contained in quantum fluctuations of the surface of the hole’s event horizon. Polchinski is considering a thought experiment to test this: If Schrödinger’s cat—teetering in a quantum state in which it is both alive and dead —were hidden behind the horizon of a black hole, could we ever measure its state in a dual theory?

Polchinski argues that the answer is "yes," implying that a single set of building blocks is recycled to construct both the inside and the outside of the black hole. "This helps to sharpen the meaning of holography and the way that space and time emerge," says Polchinski.

So how far away is he from finding a unifying theory? "We keep learning new and surprising things, with duality and holography being the latest," says Polchinski. "But all we can say is that we are not finished yet."