Trespassing on Einstein's Lawn (37 page)

At first that didn't sound right—the curvature near a black hole horizon was
small
? You'd think it would be pretty big, considering a black hole has the strongest gravitational pull of any object in the universe. But if the black hole was big enough, Susskind explained, gravity's tidal forces at the horizon would be negligible. Given any horizon size, really, you could always look at some segment that was small enough to make space appear flat and ordinary, not capable of blocking information or betraying Einstein.

It was a perfect paradox: information couldn't be lost without violating quantum mechanics, and it couldn't be saved without violating general relativity. Hawking took Einstein's side, saving relativity by sacrificing elephants and quantum mechanics. But Susskind was convinced that quantum mechanics couldn't just fall apart, not without the world around us falling apart, too. He had a nagging hunch that
information never crosses the horizon in the first place, but he had to find a way to keep the equivalence principle intact.

Actually, it's not hard to show that the information never crosses the horizon from the point of view of an accelerated observer outside the black hole. In studying Hawking radiation I had already seen how Safe, my accelerated observer, would see light stretched to perverse proportions and time slow down until it freezes at the horizon's edge. Safe sees nothing cross to the other side because as far he's concerned,
there is no other side.
For him, the horizon marks the edge of reality, the end of the world. Safe can't lose any information, because there's nowhere for it to go.

But that story becomes tricky to uphold when you think about what's happening to Screwed. Screwed sails right through the horizon, because, thanks to the equivalence principle, the horizon doesn't exist for Screwed. As far as he's concerned, information, such as the vast amount of it contained in his own body, can easily cross into the black hole, even if it can't climb back out. Safe says the information remains outside the horizon; Screwed says it's inside the black hole. Susskind knew that if somehow
both
stories were true, then neither quantum mechanics nor general relativity would be violated and all would be right in the universe.

The problem was that for both stories to be true, it seemed like the information had to be in two places at once, as if there were two identical clones of every bit of information. Unfortunately, such a scenario was expressly forbidden by Zurek's no-cloning theorem. The reason is simple: if you could clone a quantum particle, you could outsmart the uncertainty principle. You could measure the position of one clone and the momentum of the other and now you have precise knowledge of two aspects of a conjugate pair, uncertainty be damned. But the uncertainty principle is a principle—there's no outsmarting it. Information can't be cloned. Once again, Susskind was stuck with a paradox: both stories have to be true and both stories couldn't be true.

When the solution came to him, even Susskind realized just how crazy it sounded. “Every other option had been eliminated, leaving one possibility,” he said. “It seemed totally absurd but I knew it had to be
right.” He had first announced his answer at a conference back in 1993.
“I don't care if you agree with what I say,” he told the audience. “I only want you to remember that I said it.”

“I feel like we should make a move while Brockman still remembers who I am,” I told my father over the phone. “I think we should write a book proposal.”

“But the idea was to write a book once we had found the answer to the universe,” my father said.

“Yes,” I said, “but if you build it, it will come.”

“What?”

“
Field of Dreams.
Ghosts playing baseball? If we have a book deal, the answer will come.”

“I'm not sure that's how it works,” my father said.

“I think if Brockman's your agent it is.”

My father was right—the book had always lived somewhere off in the vague future, an event horizon that receded as quickly as we approached, and I think we both wanted it that way, because we knew that no actual book would ever measure up to the idea of Our Book, and because we knew that the day the book became a physical object would be the day our journey was over.

But Wheeler's death had made the clock tick a little louder. I didn't want to wake up ten or twenty or thirty years from now a magazine editor who once had talked about the meaning of nothing with her father. I wanted something tangible to keep us on track. To keep us together. Something like a book contract.

“Okay,” my father said, sounding apprehensive but excited. “If you think now is the time to go for Brockman, let's do it.”

“To be? To be? What does it mean to be?” Niels Bohr demanded when asked where a particle can be said to be prior to being observed.

Susskind was following not only in Bohr's footsteps but in Einstein's when he proposed his radical solution to the black hole information-loss
paradox: there is no observer-independent meaning to the location of a bit of information. If you want to ask where the information is, you have to answer the question “According to whom?”

In order to uphold quantum mechanics and its conservation of information, Safe has to see information remain outside the black hole's horizon. In order to uphold general relativity and its equivalence principle, Screwed has to see
that same information
inside the black hole. The quantum no-cloning theorem forbids the duplication of information. But that doesn't matter, Susskind said. After all, who can see the information in both places? No one can be inside and outside an event horizon at the same time.

The key to solving the paradox, Susskind discovered, was realizing that there's no frame of reference in which the information has been cloned. As long as you stick to what a given observer can actually see, there's either Safe's story or Screwed's, but never both. It was sort of a mindfuck: both stories are equally true, but you can only talk about one at a time. You have to pick a reference frame and stick to it. Within any given reference frame, no observer ever witnesses a violation of the laws of physics. Violations only show up in the God's-eye view, a view that luckily no observer can ever actually have. The two descriptions—inside and outside the horizon—are complementary, Susskind said, in the same way that wave and particle are mutually exclusive but complementary descriptions of, say, an electron. He called the principle black hole complementarity, or, more generally, horizon complementarity.

Physicists were intrigued by Susskind's argument, but Hawking stubbornly maintained that information really did disappear behind the horizon and evaporate into oblivion, and many physicists followed Hawking's lead, living in a state of shared denial about the fate of quantum mechanics. Susskind, however, saw the problem all too clearly. The black hole information-loss paradox loomed like a dark cloud over everything. Cumulus chaos.

Then, in 1997, came a game changer. Physicist Juan Maldacena had been working on a model of string theory in anti–de Sitter, or AdS, space. Unlike our de Sitter space, which is defined by the positive value of its cosmological constant, AdS space has a negative cosmological
constant. Our positive cosmological constant pushes outward on space, causing the universe's expansion to accelerate. Flip the sign and instead of pushing it pulls, causing space to bend in on itself, curving like a saddle at every point, distorting space and time in ways that only M. C. Escher could imagine and making possible the seemingly impossible, such as the ability of a light beam to travel to infinity and back in a finite amount of time. To make things more complicated, the AdS space in Maldacena's model was ten-dimensional, five of its dimensions curled up like origami at every point. To make life easier, Susskind told me, just picture it as a sphere, one with five large dimensions (plus time) surrounded by a four-dimensional boundary.

Through some genius intuition and complicated mathematics, Maldacena had discovered that the string theory operating in the ten-dimensional interior of the AdS sphere was mathematically equivalent to an ordinary quantum theory of particles operating on the four-dimensional boundary. The quantum theory of particles, he found, was remarkably similar to QCD, the theory that describes the interactions of quarks and gluons here in our universe. The only difference was that Maldacena's quantum theory was a conformal field theory—a CFT—which meant that it was the same at every scale, unlike QCD, in which the strong force grows weaker as you look to smaller distances. This equivalence between string theory in AdS and the CFT on its boundary became known as the AdS/CFT duality.

It all sounded pretty abstruse, but the more I thought about it, the more amazing I realized it was. First of all, it showed that string theory, a theory
with
gravity, was completely equivalent to an ordinary theory of quantum particles
without
gravity. Everyone had been trying to unite quantum mechanics and general relativity by shoehorning them into a single “theory of everything,” but AdS/CFT suggested that maybe gravity is what quantum mechanics looks like when viewed through a different geometry. No wonder the world's leading physicists got up and danced the Macarena when they first heard the idea. (“Ehhh, Maldacena!”) Second, there was that weird issue of dimensionality again. A theory with five large dimensions could be perfectly mapped onto a different theory in four.

Susskind had been thinking about the dimension issue ever since
Bekenstein had discovered that a black hole's entropy scaled with the area of its horizon, and not with its volume. If entropy counts the amount of information hidden within the black hole's three-dimensional interior, why would its value be determined by the two-dimensional area of its boundary? It was as if the three-dimensional black hole was somehow also two-dimensional. It had bugged me when I had first learned about it, and I was glad to hear it had bugged Susskind, too.

Susskind realized that the curious relationship between entropy and area wasn't confined to black holes—it applied to any region of space. After all, any region of space can be made into a black hole if you stick enough mass in it. Black holes are the highest-entropy objects around, so if
their
entropy can fit on a lower-dimensional surface, so can the entropy of anything else.

It was insane, counterintuitive, and undeniable: the total amount of information in any region of three-dimensional space scales with the area of its two-dimensional boundary. Susskind called the idea the holographic principle, reminiscent as it was of holograms, two-dimensional films that encode all the information necessary to reconstruct a three-dimensional image.

I was looking around the
New Scientist
office as he explained this to me over the phone one afternoon, and it dawned on me just how impossible it seemed. Every chair, every journalist, every air molecule from floor to ceiling could be precisely mapped,
with no loss of resolution
, onto the surfaces of the walls. A three-dimensional volume of space is far bigger than the surface area of its boundaries, yet the information content is the same? It was as if one of those three dimensions is just totally useless. As if we'd been thinking about dimensionality all wrong.

Susskind had suggested that the world itself was a kind of hologram, a projection of some lower-dimensional gravityless theory encoded on the edge of the universe. I wondered which was weirder, the idea that I was nothing but a computer simulation or the idea that I was a holographic projection from the edge of the world. Probably the hologram. In any case, Maldacena's AdS/CFT duality was the perfect embodiment of Susskind's holographic principle. It convinced the
doubting physicists, including Hawking, that information couldn't be lost in black holes.

In AdS/CFT, there's a one-to-one mathematical mapping between the five-dimensional interior of the space and the four-dimensional boundary, so given any object or physical process in the higher-dimensional bulk spacetime you can follow the math to find its precise counterpart on the boundary. That raised a fascinating question: what's the lower-dimensional counterpart of a black hole? Black holes are made of gravity, but in Maldacena's model, there's no gravity on the boundary. What could a gravityless black hole possibly look like? Maldacena calculated the answer. It would look like a hot gas of ordinary particles. In fact, it would look like a quark-gluon plasma.

Quark-gluon plasma? Suddenly I remembered the reminder I had written for myself in my notebook back when I wrote my article on the plasma observed at RHIC, the one that, to everyone's surprise and confusion, had a viscosity that made it the most ideal liquid ever observed, up to twenty times more liquid than water, a fact that ordinary physics couldn't explain.
Look into AdS/CFT … explains liquid fireball?

“The quark-gluon plasma is dual to a black hole?” I asked Susskind, amazed. “I read somewhere that AdS/CFT can explain the RHIC measurements.”

That's right, Susskind said. The plasma is dual to a black hole, and a black hole's event horizon has a calculable viscosity. As it turns out, the viscosity of Maldacena's ten-dimensional black hole is nearly the exact value measured for the quark-gluon plasma at RHIC.

“So wait,” I said. “Is the idea that we can use the mathematics of ten-dimensional black holes to calculate the viscosity of a four-dimensional quark-gluon plasma? Or is it that when we measure the quark-gluon plasma we are literally looking at a ten-dimensional black hole through four-dimensional glasses?” As an ontic structural realist, I had a pretty strong inkling of what the answer ought to be.

“It depends who you ask,” Susskind said. “Maybe the quark-gluon plasma is analogous to a ten-dimensional black hole. But the connection may be deeper. A lot of us think it's probably deeper.”