The Cosmic Landscape (52 page)

Let’s pursue the prison analogy a little further. Imagine that the lieutenant sent a message into the prison with some irreplaceable information. In fact we can even imagine a steady stream of information flowing in. The prison has its limits. It can’t keep absorbing scraps of paper indefinitely. At some point it will have to dump them back out in the trash. According to Hawking the messages go in, the trash comes out, but inside the prison the information in the message is destroyed by this new kind of randomness. But ’t Hooft and I said no: the message is in the trash. It’s indestructible. We argued that the quantum bits that fall into the black hole are always there to recover—but only if you know the code.
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The position that ’t Hooft and I held was not without its problems. We insisted that information escapes from the horizon, but how could it if that requires exceeding the speed of light? What is the mechanism? The answer must be that it never goes in.

Let’s send a message into a black hole with the star traveler. According to the usual rules of the General Theory of Relativity, the message together with the traveler should sail right through the horizon. On the other hand, ’t Hooft and I, in order to rescue the basic principles of quantum mechanics, were claiming that the bits of information in the message would be transferred to the outgoing Hawking radiation just before passing in to the horizon and then radiated out. It was as though the message were torn out of the hands of its messenger and put in the outgoing trash just before passing the point of no return.

This conflict of principles created a very serious dilemma. General relativity said that the bits enter the horizon and continue on their way, deep into the interior of the black hole. But the rules of quantum mechanics forbid information to be lost to the outside world. One possibility might resolve the dilemma. Let’s go back to the prison analogy. Suppose that at the entrance to the prison, a guard were stationed at a Xerox machine, and that every incoming message was xeroxed—one copy going into the prison and one sent back out after nonrandom shuffling. That should satisfy everyone. Inside the prison they would see the message entering as if it were undisturbed on its way in. Outside the observers would find that the information was never lost. Everyone is right.

Here the problem gets interesting. A very basic principle of quantum mechanics says that a quantum Xerox machine is impossible. Quantum information cannot be faithfully copied. No matter how well the machine copies some kinds of information, it will always fail badly with other kinds. I called this the No Quantum Xerox Principle. The quantum-information experts call it the No Cloning Theorem. What it states is that no physical system can ever function completely faithfully to replicate information in a quantum world.

Here is a way to understand the No Quantum Xerox Principle. Start with a single electron. The Heisenberg Uncertainty Principle tells us that it is never possible to know both the position of the electron and its velocity. But now suppose we could quantum Xerox the electron in exactly its original state. Then we could measure the position of one copy and the velocity of the other, thereby learning the forbidden knowledge.

So, here is the new dilemma: general relativity tells us that information should fall straight through the horizon toward the deep interior of the black hole. On the other hand, the principles of quantum mechanics tell us that the same information must remain outside the black hole. And the No Cloning Theorem assures us that only one copy of each bit is possible. That’s the confusing situation that Hawking, ’t Hooft, and I found ourselves in. By the early nineties the situation had reached a crisis: who is right? The observer on the outside who expects the rules of quantum mechanics to be respected? For him the bits of information should be located just above the horizon, where they are scrambled and then sent back out in the Hawking radiation. Or is the observer who falls through the horizon correct in expecting the bits to accompany her into the heart of the black hole?

The solution to the paradox was eventually provided by two new principles of physics that ’t Hooft and I introduced in the early 1990s. Both of them are very strange, far stranger than Hawking’s idea that information can be lost; so strange that, in fact, no one else besides ’t Hooft and me believed them at first. But as Sherlock Holmes once told Watson, “When you have eliminated all that is impossible, whatever remains must be the truth, no matter how improbable.”

With the possible exception of Einstein, Niels Bohr was the most philosophical of the fathers of modern physics. To Bohr the philosophical revolution that accompanied the discovery of quantum mechanics was all about
complementarity.
The complementarity of quantum mechanics was manifest in many ways, but Bohr’s favorite example was the particle-wave duality that had been forced on physics by Einstein’s photon. Is light a particle? Or is it a wave? The two are so different that they seem totally irreconcilable.

Nevertheless, light is both a wave and a particle. Or more accurately, for certain kinds of experiments light behaves like particles. A very dilute beam of light falling on a photographic plate leaves tiny black dots: discrete evidence of the indivisible particle nature of the photon. On the other hand, those dots will eventually add up to a wavy interference pattern, a phenomenon that makes sense only for waves. It all depends on how you observe the light and what experiment you do. The two descriptions are complementary, not contradictory.

Another example of complementarity has to do with Heisenberg’s Uncertainty Principle. In classical physics the state of motion of a particle involves both its position and its momentum. But in quantum mechanics you either describe a particle by its position or its momentum—never both. The sentence, “A particle has a position AND a momentum,” must be replaced by, “A particle has a position OR a momentum.” Likewise, light is particles, OR light is waves. Whether you use one description or the other depends on the experiment.

Black hole complementarity is the new kind of complementarity that results from combining quantum mechanics with the theory of gravity. There is no single answer to the question, “Who is right? The observer who remains outside the black hole and sees all information radiated from just above the horizon? Or the observer who falls through with the bits that are heading toward the center of the black hole?” Each is right in its own context: they are complementary descriptions of two different experiments. In the first the experimenter stays outside the black hole. He may throw things in, collect photons as they come out, lower probes down to just above the horizon, observe the effects on the trajectories of particles passing near the black hole, and so on.

But in the second kind of experiment, the physicist prepares an experiment in her lab. Then, lab and all, she jumps into the black hole, crossing the horizon, while performing the experiment.

The complementary descriptions of the two experiments are so radically different that it hardly seems credible that they could both be right. The external observer sees matter fall toward the horizon, slow down, and hover just above it.
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The temperature just above the horizon is intense and reduces all matter to particles, which are finally radiated back out. In fact the external observer, monitoring the in-falling observer, sees her vaporized and reemitted as Hawking radiation.

But this is nothing like what the freely falling observer experiences. Instead she passes safely through the horizon without even noticing it. No bump or jolt, no high temperature, no warning of any kind signals the fact that she has passed the point of no return. If the black hole is big enough, let’s say, with a few million light-year radius, she would sail on for another million years with no discomfort. No discomfort, that is, until she reaches the heart of the black hole, where tidal forces—the distorting forces of gravity—eventually become so strong that… never mind, it’s too gruesome.

Two such different descriptions sound contradictory. But what we have learned from Bohr, Heisenberg, and others after them is that apparent paradoxes of this type signal genuine contradictions only when they lead to conflicting expectations for a single experiment. There is no danger of incompatible experimental results because the freely falling observer can never communicate her safe passage to the outside. Once she has safely passed the horizon, she is permanently out of contact with all observers who remain outside the black hole. Complementarity is strange but true.

The other major revolution of the early twentieth century was Einstein’s Theory of Relativity. Certain things are relative to the state of motion of the observer. Two different observers moving rapidly past each other will disagree about whether two events occurred at the same time. One observer might see two flashbulbs flash at exactly the same time. The other would see one flash take place before the other.

The Principle of Black Hole Complementarity is also a new and stronger relativity principle. Once again the description of events depends on the state of motion of the observer. Remaining at rest outside the black hole, you see one thing. Falling freely toward the interior of the black hole, you see the same events entirely differently.

Complementarity and relativity—the products of the great minds of the early twentieth century—are now being united in a radically new vision of space, time, and information.

Perhaps the error that Hawking made is to think that a bit of information has a definite location in space. A simple example of a quantum bit is the polarization of a photon. Every photon has a screw sense to it. Imagine the electric field of a photon as it moves. The tip of the electric field moves with a helical motion—a corkscrewlike motion. Think of yourself as following behind the light ray. The corkscrewing motion can be either clockwise or counterclockwise. In the first case the photons making up the beam are called right-handed photons; in the second case, they are left-handed. It’s like the direction that you would have to twist a screwdriver in order to drive a screw into the wall in front of you. Ordinary screws are right-handed, but no law of nature forbids left-handed screws. Photons come in both types. The distinction is called the circular polarization of the photon.

The polarization of a single photon is composed of a single quantum bit of information. Morse code messages could be sent in the form of a sequence of photons, the messages being coded in the sequence of polarizations instead of a sequence of dots and dashes.

What about the location of that bit of information? In quantum mechanics the location of a photon may not be definite. After all, you can’t specify both the location and momentum of the photon. Doesn’t that mean that the bit of information is not at a definite place?

You may not know exactly where the photon is, but you can measure its location if you choose. You just can’t measure both its position and its momentum. And once you measure the photon’s location, you know exactly where that bit of information is. Furthermore, in conventional quantum mechanics and relativity, every other observer will agree with you. In that sense the quantum bit of information has a definite location. At least that’s what was always thought to be the case.

But the Principle of Black Hole Complementarity says that the location of information is not definite, even in that sense. One observer finds the bits making up her own body are somewhere far behind the horizon. The other sees those same bits radiated back out from a region just outside the horizon. So it seems that the idea that information has a definite location in space is wrong.

There is an alternative way to think about it. In this view the bits have a location, but they’re not at all where you think they are. This is the holographic view of nature that grew out of thinking about black holes. How do holograms apply?

A picture, a photograph, or a painting is not the real world that it depicts. It’s flat, not full with three-dimensional depth like the real thing. Look at it from the side—almost edge on. It doesn’t look anything like the real scene viewed from an angle. In short it’s two-dimensional, while the world is three-dimensional. The artist, using perceptual sleight of hand, has conned you into producing a three-dimensional image in your brain, but in fact the information just isn’t there to form a three-dimensional model of the scene. There is no way to tell if that figure is a distant giant or a close midget. There is no way to tell if the figure is made of plaster or if it’s filled with blood and guts. The brain is providing information that is not really present in the painted strokes on the canvas or the darkened grains of silver on the photographic surface.

The screen of a computer is a two-dimensional surface filled with pixels. The actual data that are stored in a single image are in the form of some digital information about color and intensity—a collection of bits for each pixel. Like the painting or the photo, it is actually a very poor representation of the three-dimensional scene.