The Cosmic Landscape (51 page)

A story of martyrdom and resurrection? A man of the cloth comforting the martyr before the auto-da-fé? The crossing of the veil that separates the living from the dead? Not at all: it is the imaginary, but entirely possible, briefing of a future star traveler, curious and brave enough to enter a giant black hole and to cross its horizon. Not a briefing by a chaplain but by the starship’s resident theoretical physicist.

Or, more to the point of this book, it could be the crossing of the cosmic horizon of an eternally inflating universe. But we will come to cosmic horizons a little later.

Spiritualists believe that communication with the dead is possible: all that’s required is the right
medium,
an adept at the darker sciences. You can guess what I think of such claims, but ironically, I have been one of the main combatants in a war of ideas about the possibility of communication with the undead on the other side of an event horizon. The war lasted for a quarter of a century, but now it’s over.

The protagonists were Stephen Hawking and his army of general relativists on one side.
¹
For the first fifteen years, it was mainly Gerard ’t Hooft and myself on the other. Later a band of string theorists came to our aid.

Gerard ’t Hooft is a Dutchman. If measured by the number of great contributions to physics per capita, the Dutch are surely the greatest physicists in the world. Christiaan Huygens, Hendrik Antoon Lorentz, Willem de Sitter, Heike Kamerlingh Onnes, George Uhlenbeck, Johannes Diderik van der Waals, Hendrik Gerhard Casimir, Martinus Veltman, Gerard ’t Hooft are just a few of the greatest names. Lorentz and ’t Hooft are arguably among the greatest historical figures of physics. To me ’t Hooft, more than any living physicist, represents the spirit of Einstein, Lorentz, and Bohr. Although he is six years younger than I am, I have always been in awe of ’t Hooft.

I am glad to say that ’t Hooft is not only one of my heroes but that he is also a good friend. Although he is mathematically far more powerful than I am, I have always found that of all my colleagues he’s the one that I feel closest to in viewpoint. Throughout the years we have often found ourselves working on the same puzzles, troubled by the same paradoxes, and with similar guesses about the resolution of these problems. I think that, like me, Gerard is a very conservative physicist who will not embrace a radical solution to a problem unless he feels that all other paths have proved futile. But then he is fearless.

If Gerard is conservative I would have to say that Stephen Hawking is the Evel Knievel of physics. Brave to the point of recklessness, Stephen is a well-known traffic menace in Cambridge, where his wheelchair is often seen careening around, way beyond safe speeds. His physics is in many ways like his wheelchair driving—bold, adventurous, audacious to the maximum. Like Evel Knievel he has had his crashes.

Three years ago Stephen turned sixty. The party was like no other physicist’s sixtieth birthday. Seminars and physics lectures—sure, plenty of them—but also music, cancan dancers, a famous rock star from U2, a Marilyn Monroe look-alike, singing physicists. It was a stupendous media event.

To give you an idea of the relationship Stephen and I have had over the years, I will quote from the birthday lecture I gave at the celebration:

Stephen, as we all know, is by far the most stubborn and infuriating person in the universe. My own scientific relation with him I think can be called adversarial. We have disagreed profoundly about deep issues concerning black holes, information, and all that kind of thing. At times he has caused me to pull my hair out in frustration—and you can plainly see the result. I can assure you that when we began to argue more than two decades ago, I had a full head of hair.

At this point I could see Stephen in the rear of the auditorium with his impishly mischievous grin. I went on:

I can also say that of all the physicists I have known he has had the strongest influence on me and on my thinking. Just about everything I have thought about since 1980 has in one way or another been a response to his profoundly insightful question about the fate of information that falls into a black hole. While I firmly believe his answer was wrong, the question and his insistence on a convincing answer [have] forced us to rethink the foundations of physics. The result is a wholly new paradigm that is now taking shape. I am deeply honored to be here to celebrate Stephen’s monumental contributions and especially his magnificent stubbornness.

That was three years ago. At the time Stephen still believed that he was right and ’t Hooft and I were wrong.

In the early days of the war there were many flip-floppers trying to position themselves to be on the winning side—whichever that would be. But Stephen, to his everlasting credit, stuck to his guns until further resistance was no longer possible. Then he gracefully and unconditionally surrendered. Indeed, had Hawking fought with less conviction, we would probably know much less than we do today.

Stephen’s point of view was simple and direct. The horizon of a black hole is a
point of no return.
Anything that crosses the horizon is trapped. To cross back it would be necessary to exceed the speed of light: a total impossibility according to Einstein. People, atoms, photons, every form of signal that can carry a message are bound by Einstein’s speed limit. No object or signal can pass from behind the horizon to the outside world. The black hole horizon is the wall of a perfect prison. Observers waiting outside the prison for a report from inside would wait an eternity for even a single bit of information from within. At least this was Hawking’s view.

To get a good idea of how black holes work without getting into the difficult mathematics of general relativity, we need an analogy. Fortunately, we have a pretty good one that is familiar and easy to understand. I’m not sure who first used it, but I learned it, or something similar, from the Canadian physicist Bill Unruh. Let’s go back to the infinite shallow lake that we used in the last chapter to illustrate an inflating universe. But now we don’t need the feeder tubes that keep injecting new water into the lake. Instead we introduce a drain at the center. The drain is a hole in the lake bottom that allows the water to escape, perhaps emptying on to some deadly rocks below. Let’s also introduce some boats with observers onto the lake. The observers must obey two rules. The first is that they can communicate only by means of surface waves, i.e., ripples on the surface of the lake. They can wiggle their fingers in the water in order to radiate waves. The second rule is to follow a speed limit on the lake. No boat, under any circumstances, is permitted to move through the water faster than the speed of these waves.

Let’s begin with observers far from the center, where the water is hardly disturbed by the drain. It’s not completely unaffected: it very slowly migrates inward but almost imperceptibly. But as we move toward the drain, the flow picks up speed, and very close to the drain the inward velocity becomes larger than the velocity of surface ripples. Waves emitted from this region get swept toward the drain even if they were directed away. Obviously any boat that unknowingly finds itself this close is doomed to be swept to its destruction. In fact there is a particular boundary where the velocity of the water exactly matches the speed of surface waves. That place is the point of no return. Once crossed, there is no getting back. Not even a message can be communicated to the outside. That point of no return is just like the horizon of a black hole, except that in the case of the black hole, space is being swept inward with the velocity of light. From behind the horizon no signal can escape without exceeding Einstein’s ultimate speed limit. Now it should be clear why Stephen was certain that information falling across a black hole horizon is irredeemably lost to the outside.

Stephen himself was responsible for the weapon that was turned against him. Building on the great work of Jacob Bekenstein in the early 1970s, Stephen had shown that black holes have thermal energy—heat. They are not icily cold as physicists had assumed. It is true that the bigger the black hole, the lower its temperature, but no matter how big, there is always a residual thermal heat. For the kind of black hole that would result from the final collapse of a star, the Hawking temperature would be only about one ten-millionth of a degree above absolute zero. But it’s not zero.

Hawking reasoned that a black hole, like any other object with heat content, would radiate energy. A hot poker that’s been left in the flame radiates light of an orange or red color. Cooler objects radiate infrared radiation invisible to the naked eye. No matter how cold, as long as an object is not at absolute zero, it will radiate energy in the form of electromagnetic radiation. In the case of a black hole, it is called Hawking radiation. That was Hawking’s great discovery.

Anything that radiates will lose energy. But mass and energy are two sides of the same thing, according to Einstein. So in time black holes lose their mass, and losing mass, they shrink until they completely evaporate away, leaving only the photons of the Hawking radiation in their place. Curiously, then, the mass of any object that falls into a black hole is inevitably radiated back out as Hawking radiation. The energy of the courageous star traveler who braved the horizon crossing eventually reappears as “pure light and radiance.”

But, said Hawking, because no signal can exceed the speed of light, no information from the interior can exit the horizon along with the Hawking radiation. Such information is trapped in a shrinking ball, until poof—it just disappears when the black hole is gone.

The first I heard of this was in 1980, when Stephen, Gerard ’t Hooft, and I attended a small conference in San Francisco. Both Gerard and I were disturbed by Stephen’s conclusion and were certain it was wrong. But neither of us could see exactly what was incorrect in the reasoning. I had a sense of deep discomfort. A paradox of very serious magnitude had been announced by Hawking: the kind of paradox that could eventually open the door to a deeper understanding of the elusive connection between gravity and quantum mechanics.

The problem was that Hawking’s conclusion violated one of the central tenets of physics. Hawking of course knew that. It was why he found the idea of
information loss
in black hole evaporation so exciting. But ’t Hooft and I felt that the
conservation of information
was just too deeply built into the basic logical foundations of physics to discard it, even in the presence of such a bizarre object as a black hole. If we were right then somehow the bits of information that fall to the horizon of a black hole are radiated back out with the Hawking radiation, thus opening the way for imprisoned information to be signaled to the outside.

One should not get the idea that information comes out of the black hole in an easily accessible form. It comes out in a form that is so scrambled that in practical terms it would be impossible to unscramble. But the debate was not about practicalities. It was about laws of nature and principles of physics.

What, exactly, constitutes information, especially if it is scrambled beyond recognition? To understand the ideas involved, let’s pursue the analogy with a prison. A Mafia kingpin in the “big house” wants to send a message to one of his lieutenants on the outside. He first writes out his message, “Tell the Piranha brothers to bet ten thousand on the Kid.” To make it hard for the censors, he adds, at the end, a much longer fake message, let’s say, the text of the
Encyclopaedia Britannica.
Next the criminal mastermind places the message on a series of cards, one letter to a card. The order of the cards retains the original message, including the interesting part and the fake addition tacked on at the end. Now he scrambles the message. The kingpin has a code for doing this. He takes the entire message and shuffles the letters, not in a random way, but according to a rule. Next he shuffles the result, again by the same rule. He does this over and over ten million times. The message is then conveyed to the lieutenant.

The cards are the analog of the Hawking photons that are radiated from the black hole.

What does the lieutenant make of it? If he doesn’t know the shuffling rule, he has nothing but a random, meaningless sequence of letters that conveys no information. But the information is there, nevertheless. Given the shuffling rule, the lieutenant can unscramble by reverse-shuffling ten million times. The message reappears at the top of the deck, and the lieutenant easily picks out the relevant part. The information was there even if scrambled. Even if the lieutenant didn’t have the shuffling rule—perhaps he lost it—the information was, nevertheless, in the cards.

Compare that with a different situation. This time the prison censor intercepts the message on the way out and shuffles it, but according to a rule that has some intrinsic randomness built into it. Once, twice, ten million times he shuffles. Now, even if the lieutenant knows that the letters were scrambled randomly, there is no way to recover the message. The information is truly lost. The randomness of the shuffling not only scrambled the message but also destroyed the information that it contained.

The real controversy that Hawking, ’t Hooft, and I were at war over had nothing to do with the practicalities of actually reconstructing the messages from inside a black hole. It had to do with the existence of rules and the kinds of rules that nature utilizes. Gerard and I claimed that nature scrambles information but never destroys it. Stephen claimed black holes create a form of randomness—a kind of noise in the system—that degrades any information before the Hawking radiation escapes the immediate environment of the black hole. Once again the issue wasn’t one of technology, but rather, it had to do with the nature of the future Laws of Physics, when quantum mechanics and gravity will both be important.

The reader may find one thing confusing, even disturbing. Doesn’t quantum mechanics introduce an element of randomness into the laws of nature? Don’t the quantum jitters destroy information? The reason is not simple, but the answer is no. Quantum information is not as detailed as the information in a classical sequence of symbols. But the randomness of quantum mechanics is of a very special, controlled kind. Hawking was claiming a degree of randomness above and beyond the kind allowed by the standard rules of quantum mechanics: a new kind of randomness that was catalyzed by the presence of a black hole.