Last year, in the latest of their celebrated bets about the way the world turns, the cosmologists John Preskill and Kip Thorne of the California Institute of Technology and Stephen Hawking of Cambridge University in England laid odds on what happens to information sucked into those bottomless pits said to lurk within galaxies across the universe. Hawking and Thorne bet that the information -- whether consisting of letters, numbers, the binary digits on a computer disk, or even the arrangement of atoms in a rock -- is gone forever. Preskill wagered that it could not possibly be. According to their signed proclamation: "The loser(s) will reward the winner(s) with an encyclopedia of the winner's choice, from which information can be recovered at will."
What is at stake is not merely the price of the books -- new Britannicas are going for $1,500 a set -- but the shape that a final theory of the universe will take. For the information paradox seems to hint that at least one of the two theories that lie at the foundation of physics -- quantum mechanics and general relativity -- is subtly flawed.
"The information paradox brings into sharp focus the most important problem of theoretical physics in the last half of the 20th century -- that of reconciling quantum mechanics and Einstein's theory of general relativity," said Steven Giddings, a physicist at the University of California, at Santa Barbara. "When we find the resolution to the information paradox, it's almost certain that we'll learn something very profound about the structure of space-time and the nature of quantum mechanics."
For describing the lives of elementary particles -- things with so little mass that gravity is generally irrelevant -- the beautiful equations of quantum mechanics are the finest of precision tools. And for dealing with enormous conglomerations of matter -- stars, galaxies, the universe itself -- general relativity, Albert Einstein's elegant explanation of gravity as the "curvature" of space-time, is unsurpassed.
Black holes provide a rare theoretical arena where quantum mechanics and general relativity come together, recreating the extreme conditions thought to have existed in the earliest moments of the big bang. But melding the two theories into a unified whole that would apply to all of creation -- what physicists call a theory of quantum gravity -- has so far proved impossible. The two theories are written in such different languages that unifying them has been like trying to reduce, say, the Internal Revenue Service code and the rules for writing computer programs with Java to the same fundamental principles.
The equations of general relativity lead to the inescapable conclusion that collapsing stars, if massive enough, will keep right on collapsing, until they tear a hole in the fabric of space-time. At such a location, called a singularity, gravity is so intense that the familiar laws of physics break down. Surrounding the singularity is a region of no return, called the horizon.
Together a singularity and its horizon form a black hole. Anything that slips past the boundary, including information, can never escape the irresistible pull. Doing so would require fleeing at a speed faster than light. And Einstein's other great theory, special relativity, holds that to be impossible. Throw in an encyclopedia, or the whole Library of Congress, and the data seem to be gone forever.
And that's where the paradox arises. One basic idea of quantum mechanics is what might be called the Law of Conservation of Information. Bits of data must never disappear. Otherwise, an important notion called "micro-reversibility" would be violated:
Whenever two particles collide and splinter into shards, and those shards into other shards, it is supposed to be possible to reverse the process. Presented with the progeny of this cascading process, one should be able to "run the film" backward and identify the parents and grandparents. If information can just leave the universe, then physical processes would not be perfectly predictable.
Even worse, it is widely believed that if information is not conserved, then neither is energy. Information, after all, is physical, not ethereal. "To transmit a given amount of information in a given amount of time requires a minimum amount of energy," Giddings explained. "To lose a given amount of information in a given amount of time requires a violation of energy conservation."
Most people would be grateful if losing data down a black hole was the worst of their worries. So far, these aberrations of space and time unambiguously exist only on paper, as a logical consequence of general relativity. Indirect evidence that can be imaginatively interpreted as black holes devouring matter has convinced most cosmologists that they surely exist. But encountering one hardly seems like a serious hazard. So what if physics breaks down in this extreme situation?
The cosmologists don't see it that way. For one thing, if information and energy can leave the universe through black holes, then the leakage may not stop there. "Information loss is highly infectious," Preskill explained at a Caltech seminar several years ago. "It is very hard to modify quantum theory so as to accommodate a little bit of information loss without it leaking into all processes, including ordinary ones that we can study in the laboratory. And there is no reason for the violations to be small."
Cutting even deeper, the paradox exposes a conflict between the two most powerful laws in physics. Black holes are apparently an inevitable consequence of the laws describing gravity and how it shapes space and time. Information conservation seems to be an inevitable consequence of quantum mechanics. Before the two can be put together into a unified theory, something has to give.
"What is at stake is either a weird property of space and time or a weird kind of lawlessness in physics," said Gerard 't Hooft, a physicist at the Institute for Theoretical Physics, at the University of Utrecht in the Netherlands. "There will have to be prices paid for a unified theory, in the sense that neither quantum mechanics nor general relativity will come out of this unaltered."
At first, the notion that information, like energy, cannot be destroyed seems like a dubious pronouncement. Tear out a page from a book and drop it into a fire and the information seems to vanish. After all, the second law of thermodynamics says that an orderly system (like a page arrayed with words and numbers) will inevitably become more and more disordered, increasing in entropy, until it eventually becomes a meaningless mess. In principle, however, information doesn't truly disappear. The markings of ink on the page are preserved in the way the flame flickers and the smoke curls, in the ripples of heat radiating through the air and the pattern of the ashes delicately falling to the ground. The practical difficulties of retrieving this subtle data and restoring the original order give the second law its vaunted power. But in theory one could reconstruct every paragraph. The information is supposed to be out there in the universe somewhere.
But if you drop the book into a black hole, it is seemingly gone without a trace. For a while, physicists were comforted by the thought that at least they knew where the information was hiding, even if they couldn't get at it. But in the mid-1970s, Hawking showed that the situation was even worse:
Quantum mechanics predicts that a black hole inevitably radiates particles along the edge of its horizon. This "Hawking radiation," like the vapor arising from dry ice, eventually carries all the mass away. The black hole evaporates, taking with it everything that ever fell into it.
Why can't one recover the information in the minute fluctuations of the Hawking radiation, as one can with the smoke from a fire? That's ruled out by another tenet: a black hole has no hair. Its radiation is featureless. Whether you throw in Volume 1 of Britannica or Volume 29, the Hawking radiation would be a senseless blur, more meaningless than the snow on a television screen. For there to be a correlation between the ripples of the radiation and the marks of ink on the pages, some kind of signal would have to leave the black hole -- and that could only happen by exceeding light speed.
"If Hawking is right, we're kind of lost at sea," Preskill said. "Quantum mechanics has to be overthrown by something new, but we don't know what is supposed to take its place."
And so a cottage industry has sprung up, churning out theories that, if nothing else, make for good science fiction. Maybe each black hole is like a new big bang, some propose, spawning its own baby universe. What people think of as the whole of creation would be simply one universe among many. To a godlike observer who could behold this entire "multiverse," information would not be lost. It would just flow from one universe to another.
Preskill, for one, finds this solution dissatisfying: "We want to know how to describe physics in the universe that we have access to."
Another possibility is that a black hole never completely evaporates. It shrinks to the size of a subatomic particle and then stops. This remnant particle -- some have called them informons, infotons, and even cornucopions -- would retain all the information about everything, every piece of dust or ray of energy, that ever fell down the hole.
But the implications of this idea are as bizarre as those of a multiverse. Unlike other particles, the tiny remnants would be overwhelmingly complex. Particles like quarks can be simply described by a handful of characteristics (called quantum numbers): mass, charge, spin, and more exotic attributes like parity, isospin, strangeness, charm, and so forth. Black holes are thought to be even simpler. They have only mass, spin, and sometimes charge.
But remnant particles, which must be capable of holding information about everything ever eaten by a black hole of any size, would have an infinite number of parameters. When infinities pop up in physicists' equations, it's often a sign of some kind of pathology -- either in the theory or in the universe.
If there are an infinite number of kinds of remnants, Giddings said, the laws of quantum mechanics predict that the particles would spontaneously pop up everywhere, making the universe a very dangerous place. "When you turn on your microwave," he said, "it would disappear in a catastrophic explosion of black hole remnants."
Hoping for a solution that won't require universes that breed like rabbits, or blow up at the touch of a button, physicists are seeking ways that information can linger at the horizon of a black hole, loitering at the gateway, where it remains accessible to outside observers.
In one version, invented by Leonard Susskind, a Stanford physicist, all the information that ever fell into a black hole is encoded on the horizon as a dense web of hypothetical entities called strings. Some theorists speculate that strings, wiggling in 10 or more dimensions, give rise to all the particles of creation, as well as space and time themselves.
But this theory has an even steeper price. Suppose an observer is reading the Britannica volume as he plunges into the black hole. If the hole were big enough, he shouldn't experience anything unusual until he is crushed by the singularity. Meanwhile, the information would have to exist both on the pages and at the surface of the black hole, violating the notion that things take place at precise locations in space and time. "Suppose the Earth falls into a black hole," Giddings said. "If it's a very big black hole, to the best of our knowledge, we won't really notice it for a long time and can live long and productive lives. Civilizations can rise and fall, all without being significantly affected by the infall."
But from the point of view of an observer outside the black hole, all this history -- past, present, and future -- would be simultaneously displayed in two dimensions on the horizon. And the phenomenon would not necessarily be limited to black holes. Information about everything happening in any large volume of space might be spread out, in two dimensions, on its surface. Some physicists compare this kind of universe to a hologram, in which a three-dimensional image is encoded on a flat surface. "The number of different particles one can have inside a box would not depend on the volume but rather on the surface area of the box," 't Hooft marveled. "What kind of world is that? This is what I would like to know." Answering that, he said, may require radical new ideas about the very nature of space and time.
Throughout all the talk of holographic universes and other exotica, Thorne, a party in the bet against Preskill, holds to the belief that the information falling down a black hole is simply lost. He is optimistic that a new interpretation of quantum theory, under construction by James Hartle, of the University of California at Santa Barbara, and Murray Gell-Mann, of the Santa Fe Institute, will clean up the mess.
But Hawking, on a recent visit to Caltech, told Preskill that he was keeping an open mind. "In my opinion, it could go either way," he said.
Copyright 1998 The New York Times Company
The Living Arts, Science Times, pages B11-12
April 7, 1998