Leonard Susskind is deeply worried about something that in all probability will never happen, at least not until long after the last star in the universe burns out. And he isn’t the only one who’s apprehensive. Susskind, a theoretical physicist at Stanford, and many of his prominent colleagues have lately been pondering the ultimate fate of black holes, those mysterious, light-swallowing chasms in space and time that form, physicists believe, when the cores of massive stars implode. In particular, Susskind and his associates have been considering the very last moments of a black hole’s existence because the death throes of these bizarre non- objects pose an enormous challenge to science.
We’ve encountered a major paradox that nobody knows how to reconcile, says Susskind.
That paradox has its roots in work done by famed British physicist (and Trekkie) Stephen Hawking. In 1974 Hawking wrote an essay titled Black Holes Aren’t Black, in which he surprised the physics community by claiming that some radiation could escape from black holes. This was completely contrary to everything physicists then knew about black holes. After all, the very name black hole reflected the certainty that nothing--not even light--could elude the object’s immense gravitational grasp. Moreover, said Hawking, the slow bleeding of radiation meant that a black hole could eventually evaporate completely, like a snowball in the sun, and vanish from the universe.
There’s not much chance that anyone will ever actually witness the demise of a black hole. Physicists believe that for a very long time to come, all black holes in the universe will continue to take in matter--gas, dust, and even whole stars--faster than they radiate it away. I once figured out how long it would take a black hole produced by a star to evaporate, says Susskind, but it was many times larger than the age of the universe.
Nevertheless, this vanishing act set in the inconceivably distant future keeps physicists like Susskind awake at night because of its thorny theoretical implications. The evaporation is the nasty point, says Susskind. That evaporation, as well as the peculiar nature of what has come to be called the Hawking radiation that black holes emit, seems to contradict one of the most fundamental principles of physics. All present physics is based very heavily on the assumption that you can recover the past from the present--in principle, if not always in practice, says Susskind. But black holes, much to the consternation of physicists, seem to break this rule.
Physicists like to be able to follow processes backward in time. With a particle accelerator, for example, they smash subatomic particles together, then retrospectively piece together details of the collision from the resulting spray of newly produced particles. Similarly, when a supernova explodes, astrophysicists can observe the radiation and gases spewed into space and work back toward an understanding of what happened before the explosion.
But strangely enough, physicists cannot do the same with an evaporating black hole. Like some furtive cosmic criminal, a black hole hides all clues about its past. Where the glowing star dust left in the wake of a supernova practically screams news of its explosive origin, the Hawking radiation streaming from a black hole is mute--it carries no information at all about what’s inside the black hole, or about how the hole formed, grew, and died.
When something falls into a black hole, says Susskind, as far as we know the information that distinguished whatever fell into it is erased. The products of the outgoing radiation appear, as far as we can tell, to be featureless and completely independent of what fell in. Black holes, in other words, sever the bonds between past, present, and future.
Of course, examples of situations in which physicists cannot reconstruct the past abound in everyday life. Burn this magazine, and from the ashes you would never be able to tell that it once contained an article about black holes. In principle, however, if you could monitor the burning process closely enough, you could trace all the molecular interactions that reduced the magazine to ash: the breakdown of the pulp into sooty carbon molecules, for example, or the transformation of some of the paper into gases such as carbon dioxide and carbon monoxide. By running these reactions backward, you could--in principle--recover the magazine. But if you throw the magazine into a black hole where the intense gravity would ultimately shred the pages to atoms, you’d find it impossible to remake the magazine by studying the black hole’s Hawking radiation. Black holes have a confounding humpty-dumpty property that makes it impossible, even theoretically, to put them--or anything that falls into them--back together again once they evaporate.
Hawking radiation gives rise to such woes because of the unusual way it’s produced. When Hawking first announced his theory of radiating black holes, physicists were nonplussed because nothing is supposed to come out of a black hole after falling in--the gravity of the hole is just too overpowering. But Hawking radiation doesn’t come from within the black hole; it erupts from the vacuum of space around but outside the hole, safely beyond the zone from which nothing escapes. So unlike the energy and debris released when a supernova explodes, or the ashes and energy produced when a magazine burns, or unlike even the steam rising from a cup of coffee, Hawking radiation doesn’t have a direct connection with its source. If cups of coffee behaved this way, the steam would materialize far from the cup and would have no unique aroma; the temperature of the steam would have nothing to do with the temperature of the coffee.
This process knows nothing about what’s inside the black hole, says Andrew Strominger of the University of California at Santa Barbara, who has spent much of his career on the enigma of Hawking radiation and evaporating black holes. And since the radiation has no information about what goes on inside the black hole, how can it carry any information out?
That question has been on the minds of physicists ever since Hawking first pointed out that black holes, like old photographs, eventually fade away. Hawking’s reasoning was based on one of the most surprising and counterintuitive discoveries of modern physics--namely, the finding that a vacuum is not empty but is instead a heaving sea of pairs of virtual particles of matter and antimatter. These particles spontaneously wink into and out of existence, annihilating each other in a display of subtle fireworks too feeble for us to notice. How do these particles arise from nothingness? According to quantum mechanics, no system, not even a vacuum, is utterly bereft of energy. Fluctuating fields of energy pervade the void. Sometimes this energy congeals into a pair of particles. For the briefest instant, a particle and its antimatter doppelgänger flash into existence, living on the energy of the vacuum. Normally these virtual particles don’t stick around for long--they mutually annihilate, transformed once more into energy before anyone even notices their existence, and so repay their debt to the vacuum.
But if there is some external source of energy apart from the vacuum--an electric field or a powerful gravitational field--the virtual particles can get enough of an energy boost from the field to survive in the observable universe. They become real particles. In physics, however, there’s no such thing as a free lunch. If one system gains energy, another must lose it.
When particle pairs pop out of the vacuum outside a black hole, they can hijack a minute fraction of the hole’s gravitational energy; the virtual particles become real by using energy that had been warping the space around the black hole. With this extra energy, the particles escape sinking immediately back into the restless void. The borrowed energy not only imbues the virtual particles with mass but also gives them a welcome- to-the-real-world kick of momentum: the particles are born on the fly, like bees boiling from a hive, with a random assortment of trajectories. Some of these trajectories point toward the black hole, some away. Usually the black hole captures both particles, and their energy simply returns to the hole. In that case there is no net loss of energy from the black hole. But occasionally, Hawking showed, some of these vacuum-spawned particles, born outside the black hole’s point of no return, have enough energy and are aimed in the right direction to flee into space, separated from their anti- partners. When these particles escape from the black hole, they take with them some of the black hole’s energy. Ever since Einstein’s theory of relativity, physicists have realized that mass and energy are interchangeable, so the black hole’s energy loss effectively translates into a loss of mass, and the hole shrinks.
For the present, all black holes are sucking in new material much faster than they are radiating, and they will do so for countless eons. Before a black hole can begin to shrink, the hole has to be hotter than its surroundings, just as a red-hot coal won’t cool until removed from the fire. Hawking radiation, however, is incredibly tepid, with a temperature just a few millionths of a degree above absolute zero. Even interstellar space, not usually thought of as particularly toasty, has a background temperature far higher than this, about 3 degrees Celsius above absolute zero, a relic of the universe’s fiery birth. But as the universe continues to expand and cool, space could conceivably--in a bleak, dark future some 1069 years hence--be chilly enough for black holes to evaporate.
Assuming the universe itself lives that long, when a black hole finally does vanish, theorists believe, it will release a flood of high- energy Hawking radiation. The amount of radiation depends on how the gravitational field around a black hole is changing in time and space. The more rapid the change, the greater the flow of Hawking radiation. According to the frequently counterintuitive precepts of general relativity, black holes and other massive objects dent the very fabric of space, much as a reclining sumo wrestler would depress a water bed. When a black hole is still very large, its gravitational field creates a relatively smooth depression across a vast region of space-time. Fluctuations in such a field--think of them as randomly generated ripples in the water bed--are barely noticeable, and Hawking radiation just trickles out.
But as the hole shrivels--replace the sumo wrestler with a jockey--the fluctuations become more pronounced relative to the reduced patch of space-time distorted by the hole’s gravity; in the smaller depression, a ripple across the water bed now becomes a wave. And like waves in the ocean tossing flotsam onto a beach, these energy fluctuations give virtual particles the extra oomph they need to leap into existence. As the hole gets smaller, the Hawking radiation steadily increases; in the end, it increases dramatically.
In fact, just before it disappears, a black hole will no longer be black at all. Instead it will be much hotter than the surrounding space, radiating energy at a tremendous rate. As you get down to the final second, the black hole would have an utterly enormous amount of power, says Don Page, a close friend of Hawking’s and a physicist with the Canadian Institute for Advanced Research. It might have as much power as a supernova for a very brief time. Very crude estimates indicate that if the final second of a black hole were spent inside the moon, it would have enough energy to blow the moon apart.
Whether the vaporization of a black hole could sunder a moon remains speculation for the far distant future. But back in the present, the issue of black hole evaporation has already riven the physics community into three distinct and rather distant camps. Some physicists, including Hawking, believe that the information contained in a black hole is simply lost forever when the hole evaporates and that our inability to understand information loss is a symptom of a fundamental flaw in modern physics. At least as many physicists, including Susskind, believe that the information is lurking somewhere in the radiation and could be retrieved if we could only figure out how to decipher it. Still a third group believes the information is stashed away in the remnants of an evaporated black hole but is forever inaccessible.
Hawking is somewhat nonchalant about the whole issue. In a telephone conversation punctuated by ten-minute pauses between question and answer (Hawking, physically wasted by Lou Gehrig’s disease, laboriously spells out his concise replies using a computer attachment that he controls with two fingers; the computer then generates a slightly metallic sounding synthetic voice), he had this to say: I don’t think the loss of information is a great problem. It just means we have to formulate quantum mechanics in a rather more general way.
Hawking, it seems, is being wickedly understated about the import of what he has wrought. Other physicists say information loss is the most serious theoretical problem in physics. And as for altering quantum mechanics, it’s anything but a trivial issue; Hawking himself attempted to do so and failed. He tried to get around the paradox by showing that information loss is simply a fact of life throughout the universe, one we have overlooked. Information could be destroyed regularly, he proposed, although perhaps only in practically undetectable homeopathic-size doses. How would this happen? As if having virtual particles pop out of the vacuum wasn’t bizarre enough, Hawking suggested that microsize black holes could also burst out of--and back into--the void, sometimes taking information with them.
For all their seeming otherworldliness, these mini-black holes-- and their larger cousins, for that matter--are disarmingly simple objects. Or as retired Princeton physicist John Wheeler, the man who coined the name black hole, once put it: Black holes have no hair. What this means is that black holes are very easy to describe. Once you know a black hole’s mass, spin, and a few other essentials, the portrait is complete. They are far less complex than stars, planets, or people--more akin to elementary particles in their simplicity. For that reason, their emergence from the vacuum isn’t as preposterous as it sounds.
Just as electrons, photons, and other particles are forever jumping in and out of the vacuum, the laws of quantum mechanics would imply that small black holes can jump out of the vacuum as well, says Andrew Strominger. There are good, sound reasons to believe that this process should be extremely rare. But there are not good reasons to believe that it should never occur. The concern is that when a small black hole jumps in and out of the vacuum, during its brief existence it may gobble up some information and disappear. This would be a tiny effect. Nevertheless, one would think that black holes jumping in and out of the vacuum at random would lead to tiny violations of physics in some processes. Physicists, in other words, would be wrong in assuming that they could trace any given process backward in time. If Hawking is right, a small black hole sitting in a cup of coffee might surreptitiously inhale some molecules before they could escape as steam.
As far back as 1983 Leonard Susskind and others were taking a hard look at Hawking’s proposal for fixing the paradox, and they found serious flaws. What we tended to find, Susskind says, was that anything that could destroy information would at the same time destroy energy conservation. And destroy it in a brutal way. Information, he notes, doesn’t exist independently from energy; the two are intertwined. In a Morse code message, for example, electrons carry energy and information along a wire. In a diamond, the interaction of the carbon atoms gives the diamond its strength, shine, and other discernible qualities. Even thinking requires an expenditure of chemical energy.
If information leaves the universe completely, it would have to be accompanied by energy to do so, says Strominger. Now we have energy leaving the universe. That is very problematic.
To date, no one, including Hawking, has come up with a theory in which information could be lost without violating the principle of energy conservation. Indeed, some physicists suspect that information cannot vanish from the universe. Gerard ’t Hooft, an eminent Dutch physicist, is one of them. For most of the past decade ’t Hooft has been trying to crack the problem, so far without luck. He belongs to the camp that believes the Hawking radiation does somehow encode information about a black hole’s history. I think it is very likely the information would simply come back disguised in the Hawking radiation, he says. It would be very difficult in practice to recover the information, but in principle it would be there. In that way, a black hole would not behave fundamentally differently from a bucket of water. If you let the water evaporate, you wouldn’t say that information is really retained, but in a theoretical sense the information is not thrown into nothing--it is disguised in the water vapor particles that carry it away.
The stumbling point again is that the Hawking radiation doesn’t come from the black hole in the way water vapor comes from the bucket. So, as Strominger asks, how could it contain any information? The answer may be, says ’t Hooft, that Hawking’s theory about black hole radiation is incomplete--that in tackling an extremely difficult problem, Hawking was inevitably forced to simplify parts of his calculations. Specifically, ’t Hooft says, Hawking ignored possible interactions between material falling into the hole and the escaping Hawking radiation.
Roughly speaking, says ’t Hooft, this is the approximation Hawking made: when you compute how many particles are being emitted by the black hole, you ignore for the time being that these particles also interact with one another. And, what I think is very important, we also ignore the fact that they may interact with the particles that fall into the black hole. These possible interactions--they could be gravitational, electromagnetic, or any other kind of encounter known in physics--would be extremely difficult to detect in practice, ’t Hooft says, but if theorists could show that the Hawking radiation does interact with material falling into a black hole, and carries information about those interactions back out into space, then the information paradox would be at least circumvented, if not solved.
Frank Wilczek, a physicist at the Institute for Advanced Study at Princeton, agrees with ’t Hooft, at least in part. It’s clear that Hawking’s is not an exact calculation. It needs significant corrections. But exactly how significant those corrections are and what qualitative changes they might make in the radiation are not so clear, because they’re very difficult to calculate. Hawking, he jokes, only did the easy part.
Strominger disagrees completely with both Wilczek and ’t Hooft. Like Hawking, he doesn’t think any information comes out of a black hole. One can always say that one simply doesn’t believe the approximations, he says. But can they write down some equations and show me the information coming back out? Rather, Strominger believes that the information is not necessarily lost but not necessarily retrievable, either; instead, it could be preserved in a way that would keep it locked away forever.
Strominger can afford to be a little cocky. In February 1992 he was one of four authors of a paper that, if nothing else, at least gave physicists interested in the problem something new to argue about after nearly 20 years of fitful progress.
That paper, titled Evanescent Black Holes, managed to simplify greatly some aspects of black hole evaporation. Rather than attempting to model a black hole’s demise in all its messy complexity, the four physicists came up with a two-dimensional model that contained many of the essential features of the real thing. Cutting a problem down to size in this way is a common strategy among theorists as a first step toward a real solution. Most of the discussions before had been in the context of the formation and evaporation of large, macroscopic black holes, says Strominger. That’s a technically very difficult problem. You couldn’t really write down equations that described that. And physicists don’t do very well without equations.
In the two-dimensional model, Strominger and his colleagues assumed that at some point a black hole might stop evaporating. This assumption is not entirely arbitrary. Eventually, says Strominger, the black hole shrinks to a size at which the laws of physics are not understood. Although the black hole might well continue evaporating until it finally disappears, the four physicists wanted to explore an alternate ending. It’s a logical possibility that the black hole might stabilize, and we should investigate the consequences of that for the information puzzle, says Strominger.
This stable mini-black hole, which the physicists call a remnant, would be smaller than a proton but about 10 billion billion times more massive. The remains of everything that fell into the original black hole would rest inside these tiny mausoleums, albeit in a very dense, compressed form. The information is literally sitting there, says Strominger, describing the material left inside a remnant. It might have gotten a little squished up by gravitational forces, but the picture is that it’s literally sitting there. The catch is, no one would be able to get at this material and reconstruct its past.
Although the remnant idea found considerable support, it also came under some heavy fire. To quote Gerard ’t Hooft, says Susskind, ‘I will never think about remnants except with the remnants of my intelligence.’
One of the major sources of resistance was the inevitable conclusion that since no two black holes would consume the same diet of gas, radiation, and stars, every black hole would leave behind its own unique remnant, resulting in a potentially infinite variety of remnant particles. And the laws of quantum mechanics say that these submicroscopic remnants, too, could pop out of the vacuum. The trouble with an infinite number of types of remnants, say remnant critics, is that the probability that they will materialize out of the vacuum also becomes infinite. They would appear everywhere, all the time. Basically the universe as we know it would never have come into existence, says Strominger, explaining the reasoning of his critics. Instead of creating mostly ordinary elementary particles at early stages of the universe, the universe would have created mostly remnants.
In response to these objections, Strominger and others, including Rutgers physicist Tom Banks, who worked with Susskind in critiquing Hawking’s attempt to modify quantum mechanics, wrote a second paper, with a more detailed description of remnants, which appeared this past May. Remnants, the paper argues, are in a sense very much like protons, neutrons, and other familiar particles--simple, nondescript objects. Remnants all have the same irreducible mass and size, weighing in at about a hundred-thousandth of a gram (an enormous mass for something smaller than an atom). Seen in this light, remnants are no more likely to swarm out of the void than any other particle in the subatomic bestiary.
Remnants are also so massive, the paper goes on to say, that they would, like the miniature black holes they are, distort space-time. So the researchers have renamed their remnants, calling them cornucopions to suggest the infinitely long, hornlike shape they believe remnants would have. They are like a drain in a sink, says Strominger. From the outside, the boundary of the drain is just a small circle. But if you look at the volume inside, you’ve got a lot of room. Trapped within the unlimited volume of the horn would be all the information about whatever fell into the original black hole.
Does the remnant idea solve the problem of information loss? The infinite interior of the remnant is still inaccessible; nothing will ever come out of it. Is it simply a comfort to physicists to know that the information is there? Strominger and Banks have markedly different opinions.
Now we’re really getting into questions that we don’t know the answers to, says Strominger, who doesn’t see much of a difference between information being lost forever or stored beyond reach in a remnant. How do we formulate physics in a context where information can be effectively lost like this? Those are questions we don’t understand right now.
Banks, on the other hand, says the important thing is that information is not truly lost. It’s there somewhere in the universe, he says, so we don’t have to, as Hawking originally suggested, make a new theory in which information is somehow lost in a fundamental way. What’s happening here is that space is stretching, and I’m getting new places for information to go, but information is not disappearing. It’s just getting to a place where I can never communicate with it anymore.
Although the remnant advocates have won some converts, a fair number, including Susskind, ’t Hooft, Wilczek, Page, and others, are still skeptical. Many of them have a gut feeling that the issue of information loss won’t be resolved until someone finds a way to achieve a goal that has eluded every physicist since Einstein: the unification of quantum mechanics and general relativity into a seamless whole. Such a theory would join the realm of the very small, described by quantum mechanics, with Einstein’s grand-scale vision of how gravity shapes the cosmos. One of the reasons so many physicists are intrigued by evaporating black holes is that in grappling with the dilemma, they hope they may just succeed where everyone else has failed. Black holes, with their relativistic distortions of space- time and quantum-style evaporation radiation, look like good places to search for connections between the two theories.
Einstein was always thinking about falling elevators, says Susskind, referring to a series of thought experiments in which Einstein ruminated on the nature of gravity. It wasn’t because he was interested in the Otis elevator company. It was a way of focusing his attention on a physical phenomenon. This is the same thing. Thinking about black holes and their evaporation is way of focusing on a phenomenon that could potentially infect all of physics. So by thinking about this problem, and perhaps sorting it out, we may see ways of making progress in formulating a quantum theory of gravity.
Whatever the outcome of those attempts, the stakes in this theoretical game are very high. If the Hawking radiation is really featureless, it means you can’t reconstruct what went into the black hole from what came out, says Frank Wilczek. And fairly basic principles of physics say that there is a unique connection between the future and the past. It’s even more than just physics. It would be a very basic blow, in my opinion, to the whole philosophy of science if there weren’t a unique connection between the future and the past.
For now, physicists will continue to squabble about just how much, if at all, present theories need to be revised. Undoubtedly a fresh bout of arguments will crop up once the scientific community has had more of a chance to respond to the idea of cornucopions. And what does the man who is largely responsible for creating all these problems think about the likelihood of a solution?
One is always a long way from solving a problem until one actually has the answer, says Hawking. But we may find it anytime. My guess is we will solve it soon.
