Betting on whether data disappear down black holes

Can the universe keep a secret? Suppose you realize there’s incriminating evidence in your diary. You could shred the diary to bits, but a tenacious detective could reassemble them into the original document. You could burn your diary, but physicists will tell you that—at least in theory—the ash, carbon dioxide, and other products of the combustion provide all the information needed to reconstruct every page. Desperate, you resort to the ultimate solution: Drop the diary into a black hole. Surely, your secret will be safe there.

Until recently, the celebrated University of Cambridge cosmologist Stephen J. Hawking would have agreed with you. But after nearly 30 years, Hawking has reversed his opinion. Even black holes can’t destroy information, he announced in July at the International Conference on General Relativity and Gravitation in Dublin.

This change of heart aligns Hawking with most physicists, who long ago adopted as a sacred and an immutable law the concept that information, like energy, is never destroyed. But mind-bending paradoxes emerge when scientists try to figure out what happens when information falls into a black hole.

According to one perspective, information seems to be in two places at once.

Understanding these paradoxes isn’t merely an esoteric undertaking, says theorist Andrew Strominger of Harvard University. With the answer to the black hole riddle, scientists will be better equipped to solve one of the most challenging problems in all of physics: tying together quantum theory, which rules the domain of the very small, and general relativity, the highly successful theory of gravity developed by Albert Einstein in 1915.

The theories have remained stubbornly estranged, although most scientists hold that the two ought to be intimately connected. Many researchers are convinced that delving into the abyss of black holes could lead to a unification of gravity and quantum theories.

In fact, they’ve been betting on it.

Universal stakes

Back in 1997, Hawking and cosmologist Kip Thorne of the California Institute of Technology in Pasadena bet another Caltech theorist, John Preskill, that if an encyclopedia got sucked into a hole, the information in those volumes would vanish forever.

Why anyone would think otherwise would appear to be puzzling. Drop a book through a black hole’s outer edge, known as the event horizon, and, according to Einstein’s theory of gravitation, it never gets out. The law of information conservation, however, would still hold. Although inaccessible, the information would be preserved.

That would be just fine if black holes were eternal, serving as permanent repositories for the information. The dilemma is that black holes aren’t completely black. They emit small amounts of radiation, Hawking reasoned in 1975, and, therefore, they slowly evaporate. A black hole the size of the sun would take 1066 years to disappear. That’s a very, very long period, but not an eternity. So, Hawking deduced that information would disappear with the black hole.

“Hawking claimed to show that the universe as a whole lost information as a result of black hole decay,” says theorist Tom Banks of the University of California, Santa Cruz.

Hawking came to this view when he introduced some of the elements of quantum theory to black hole physics. According to quantum theory, the vacuum of space isn’t empty but seethes with pairs of elementary particles winking in and out of existence. One partner in each pair has negative energy, which keeps that particle gravitationally bound to the black hole, while the other has positive energy, which gives it enough oomph to escape from a black hole.

If such pairs come into existence just outside the event horizon, sometimes the negative-energy particle will fall into the hole, while the particle with positive energy will remain outside and eventually escape, Hawking realized.

From the point of view of a distant observer, the black hole’s event horizon radiates positive-energy particles, a phenomenon known as Hawking radiation. However, these particles seem to carry no information about the contents of the black hole.

Now, consider the negative-energy particles that the black hole has absorbed. According to general relativity theory, mass and energy are equivalent. Therefore, a black hole that absorbs a negative-energy particle loses mass. If there are no nearby planets or other detritus to nourish it, a black hole absorbing negative-energy particles will eventually vanish.

When the black hole fades out of existence, so too does any information it might have contained.

If information can be destroyed this way, it would violate a notion at the heart of all theories of physics, including quantum theory and general relativity. Conservation of information, it turns out, is tantamount to saying you can always run a film backward. If you know absolutely everything about an event—say, the collision of two cars—you can always reconstruct their past, what paths the cars were on before they struck. Similarly, tracing the history of the universe from its current contents is, in theory, always possible.

So, if Hawking were right in his original conjecture that information could vanish with a dying black hole, physicists would have to cast aside one of the cornerstones of their field.

Hawking seems relieved by his reversal of opinion. “It is great to solve a problem that has been troubling me for nearly 30 years,” he said at the Dublin meeting.

At the conference, he conceded his 1997 bet by presenting Preskill with a baseball encyclopedia. Although Preskill graciously accepted the book, he told Science News he won’t consider the bet decided until Hawking fully explains the physics behind his reversal.

Even Thorne, Hawking’s betting partner, is reserving judgment. He says that mathematical lines of evidence also lead to the idea of information loss.

“I’m not going to sign off on the bet until I’m convinced, through a mixture of trying to understand what’s going on and seeing the reaction of other people,” says Thorne.

Presumably, the argument will be elucidated in a paper that Hawking is now preparing, Preskill and other physicists say.

Even when Hawking does spell out his reasoning, physicists may still be left with the puzzle of how information from an evaporating black hole manages to survive or how it could be reconstructed. Piecing together the history of the universe is turning out to be far more difficult than reconstructing a traffic accident from evidence at the scene.

Surface secrets

How might information avoid being lost from a fading black hole? It would have to be carried by the Hawking radiation, which is the only stuff that travels away from the hole. But Hawking radiation originates just outside the event horizon, not inside the hole. How can radiation from outside the black hole contain information about what fell in?

“That’s the puzzle,” says Strominger. “This is exactly what we don’t understand.”

Preskill agrees. “If we try to follow the process of black hole evaporation from beginning to end from the physics we know, we reach a contradiction,” he notes.

“This kind of contradiction or paradox has been a recurring theme in physics,” says Strominger. “Every major advance in our understanding of the nature of the universe has been preceded by a contradiction of this type. And so instead of being upset by this [paradox], it’s very exciting.”

To help solve the black hole–information conundrum, Strominger and other physicists are turning to a branch of quantum theory known as string theory. String theory postulates that every particle, instead of being represented as a point, can be thought of as a tiny, vibrating string.

In one picture emerging from string theory, the essential properties of an object can be deduced entirely from the object’s surface, just as the full shape of a three-dimensional object can be captured in the patterns imprinted on a flat, two-dimensional hologram.

This holographic view of the universe was first proposed a decade ago by Gerard ‘t Hooft of the University of Utrecht in the Netherlands and has been further developed by other scientists, including Lenny Susskind of Stanford University.

String theory suggests that nothing ever actually falls into a black hole. Material is instead smeared out around the horizon. In this framework, the interior of a black hole is not only inaccessible to someone who stays on the outside but is also one enormous illusion.

If nothing falls into a black hole, there’s no paradox. Hawking radiation can carry information from the premises because the information never went into the black hole in the first place.

There’s one concrete calculation suggesting string theory and the holographic principle are relevant to understanding the flow of information at black holes. Strominger and Cumrun Vafa of Harvard have used string theory to calculate the entropy of a black hole, a measure of its information content. There’s a perfect match between the result of that operation and the entropy that Hawking calculated by using more-traditional concepts of quantum theory 3 decades ago, before string theory was developed.

The matching numerical values of entropy are encouraging, but another feature of the calculations is even more tantalizing. In both cases, the entropy is related only to the surface area, or event horizon, of a black hole. The black hole’s volume, or any other property of its interior, is irrelevant. This implies that the information is at the black hole surface rather than inside.

“In string theory, we’ve found a description of a black hole which looks very different” from the one described by general relativity, says Strominger.

What’s still missing, he says, is the Rosetta stone that would translate the language of string theory into the traditional view of a black hole as a gravitational gobbler. Researchers have yet to discover a one-to-one correspondence between submicroscopic strings and these massive cosmological beasts.

Toward a resolution?

The seemingly bizarre idea that you can learn everything about a black hole by studying only its surface has its roots in what physicists call a thought experiment.

Consider the viewpoint of an observer outside a black hole, who sees someone moving toward the event horizon and therefore seems doomed to fall in. The observer never actually sees the person passing through the event horizon into oblivion. That’s because the gravity at the event horizon, which warps space-time severely, causes clocks to tick ever more slowly, ultimately freezing time altogether.

Light signals sent to the distant observer from the black hole voyager, therefore, get shifted to longer and longer wavelengths until they can no longer be detected. The final image the observer receives is of the doomed traveler smeared out, or flattened, around the event horizon. It’s as if there’s no interior to the black hole.

Preskill and other scientists take this scenario a step further. They consider the doomed voyager, who sees a different picture. He rushes right through the horizon without any ill effects. From his point of view, anything that crosses the event horizon with him—whether it’s an encyclopedia or a planet—proceeds into the black hole, only to be torn apart later by the immense gravitational field within.

“This extreme difference between the description of the same process in two different frames of reference is responsible for many of the bizarre and amazing properties of black holes,” says Preskill.

The outsider says that all the information resides on a black hole’s surface. The insider says that information lies inside the hole, says Susskind. “But it’s the same information,” he notes.

One way out of the morass, according to Susskind, is to accept that no one can ever simultaneously describe a black hole in terms of what an insider and an outsider see. “You get into trouble when you try to reconcile the two perspectives,” he notes.

He and two colleagues developed the idea a decade ago that the perceptions of black hole insiders and outsiders must be considered separately, never at the same time. The notion, Susskind points out, is reminiscent of quantum theory’s Heisenberg uncertainty principle, which holds that it’s impossible to know at the same time the precise position and momentum of an object.

Since the insider and the outsider can never communicate, maybe it’s OK that the same data can exist in both places at the same time, Susskind suggests. That would imply that information somehow gets copied for free. New applications of quantum theory might help solve the puzzle, he says.

“One of the mistakes that has been so pervasive is to assume that ‘quantum’ [only] means small,” says Susskind. In past decades, some scientists found it counterintuitive that quantum mechanics could wield its influence over large space-time distances, he notes. But string theory suggests that the quantum universe becomes important “when you look at the world through the lens of a black hole horizon,” says Susskind.

“When theories that we use to describe nature lead us to incompatible or self-contradictory statements, we’re faced with a great challenge . . . and a great opportunity,” says Preskill.

References:

Hawking, S. 2004. The information paradox for black holes. 17th International Conference on General Relativity and Gravitation. July 18-23. Dublin. Transcript and commentary available at http://math.ucr.edu/home/baez/week207.html.

Further Readings:

Hawking, S.W. 1976. Breakdown of predictability in gravitational collapse. Physical Review D 14(Nov. 15):2460–2473. Abstract available at http://prola.aps.org/abstract/PRD/v14/i10/p2460_1.

Preskill, J. 1994. Black holes and information: A crisis in quantum physics. Caltech Theory Seminar. Oct. 21. Transcript available at http://www.theory.caltech.edu/%7Epreskill/talks/blackholes.pdf.

For the exact wording of the bet Hawking and Thorne made with Preskill in 1997, go to http://www.theory.caltech.edu/%7Epreskill/info_bet.html.

Information from Stephen Hawking’s Web site about why he conceded the bet can be found at http://www.hawking.org.uk/info/iindex.html.

To read more about the black-hole bet, go to John Preskill’s Web site at http://www.theory.caltech.edu/~preskill/jp_24jul04.html.

Sources:

John Preskill

Division of Physics, Mathematics, and Astronomy

California Institute of Technology

Pasadena, CA 91125

Andrew Strominger

Harvard University

Department of Physics

17 Oxford Street

Cambridge, MA 02138

Leonard Susskind

Department of Physics

Stanford University

Room 332

Varian Physics Building

382 Via Pueblo Mall

Stanford, CA 94305-4060

Gerard ‘t Hooft

Institute for Theoretical Physics

Universiteit Utrecht

Leuvenlaan 4

3584 CC Utrecht

Netherlands

Lárus Thorlacius

Science Institute

University of Iceland

Dunhaga 3

IS-207 Reykjavik

Iceland

Kip S. Thorne

California Institute of Technolgy

Mail Stop 130-33

Pasadena, CA 91125

Cumrun Vafa

Harvard University

Department of Physics

17 Oxford Street

Cambridge, MA 02138

Ron Cowen, Science News

http://fairuse.stanford.edu/Copyright_and_Fair_Use_Overview/chapter9/index.html

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