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The Alternate View
John G. Cramer

HAWKING’S RETREAT

Seattle, the city where I live, teach, and do physics research, is the home of Paul Allen’s new Science Fiction Museum (SFM), located in the Experience Music Project building at Seattle Center, in the shadow of the Space Needle. The SFM is well worth a visit, offering a fascinating display of collected TV and movie props (e.g., Captain Kirk’s Chair from Star Trek), SF memorabilia, and treasured books and manuscripts from the classic works of science fiction. In early December 2005, Stephen Hawking was on a fund-raising tour in celebration of the 800th anniversary of the founding of Cambridge University, where he holds the same Chair once occupied by Isaac Newton. Hawking paid a visit to the West Coast during this tour, and he took the opportunity to make a virtual appearance (by closed-circuit TV) to a gathering at the SFM (including my wife and me) in order to present to the SF Museum the manuscript of a 1976 physics paper which, as he put it, had just entered the realm of science fiction (because it turns out to be wrong).

Hawking’s 1976 paper, “Breakdown of predictability in gravitational collapse,” describes a physics paradox, the apparent loss of information in black holes. Basically, information can be considered to be a form of entropy, and as such is subject to the 2nd Law of Thermodynamics. In classical physics, it is expected that information can be scrambled, but not really destroyed. As Hawking puts it, if you burned an encyclopedia, you could in principle recover the information it contained from a detailed study of the resulting light, smoke, and ashes.

However, suppose you dropped the same encyclopedia down a small black hole, and the black hole subsequently “evaporated” through the emission of Hawking radiation. In that situation, where did the information go? The evaporating black hole emits radiation with a “thermal” spectrum of frequencies (i.e., the same spectrum as that the radiation would have if radiated from a hot object), and it therefore contains no information passed to it from the interior of the black hole. Ultimately, a black hole will evaporate away all of its mass-energy and disappear, so the information that had previously passed into the black hole has apparently vanished without a trace. This is the information paradox described in Hawking’s 1976 paper.

The initial publication of this work created quite a stir in the theoretical physics community. Whole physics conferences were devoted to the subject, at which theorists gave several days of talks and speculated on whether or not information could vanish into a black hole. At the time, Hawking suggested that the interior of the black hole might spawn one or more “baby universes” containing the missing information, and that it might therefore be possible to use a black hole as a vehicle for travel from our universe to other universes.

Some distinguished theorists doubted Hawking’s conclusion that information could vanish without a trace. In particular, in 1997, Hawking and CalTech theorist Kip Thorne made a bet about the predicted information loss with CalTech physicist John Preskill, who works in quantum computation. Here’s the text of their wager:

 

Whereas Stephen Hawking and Kip Thorne firmly believe that information swallowed by a black hole is forever hidden from the outside universe, and can never be revealed even as the black hole evaporates and completely disappears,

And whereas John Preskill firmly believes that a mechanism for the information to be released by the evaporating black hole must and will be found in the correct theory of quantum gravity,

Therefore Preskill offers, and Hawking/Thorne accept, a wager that:

When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.

The loser(s) will reward the winner(s) with an encyclopedia of the winner’s choice, from which information can be recovered at will.

 

Stephen W. Hawking,

 Kip S. Thorne,

John P. Preskill

 

Pasadena, California

6 February 1997

 

Hawking’s new paper on this subject, “Information loss in Black Holes”, was released as a revised preprint on September 15, 2005. It constitutes a de-facto retraction of the 1976 paper. In it, Hawking builds on work from string theory, which has shown a “duality” (a 1:1 mapping) between conformal field theory (in which information is definitely conserved because of a property called unitarity) and string theory (which should include quantum gravity) in “anti de Sitter space” (symmetric space with constant negative curvature) at very large distances from gravitating objects. This connection is interpreted as telling us that if we could only do quantum gravity properly, we would find that no information is lost in black holes.

In his calculations, Hawking pulls several techniques from his bag of tricks, using scattering theory, imaginary time, and semi-classical constraints. Rather than entering the strong-field mess created by quantum gravity, he considers an observer standing off aloofly at infinity, sending a flood of particles and radiation into the heart of the system (where they may or may not form a black hole that evaporates) and observing the particles and radiation that come back to him. In tracking the particles and radiation, Hawking replaces the time variable T by iT, where i is the square root of—1, thereby changing normal 3+1 dimensional space-time into “timeless” 4 dimensional space. In principle, he should then sum over all of the paths that all of the particles might take in this 4-D space, sum the results, and transform back to 3+1 dimensional space-time. Instead, he sums only those paths that are close to semi-classical solutions of the same system, while assuming that contributions from the other more complicated paths can be neglected.

Hawking focuses on two scenarios: (1) the input particles have formed a static black hole, and (2) no black hole is formed, and he demonstrates that it is not possible to determine from the returning particles and radiation which of these scenarios actually happened. He further shows that information is not lost in scenario 2 (not surprising), and that in scenario 1 has differences that decay away exponentially as the particles return to the observer at infinity.

His conclusion from these mathematical gymnastics is that (a) no information is lost, and (b) that the price of this result is that it is not possible for the observer at infinity to tell whether a black hole is formed or not. In the conclusion of the paper, he suggests that the information “tunnels” out of the black hole and appears as subtle correlations between the photons of the emitted Hawking radiation. Hawking’s point seems to be that if there is an uncertainty about whether or not the black hole exists, this uncertainty leaves room for the survival of the information. This might be considered to be a new uncertainty principle, applicable to the unknown formalism of quantum gravity.

Hawking considers that he has now resolved the paradox, and that he has lost the bet. On July 21, 2004 at the 17th International Conference on General Relativity and Gravitation, held in Dublin, Ireland, Hawking presented a copy of the Encyclopedia of Baseball to John Preskill in payment of his end of the wager. To my knowledge, Kip Thorne has not yet conceded his end.

 

How has the physics community received Hawking’s new paper? It’s difficult for me to tell. Following the initial release of the preprint, there have been 16 new papers referring to the work. None of them are particularly critical of Hawking’s work, but neither do they directly build on that work. There have also been two blog-type extended internet comments posted by physicists. Neither is devastatingly critical, but both raise unanswered questions about what Hawking actually did. I would conclude that Hawking may have answered his own questions about information loss in black holes, but he has not satisfied the physics community as a whole. In particular, the actual form taken by the emerging information remains very vague and ephemeral, even if Hawking’s mathematics, taken at face value, insists that the information is actually there.

 

What are the SF implications of this work? First, the widely used SF gimmick of entering another universe through a black hole seems to have had the rug pulled out from under it. Further, the spawning of baby universes by black holes, which has been used in some SF, seems to have also received a dose of strong contraceptive.

It’s perhaps nice to know that the fundamental laws of physics like the 2nd Law of Thermodynamics work even for black holes, and that information cannot be irretrievably lost. But so far, not much of SF depends on either of those ideas.

 

AV Columns Online: Electronic reprints of over 120 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl.washington.edu/av. Preprints referenced below can be obtained at: http:// www.arxiv.org.

 

References:

Hawking’s 1976 paper:

“Breakdown of predictability in gravitational collapse,” S. W. Hawking, Physical Review D14, 2460-2473 (1976).

Hawking’s 2005 paper:

“Information loss in Black Holes,” S. W. Hawking, preprint hep-th/0507171 (2005).

Blog Comments on Hawking’s 2005 Paper:

“Hawking and Unitarity,” Lubos Motl, http://motls.blogspot.com/2005/07/ hawking-and-unitarity.html

“This Week’s Finds in Mathematical Physics (Week 207),” John Baez, http:// math.ucr.edu/home/baez/week207.html