Three Monkeys Online

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Every wave is made of tiny drops. Reflections on Stephen Hawking and the paradox of information loss.

Stephen Hawking was inspired by these results – if rotating black holes could emit radiation, why shouldn’t other types of black holes also emit radiation? He showed, in a famous paper in 1975, that all black holes can emit radiation. He proved that when a field is in a certain state, a distant observer sees (insofar as we can `see’ such phenomena) a bath of particles that is in thermal equilibrium with the black hole. In effect, the black hole’s energy is slowly radiated away until after a certain amount of time it ceases to exist – the black hole `evaporates’.

Fantastic! The general theory of relativity had given us black holes, and now Penrose, Churilov, Starobinsky, Zel’dovich, Unruh, Hawking and many others had lit them up! All nice, clear and beautiful – except for one particularly troubling issue. According to the theory of general relativity, when a star collapses to form a black hole, no information about the star can be recovered except for its mass, angular momentum (effectively, how fast the black hole rotates, if at all) and electric charge, if any. These magnitudes determine the gravitational field of the black hole, its size, the temperature of the thermal radiation and any effect the black hole has on the rest of the universe. Any other information about the black hole or about anything falling into it is non-recoverable by observers outside the black hole; this information is locked inside forever. By information is meant absolutely any data that describes an object: its size, material, colour, velocity, etc. As far as general relativity goes, the information does exist inside the black hole: it is just not accessible. When quantum effects are taken into account, however, eventually the black hole completely evaporates, meaning that the information has somehow disappeared (the thermal radiation emitted only reveals the three magnitudes mentioned above). This problem of loss of information has remained unsolved until – maybe – the 21st of July, 2004.

The 17th conference on General Relativity and Gravitation was held in Dublin from July 18-23, 2004. Shortly before the start of the conference Stephen Hawking asked Curt Cutler in the organising committee if he could give a talk. Hawking said that he had solved the paradox of information loss and that he would explain the results in his talk. How could Cutler refuse? Hawking’s talk aroused great excitement within the media but more skepticism than excitement within the scientific community. The shenanigans surrounding Stephen Hawking’s talk were frowned upon by some at the conference and welcomed by others. In his talk, Hawking argued that information is not, after all, lost in the formation and evaporation of a black hole. Information absorbed by the black hole is somehow returned to a distant observer. In other words, say you wished to throw someone into a black hole (heh heh), hoping to lose him forever…. well unfortunately the black hole will somehow spit him back out at you! The person may not be recovered in the exact form he had when you threw him in, but the black hole will indeed return to you the information about their make-up, so that if you regretted your mischief you could somehow &ldquoreconstruct” the person in his original form. This is an interesting, philosophical turn with respect to the understanding we had so far of quantum black holes, since such information about the make-up of objects that fall into black holes was not contained in the thermal radiation that it was thought until now they emitted.

Hawking’s talk was abstruse but details were conspicuous in their absence. How information is recovered from black holes was not clear to me or to many others present at the talk. Furthermore, in the abstract for his talk, Hawking mentioned that an actual black hole was not really created, but only an apparent one. Strangely, this was not referred to in his talk. Unfortunately the round of questions following the talk did not help to clarify matters either. Hawking, obviously limited in his speech capacity, answered the questions posed by the media whereas his PhD student, Christophe Galfard, who contributed to the above result, answered those posed by the scientists in the audience. The PhD student could only dodge the scientific questions. My understanding of the solution of the paradox as given by Hawking is as follows. According to quantum theory, one must consider both the possibility that black holes exist and also the possibility that no black holes exist in the universe (this is similar to the Schroedinger’s cat paradox where both a universe with a live cat and one with a dead cat are considered). Therefore the contributions from a universe containing a black hole and also from a universe void of black holes must be considered in all calculations. Hawking seemed to argue that the effect on the information from a universe containing a black hole is (mathematically) negligible compared to that from a universe void of black holes. Information would then not be lost, just as if there were no black holes present. It is expected that an article with the full results will soon be published in a scientific journal. We intend to then write another article on reviewing these latest, exciting results in depth. Meanwhile, the waves in the sea keep leaping playfully to and fro, tossed by the contribution of all the tiny drops of water.

This Week’s Finds in Mathematical Physics (Week 207)

Laser Interferometer Space Antenna

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