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The Holes Are Defined by the String Edward Witten

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The Holes Are Defined by the String Edward Witten AND VIEWS The holes are defined by the string Edward Witten Must general relativity finally bow to quantum mechanics? Calculations that describe black-hole properties using collections of superstrings have gone some way towards resolving one of the most vexing puzzles in physics. AccoRDJNG to Einstein's theory of general made it possible for astrophysicists to When one tries to think about black relativity, if a sufficiently large mass col­ identify candidate black holes both in our holes quantum mechanically, one runs lapses into a sufficiently small space, Galaxy and in distant quasars. into many difficulties. At the most basic a black hole is formed. To the extent Black holes are also a fascinating test level, quantum-mechanical unitarity (the that quantum-mechanical effects can be case for trying to combine quantum me­ requirement that the probabilities of all neglected, a black hole has the property chanics and general relativity. Physicists possible outcomes add up to one) does that nothing, not even a light ray, can have found it vexingly difficult to unify, or not permit the existence of an object that escape from it. That explains the name: an even reconcile, these two theories. The can absorb matter but cannot emit matter. isolated black hole looks literally like a problems are hard to explain in non-techni­ This particular question was addressed black hole in space, from which no light cal terms, but they are definitely there: the 20 years ago by Stephen Hawking, who emerges. delicate constructions that are required showed that, quantum mechanically, an Although classical black holes do not in quantum field theory (the most fully isolated black hole is not completely emit anything, they absorb anything that known expression of quantum mechanics) black, but emits radiation at a rate which comes near enough. When an object falls seem incompatible with the requirements is proportional to Planck's constant h into a black hole, its entire rest energy - of general relativity. The contradiction be­ ( and so the rate is zero in the absence of Einstein's E=mc2 - can potentially be re­ tween quantum mechanics and general rel­ quantum mechanics) 1• leased in the form of radiation, which can ativity - which together are the basis for Following earlier heuristic work by escape and be seen by a distant observer. what we know of the fundamental laws of Jacob Bekenstein2, Hawking's discovery Therefore, although an isolated classical nature - is generally seen as a central led to the idea that a black hole has a black hole is altogether dark, if a black challenge in physics, to say the least. Physi­ certain temperature and entropy at the hole is embedded in a suitable astrophysi­ cists have sought to meet this challenge quantum-mechanical level (generally, en­ cal environment, the region just outside through the new framework of string tropy is a measure of disorder; in standard the hole can shine brilliantly. This has theory, about which we will say more later. quantum systems, it is the logarithm of Circling the inverse square ONE bit of physics that almost everyone created by the inverse square law) of role analogous to that of the quantum knows is that the force between two Feynman, Schwinger, Tomonaga and uncertainty principle, and avoids the ,-2 electric charges, or two masses, follows Dyson. Finally, by about 1950, a satis­ singularity. As a result, gravity becomes an inverse square law. That is, if they factory account of atoms could be made, compatible with quantum mechanics. are separated by a distance r then including the effects of both quantum In fact, when physicists began, more the force between them is proportional mechanics and special relativity. than 25 years ago, to develop string to r· 2 • A natural hope was that having un­ theory, they unearthed a remarkably If one takes the inverse square law derstood how to treat the r -2 force be­ rich and subtle structure and learned to seriously, one must face the fact that tween electric charges, one could treat their amazement that gravity is required the force becomes infinite as r goes to the r · 2 gravitational force similarly. That for the consistency of string theory. So zero. Early in this century, physicists re­ hope was frustrated: because of the one may fairly say that pre-string quan­ alized that a classical electron orbiting nonlinear mathematics used in general tum theory makes gravity impossible, an atomic nucleus should emit electro­ relativity, the new concepts that en­ whereas string theory makes it neces­ magnetic radiation and spiral into the abled physicists to cope with electro­ sary. nucleus in a finite time, driven by the magnetism fail dismally for gravity. Even after 25 years, the understand­ singularity of the r · 2 force at small r. And so we face a contradiction be­ ing of string theory is in its infancy, and From grappling with this contradic­ tween quantum field theory and general surprises are the norm. It was believed tion, quantum mechanics was born. By relativity similar to the contradictions for many years that there were five pos­ the mid-1920s, the Schrodinger equa­ that led to quantum mechanics. Many sible string theories, prompting the tion gave a sensible description of physicists believe that this contradiction question: if one of these theories de­ atoms at the non-relativistic level. The contains the seeds of an upheaval as scribes our Universe, who lives in the quantum uncertainty principle effec­ profound in its own way as the discov­ other four worlds? But recently it has tively smeared out the electron and pre­ ery of quantum mechanics or relativity. become clear that those five string vented it from seeing the singularity. String theory is the one concrete pro­ theories are limiting cases of one majes­ Extending this success to take account posal for a new framework in which the tic and still-mysterious theory. This of special relativity was more difficult. It r · 2 force of quantum gravity is tamed. theory, which is sometimes called M­ was necessary to develop quantum field In string theory, elementary particles theory (according to taste, M stands for theory, quantum electrodynamics and are re-interpreted as small loops of vi­ magic, mystery, marvel or membrane) is the renormalization theory (a systematic brating string. Their 'stringiness' gives a seen by many as a likely candidate for a procedure for subtracting the infinities new kind of uncertainty, which plays a complete description of nature. E. W. NATURE · VO L 383 · 19 SEPTEMBER 1996 215 .
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