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Monday, May 4, 2009

Reading List: The Black Hole War

Susskind, Leonard. The Black Hole War. New York: Little, Brown, 2008. ISBN 978-0-316-01640-7.
I hesitated buying this book for some months after its publication because of a sense there was something “off” in the author's last book, The Cosmic Landscape (March 2006). I should learn to trust my instincts more; this book treats a fascinating and important topic on the wild frontier between general relativity and quantum mechanics in a disappointing, deceptive, and occasionally infuriating manner.

The author is an eminent physicist who has made major contributions to string theory, the anthropic string landscape, and the problem of black hole entropy and the fate of information which is swallowed by a black hole. The latter puzzle is the topic of the present book, which is presented as a “war” between Stephen Hawking and his followers, mostly general relativity researchers, and Susskind and his initially small band of quantum field and string theorists who believed that information must be preserved in black hole accretion and evaporation lest the foundations of physics (unitarity and the invertibility of the S-matrix) be destroyed.

Here is a simple way to understand one aspect of this apparent paradox. Entropy is a measure of the hidden information in a system. The entropy of gas at equilibrium is very high because there are a huge number of microscopic configurations (position and velocity) of the molecules of the gas which result in the same macroscopic observables: temperature, pressure, and volume. A perfect crystal at absolute zero, on the other hand, has (neglecting zero-point energy), an entropy of zero because there is precisely one arrangement of atoms which exactly reproduces it. A classical black hole, as described by general relativity, is characterised by just three parameters: mass, angular momentum, and electrical charge. (The very same basic parameters as elementary particles—hmmmm….) All of the details of the mass and energy which went into the black hole: lepton and baryon number, particle types, excitations, and higher level structure are lost as soon as they cross the event horizon and cause it to expand. According to Einstein's theory, two black holes with the same mass, spin, and charge are absolutely indistinguishable even if the first was made from the collapse of a massive star and the second by crushing 1975 Ford Pintos in a cosmic trash compactor. Since there is a unique configuration for a given black hole, there is no hidden information and its entropy should therefore be zero.

But consider this: suppose you heave a ball of hot gas or plasma—a star, say—into the black hole. Before it is swallowed, it has a very high entropy, but as soon as it is accreted, you have only empty space and the black hole with entropy zero. You've just lowered the entropy of the universe, and the Second Law of Thermodynamics says that cannot ever happen. Some may argue that the Second Law is “transcended” in a circumstance like this, but it is a pill which few physicists are willing to swallow, especially since in this case it occurs in a completely classical context on a large scale where statistical mechanics obtains. It was this puzzle which led Jacob Bekenstein to propose that black holes did, in fact, have an entropy which was proportional to the area of the event horizon in units of Planck length squared. Black holes not only have entropy, they have a huge amount of it, and account for the overwhelming majority of entropy in the universe. Stephen Hawking subsequently reasoned that if a black hole has entropy, it must have temperature and radiate, and eventually worked out the mechanism of Hawking radiation and the evaporation of black holes.

But if a black hole can evaporate, what happens to the information (more precisely, the quantum state) of the material which collapsed into the black hole in the first place? Hawking argued that it was lost: the evaporation of the black hole was a purely thermal process which released none of the information lost down the black hole. But one of the foundations of quantum mechanics is that information is never lost; it may be scrambled in complex scattering processes to such an extent that you can't reconstruct the initial state, but in principle if you had complete knowledge of the state vector you could evolve the system backward and arrive at the initial configuration. If a black hole permanently destroys information, this wrecks the predictability of quantum mechanics and with it all of microscopic physics.

This book chronicles the author's quest to find out what happens to information that falls into a black hole and discover the mechanism by which information swallowed by the black hole is eventually restored to the universe when the black hole evaporates. The reader encounters string theory, the holographic principle, D-branes, anti de Sitter space, and other arcana, and is eventually led to the explanation that a black hole is really just an enormous ball of string, which encodes in its structure and excitations all of the information of the individual fundamental strings swallowed by the hole. As the black hole evaporates, little bits of this string slip outside the event horizon and zip away as fundamental particles, carrying away the information swallowed by the hole.

The story is told largely through analogies and is easy to follow if you accept the author's premises. I found the tone of the book quite difficult to take, however. The word which kept popping into my head as I made my way through was “smug”. The author opines on everything and anything, and comes across as scornful of anybody who disagrees with his opinions. He is bemused and astonished when he discovers that somebody who is a Republican, an evangelical Christian, or some other belief at variance with the dogma of the academic milieu he inhabits can, nonetheless, actually be a competent scientist. He goes on for two pages (pp. 280–281) making fun of Mormonism and then likens Stephen Hawking to a cult leader. The physics is difficult enough to explain; who cares about what Susskind thinks about everything else? Sometimes he goes right over the top, resulting in unseemly prose like the following.

Although the Black Hole War should have come to an end in early 1998, Stephen Hawking was like one of those unfortunate soldiers who wander in the jungle for years, not knowing that the hostilities have ended. By this time, he had become a tragic figure. Fifty-six years old, no longer at the height of his intellectual powers, and almost unable to communicate, Stephen didn't get the point. I am certain that it was not because of his intellectual limitations. From the interactions I had with him well after 1998, it was obvious that his mind was still extremely sharp. But his physical abilities had so badly deteriorated that he was almost completely locked within his own head. With no way to write an equation and tremendous obstacles to collaborating with others, he must have found it impossible to do the things physicists ordinarily do to understand new, unfamiliar work. So Stephen went on fighting for some time. (p. 419)
Or, Prof. Susskind, perhaps it's that the intellect of Prof. Hawking makes him sceptical of arguments based a “theory” which is, as you state yourself on p. 384, “like a very complicated Tinkertoy set, with lots of different parts that can fit together in consistent patterns”; for which not a single fundamental equation has yet been written down; in which no model that remotely describes the world in which we live has been found; whose mathematical consistency and finiteness in other than toy models remains conjectural; whose results regarding black holes are based upon another conjecture (AdS/CFT) which, even if proven, operates in a spacetime utterly unlike the one we inhabit; which seems to predict a vast “landscape” of possible solutions (vacua) which make it not a theory of everything but rather a “theory of anything”; which is formulated in a flat Minkowski spacetime, neglecting the background independence of general relativity; and which, after three decades of intensive research by some of the most brilliant thinkers in theoretical physics, has yet to make a single experimentally-testable prediction, while demonstrating its ability to wiggle out of almost any result (for example, failure of the Large Hadron Collider to find supersymmetric particles).

At the risk of attracting the scorn the author vents on pp. 186–187 toward non-specialist correspondents, let me say that the author's argument for “black hole complementarity” makes absolutely no sense whatsoever to this layman. In essence, he argues that matter infalling across the event horizon of a black hole, if observed from outside, is disrupted by the “extreme temperature” there, and is excited into its fundamental strings which spread out all over the horizon, preserving the information accreted in the stringy structure of the horizon (whence it can be released as the black hole evaporates). But for a co-moving observer infalling with the matter, nothing whatsoever happens at the horizon (apart from tidal effects whose magnitude depends upon the mass of the black hole). Susskind argues that since you have to choose your frame of reference and cannot simultaneously observe the event from both outside the horizon and falling across it, there is no conflict between these two descriptions, and hence they are complementary in the sense Bohr described quantum observables.

But, unless I'm missing something fundamental, the whole thing about the “extreme temperature” at the black hole event horizon is simply nonsense. Yes, if you lower a thermometer from a space station at some distance from a black hole down toward the event horizon, it will register a diverging temperature as it approaches the horizon. But this is because it is moving near the speed of light with respect to spacetime falling through the horizon and is seeing the cosmic background radiation blueshifted by a factor which reaches infinity at the horizon. Further, being suspended above the black hole, the thermometer is in a state of constant acceleration (it might as well have a rocket keeping it at a specified distance from the horizon as a tether), and is thus in a Rindler spacetime and will measure black body radiation even in a vacuum due to the Unruh effect. But note that due to the equivalence principle, all of this will happen precisely the same even with no black hole. The same thermometer, subjected to the identical acceleration and velocity with respect to the cosmic background radiation frame, will read precisely the same temperature in empty space, with no black hole at all (and will even observe a horizon due to its hyperbolic motion).

The “lowering the thermometer” is a completely different experiment from observing an object infalling to the horizon. The fact that the suspended thermometer measures a high temperature in no way implies that a free-falling object approaching the horizon will experience such a temperature or be disrupted by it. A co-moving observer with the object will observe nothing as it crosses the horizon, while a distant observer will see the object appear to freeze and wink out as it reaches the horizon and the time dilation and redshift approaches infinity. Nowhere is there this legendary string blowtorch at the horizon spreading out the information in the infalling object around a horizon which, observed from either perspective, is just empty space.

The author concludes, in a final chapter titled “Humility”, “The Black Hole War is over…”. Well, maybe, but for this reader, the present book did not make the sale. The arguments made here are based upon aspects of string theory which are, at the moment, purely conjectural and models which operate in universes completely different from the one we inhabit. What happens to information that falls into a black hole? Well, Stephen Hawking has now conceded that it is preserved and released in black hole evaporation (but this assumes an anti de Sitter spacetime, which we do not inhabit), but this book just leaves me shaking my head at the arm waving arguments and speculative theorising presented as definitive results.

Posted at May 4, 2009 23:48