- 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.
April 2009 