Three Roads To Quantum Gravity

86 THREE ROADS TO QUANTUM GRAVITY
the positions and motions of the molecules that does not get
speci®ed when one describes the gas in terms of quantities
such as density and temperature. These quantities are
averaged over all the atoms in the gas, so when one talks
about a gas in this way most of the information about the
actual positions and motions of the molecules is thrown
away. The entropy of a gas is a measure of this information ±
it is equal to the number of yes/no questions that would have
to be answered to give a precise quantum theoretic description
of all the atoms in the gas.
Information about the exact states of the hot photons seen by
the accelerating observer is missing because it is coded in the
states of the photons in her hidden region. Because the randomness
is a result of the presence of the hidden region, the
entropy should incorporate some measure of how much of the
world cannot be seen by the accelerating observer. It should
have something to do with the size of her hidden region. This is
almost right; it is actually a measure of the size of the boundary
that separates her from her hidden region. The entropy of the
hot radiation she observes as a result of her acceleration turns
out to be exactly proportional to the area of her horizon! This
relationship between the area of a horizon and entropy was
discovered by a Ph.D. student named Jacob Bekenstein, who
was working at Princeton at about the time that Bill Unruh
made his great discovery. Both were students of John Wheeler,
who a few years before had given the black hole its name.
Bekenstein and Unruh were in a long line of remarkable
students Wheeler trained, which included Richard Feynman.
What those two young physicists did remains the most
important step yet made in the search for quantum gravity.
They gave us two general and simple laws, which were the
®rst physical predictions to come from the study of quantum
gravity. They are:
. Unruh's law Accelerating observers see themselves as
embedded in a gas of hot photons at a temperature
proportional to their acceleration.
. Bekenstein's law With every horizon that forms a boundary