Three Roads To Quantum Gravity

82 THREE ROADS TO QUANTUM GRAVITY
gas of photons and other particles, all at a temperature which
increases in proportion to her acceleration.
I must stress that what I am describing has never been
observed. It is a prediction that was ®rst made in the early
1970s by a brilliant young Canadian physicist, Bill Unruh,
who was then barely out of graduate school. What he found
was that, as a result of quantum theory and relativity, there
must be a new effect, never observed but still universal,
whereby anything which is accelerated must experience itself
to be embedded in a hot gas of photons, the temperature of
which is proportional to the acceleration. The exact relation
between temperature T and acceleration a is known, and is
given by a famous formula ®rst derived by Unruh. This
formula is so simple we can quote it here:
T = a(h Å /2pc)
The factor h Å /2pc, where h Å is Planck's constant and c is the
speed of light, is small in ordinary units, which means that
the effect has so far escaped experimental con®rmation. But it
is not inaccessible, and there are proposals to measure it by
accelerating electrons with huge lasers. In a world without
quantum theory, Planck's constant would be zero and there
would be no effect. The effect also goes away when the speed
of light goes to in®nity, so it would also vanish in Newtonian
physics.
This effect implies that there is a kind of addendum to
Einstein's famous equivalence principle. According to Einstein,
a constantly accelerating observer should be in a
situation just like an observer sitting on the surface of a
planet. Unruh told us that this is true only if the planet has
been heated to a temperature that is proportional to the
acceleration.
What is the origin of the heat detected by an accelerating
observer? Heat is energy, which we know cannot be created
nor destroyed. Thus if the observer's thermometer heats up
there must be a source of the energy. So where does it come
from? The energy comes from the observer's own rocket
engines. This makes sense, for the effect is present only as
long as the observer is accelerating, and this requires a