Three Roads To Quantum Gravity

80 THREE ROADS TO QUANTUM GRAVITY
clocks, her time seems to run slower and slower as her speed
approaches, but never reaches, that of light. This goes on for
as long as she keeps her engines on and continues to
accelerate.
What we are describing here is a metaphor which is very
useful for thinking about black holes. An observer hovering
just above the surface of a black hole is in many ways just like
an observer who is continually accelerating in a region far
from any star or black hole. In both cases there is an invisible
region whose boundary is a horizon. The horizon is made of
light that travels in the same direction as the observer, but
never comes any closer to her. To fall through the horizon, the
observer has only to turn off her engines. When she does, the
light that forms the horizon catches her up and she passes into
the hidden region behind it.
But while the situation of an accelerating observer is
analogous to that of an observer just outside a black hole, in
some ways her situation is simpler. So in this chapter we shall
take a small detour and consider the world as seen by an
observer who constantly accelerates. This will teach us the
concepts we need to understand the quantum properties of a
black hole.
Of course, the two situations are not completely analogous.
They differ in that the black hole's horizon is an objective
property of the black hole, which is seen by many other
observers. However, the invisible region and horizon of an
accelerating observer are consequences only of her acceleration,
and are seen only by her. Still, the metaphor is very
useful. To see why, let us ask a simple question: what does
our continually accelerating observer see when she looks
around her?
Assume that the region she accelerates through is completely
empty. There is no matter or radiation anywhere nearby ±
there is nothing but the vacuum of empty space. Let us equip
our accelerating observer with a suite of scienti®c instruments,
like the ones carried by space probes: particle detectors,
thermometers, and so on. Before she turns on her engines she
sees nothing, for she is in a region where space is truly empty.
Surely turning on her engines does not change this?