Three Roads To Quantum Gravity

74 THREE ROADS TO QUANTUM GRAVITY
It helps to know that horizons are themselves surfaces of
light. They are made up of those light rays that just fail to
reach the observer (Figure 14). The horizon of a black hole is a
surface of light that has begun to move outwards from the
black hole but, because of the black hole's gravitational ®eld,
fails to get any farther from its centre. Think of the horizon as
a curtain made of photons. Photons leaving from any point
just inside the horizon are drawn inwards, even if they were
initially moving away from the centre of the black hole.
On the other hand, a photon that starts just outside the
horizon of a black hole will reach us, but it will be delayed
because light cones near the horizon are tilted almost so far
that no light can escape. The closer to the horizon the photon
starts, the longer will be the delay. The horizon is the point
where the delay becomes in®nite ± a photon released there
never reaches us.
This has the following interesting consequence. Imagine
that we are ¯oating some distance from a black hole. We drop
a clock into the black hole, which sends us a pulse of light
every thousandth of a second. We receive the signal and
convert it to sound. At ®rst we hear the signal as a highpitched
tone, as we receive the signals at a frequency of a
thousand times a second. But as the clock nears the horizon of
the black hole, each signal is delayed more and more by the
fact that it takes a little more time for each successive pulse to
arrive. So the tone we hear falls in pitch as the clock nears the
horizon. Just as the clock crosses the horizon, the pitch falls to
zero, and after that we hear nothing.
This means that the frequency of light is decreased by its
having to climb out from the region near the horizon. This can
also be understood from quantum theory, as the frequency of
light is proportional to its energy, and, just as it takes us
energy to climb a ¯ight of stairs, it takes a certain amount of
energy for the photon to climb up to us from its starting point
just outside the black hole. The closer to the horizon the
photon begins its ¯ight, the more energy it must give up as it
travels to us. So the closer to the horizon it starts, the more its
frequency will have decreased by the time it reaches us.
Another consequence is that the wavelength of the light is