Three Roads To Quantum Gravity

100 THREE ROADS TO QUANTUM GRAVITY
few others, such as his friend Paul Ehrenfest, to apply the
same reasoning to light. According to the theory published by
James Clerk Maxwell in 1865, light consisted of waves
travelling through the electromagnetic ®eld, each wave
carrying a certain amount of energy. Einstein and Ehrenfest
wondered whether they could use Boltzmann's ideas to
describe the properties of light on the inside of an oven.
Light is produced when the atoms in the walls of the oven
heat up and jiggle around. Could the light so produced be said
to be hot? Could it have an entropy and a temperature? What
they found was profoundly puzzling to them and to everyone
else at the time. They found that horrible inconsistencies
would arise unless the light were in a sense also to consist of
atoms. Each atom of light, or quantum as they called it, had to
carry a unit of energy related to the frequency of the light. This
was the birth of quantum theory.
I shall tell no more of this story, for it is indeed a very
twisted one. Some of the results that Einstein and Ehrenfest
employed in their reasoning had been found earlier by Max
Planck, who had studied the problem of hot radiation ®ve
years earlier. It was in this work that the famous Planck's
constant ®rst appeared. But Planck was one of those physicists
who believed neither in atoms nor in Boltzmann's work,
so his understanding of his own results was confused and, in
part, contradictory. He even managed to invent a convoluted
argument that assured him that photons did not exist. For this
reason the birth of quantum physics is more properly
attributed to Einstein and Ehrenfest.
The moral of this story is that it was an attempt to
understand the laws of thermodynamics that prompted two
crucial steps in our understanding of atomic physics. These
were the arguments that convinced physicists of the existence
of atoms, and the arguments by which the existence of the
photon were ®rst uncovered. It was no coincidence that both
these steps were taken by the same young Einstein in the same
year.
We can now turn back to quantum gravity, and in particular
to quantum black holes. For what we have seen in the last few
chapters is that black holes are systems which may be