Three Roads To Quantum Gravity

THE SOUND OF SPACE IS A STRING
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metal. Quantum theory associates a particle with such sound
waves; it is called a phonon. Suppose I disturb the empty
space around us by making a gravitational wave. This can be
done by waving around anything with mass ± one of my arms
will do, or a pair of neutron stars. A gravitational wave can be
understood as a tiny ripple moving against a background,
which is the empty space.
The particle associated with gravitational waves is called
the graviton. No one has ever observed a graviton. It is hard
enough even to detect a gravitational wave, as they interact
only very weakly with matter. But as long as quantum theory
applies to gravitational waves, gravitons must exist. We know
that gravitons must interact with matter, for when anything
massive oscillates it produces gravitational waves. Quantum
theory says that, just as there are photons associated with
light, there must be gravitons associated with gravitational
waves.
We know that two gravitons will interact with each other.
This is because gravitons interact with anything that has
energy, and gravitons themselves carry energy. As with the
photon, the energy of a graviton is proportional to its
frequency, so the higher the frequency of a graviton, the
more strongly it will interact with another graviton. We can
then ask what happens when two gravitons interact. We know
that they will scatter from each other, changing their
trajectories. A good quantum theory of gravity must be able
to predict what will happen whenever two gravitons interact.
It ought to be able to produce an answer no matter how strong
the waves are and no matter what their frequencies are. This
is just the kind of question that we know how to approach in
quantum theory. For example, we know that photons will
interact with any charged particle, such as an electron. We
have a good theory of the interactions of photons and
electrons, called quantum electrodynamics, QED for short. It
was developed by Richard Feynman, Julian Schwinger, Sinitiro
Tomonaga and others in the late 1940s. QED makes
predictions about the scattering of photons and electrons and
other charged particles that agree with experiment to an
accuracy of eleven decimal places.