the force) on the surface of the larger sphere is^1 / 9 ^1 / 32 , the photon den-
sity on the surface of the smaller sphere.
Just as Newton almost certainly realized, it is reasonable to postulate a
similar mechanism to account for the strength of the gravitational field.
But it is here that we encounter one of the major unsolved problems con-
fronting contemporary physics. The three theories that account for the
behavior of the nongravitational forces are all quantum theories that ac-
count for the forces by describing the behavior of particles. Relativity, the
theory that best describes the gravitational force, is a field theory; it
speaks of a gravitational field that extends throughout space, and de-
scribes the behavior of this field.
This was also the case with Maxwell’s equations, the original description
of the electromagnetic force. These equations describe how the electric
and magnetic fields relate to each other. In the first half of the twentieth
century, quantum electrodynamics was invented, which described how
the electromagnetic fields were produced as the result of electrically
charged particles (which are fermions) interacting by exchanging photons
(which are bosons). Quantum electrodynamics served as the model for
subsequent quantum theories—the electroweak theory, which provides a
unified description of the electromagnetic and weak forces, and the charm-
ingly named quantum chromodynamics, which provides a description of
the strong force. However, even though the particle transmitting the grav-
itational force is in place—at least theoretically—a successful quantum
theory of gravity has yet to emerge. The development of this theory is per-
haps the most important goal of contemporary theoretical physics.
Lightning in a Bottle
In 1919, Einstein’s general theory of relativity was spectacularly confirmed
by Eddington’s observations of the gravitational def lection of light by the
Sun of light from stars. In the same year, Einstein received an extraordinary
paper from Theodor Kaluza,^10 a little-known German mathematician.
Kaluza had done something frequently done by mathematicians, but
only occasionally by physicists: he had taken well-known results and
placed them in a new and hypothetical environment. The well-known re-
sults in this case were Einstein’s treatment of general relativity; the hypo-
thetical environment in which he placed them was a universe consisting
of four space dimensions (rather than the three familiar to us) and one
time dimension.
Kaluza probably chose four space dimensions because it is the next step
up the complexity ladder from three dimensions. However, Kaluza’s ap-
146 How Math Explains the World