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Thirty Years That Shook Physics:
CHAPTER VI
P. A. M. DIRAC AND ANTI-PARTICLES
The Theory of Relativity and the Quantum Theory,
which appeared almost simultaneously at the start of
the present century, were two great explosions of the
human mind and shook the very foundations of classi-
cal physics: relativity in the case of velocities approach-
ing that of light; quantum in the case of motions
confined to very small (atomic) dimensions. But for al-
most three decades these two great theories stood
apart, more or less, from each other. Bohr's original
theory of quantized orbits, as well as Schrödinger's
wave equations into which it developed, were essen-
tially non-relativistic; both were applicable only to par-
118
ticles moving with a velocity small as compared with
that of light. But the velocities of electrons within the
atoms are not that small. For example, the electron
on the first hydrogen orbit, calculated on the basis of
Bohr's theory, has the velocity of 2.2 x 10^8 cm/sec,
which is only a little less than 1 per cent of the speed
of light. The velocity of electrons inside heavier atoms
is considerably larger. Of course, a few per cent is not
too much, and the calculated value could be improved
by introducing "relativistic corrections," which would
make the agreement with direct experimental measure-
ment somewhat better. But this was only an improve-
ment and not the completion of the theory.
Another trouble arose in the case of the electron's
magnetic moment. In 1925, Goudsmit and Uhlenbeck
showed that in order to explain certain details of atomic
spectra it is necessary to ascribe to the electron certain
angular and magnetic momenta commonly known as
the
electron spin. The naïve picture at the time was
that the electron is a little charged sphere about
3 x 10^-18 cm in diameter. The rapid rotation of this
sphere around its axis was supposed to produce a mag-
netic moment, resulting in additional interaction with
its orbital motion and with the magnetic moments of
other electrons. It turned out, however, that in order
to produce the necessary magnetic field the electron
would have to rotate so fast that the points on its equa-
tor would move at much higher velocities than light!
Here again one encountered a conflict between quan-
tum and relativistic physics. It was becoming clear that
relativity and quantum physics could not just be added
together. A more general theory which would contain
both relativistic and quantum ideas in a harmoniously
unified form was needed.
