BERNARD GROSSMAN
285
manifestation of the other . Symmetry considerations allow us to
view one set of events in different ways . Consider a moving charge,
for example, a current through a wire . The moving charge creates a
magnetic field perpendicular to the wire. Moreover, if one moves a
bar magnet through a coil of wire , a current in the wire is created. In
short, a changing electric field produces a magnetic field and a
changing magnetic field produces an electric field. The principle of
relativity allows one to view electric and magnetic fields as
manifestations of a single phenomenon, the motion of a charge rela–
tive to some observer. Further unification of the electromagnetic in–
teractions with the weak interactions can be made. Steven
Weinberg, Abdus Salam, and Sheldon Glashow unified these forces
using the idea of symmetry breaking explained earlier. These results
were recently confirmed by Carlo Rubbia at CERN.
Quantum electrodynamics (QED) is an example of a theory
that is relativistic and quantum mechanical with an unbroken sym–
metry; yet the theory is incomplete (over and above the fact that
there are other interactions). Recall that after answering the ques–
tion of what are the observed symmetries of an interaction,
physicists want to calculate the consequences of the theory and com–
pare them with experiment. Unless we can do this, the work remains
within a solipsistic realm of philosophical speculation. Although we
can calculate remarkably well within the realm of validity of quan–
tum electrodynamics, in the realm where one can neglect the other
interactions, infinities appear in intermediate stages of the calcula–
tion. These infinities are similar to what happens when a sound
system gets noisier and noisier because of feedback. They are a
distinctly quantum mechanical effect . There exists a self-consistent
rule for handling these divergences, but most physicists feel that the
divergences that appear are the first indications that a more
sophisticated and comprehensive theory that contains quantum elec–
trodynamics as a limit is needed. One of the strengths of string
theory as a unifying theory is that it is believed to be such a finite
theory. The unification of the weak and electromagnetic interactions
can be thought of as the simplest way to begin to cure some of the in–
finities that arise in the coupling of nuclear matter to elec–
tromagnetism. However, this theory develops side effects as a result
of the treatment. That string theory has fewer infinities than quan–
tum electrodynamics is related to the fact that it is not based upon a
geometry of points . The infinities that arise in QED occur when two
particles, like electrons, which are pointlike in nature in QED, are
