The Stability of Matter and Quantum Electrodynamics,
or There Is More to Physics Than The Hydrogen Atom

Ordinary matter is held together with electromagnetic forces, and the
dynamical laws governing the constituents (electrons and nuclei) are those
of quantum mechanics.  These laws, found in the beginning of this century,
were able to account for the fact that electrons do not fall into the
nuclei and thus atoms are quite robust.  It was only in 1967 that Dyson
and Lenard were able to show that matter in bulk was also stable and that
two stones had a volume twice that of one stone.  Simple as this may
sound, the conclusion is not at all obvious and hangs by a thread-- namely
Pauli's "exclusion principle."  In the ensuing three decades much was
accomplished to clarify, simplify and extend this result.  We now
understand that matter can, indeed, be unstable when relativistic effects
and magnetic fields are taken into account -- unless the electron's charge
is small enough (which it is, fortunately).  These delicate and
non-intuitive conclusions will be summarized.  We can now hope to begin an
analysis of the half-century old question about the ultimate theory of
ordinary matter, called quantum electrodynamics (QED).  This is an
experimentally successful theory, but one without a decent mathematical
foundation.  Some recent, preliminary steps in resolving some of the
problems of QED will be presented.