Quantum Mechanics, the Stability of Matter, and Quantum

Topic

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 last
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' (which states that two
electrons cannot be in the same state). In the ensuing 3 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. The
requisite mathematical apparatus needed for these results is itself
interesting. Finally, 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 to resolve the problems of QED will be
presented.