## Quantum Mechanics, the Stability of Matter, and Quantum

- Date: 04/10/2007

Elliott H. Lieb (Princeton University)

University of Washington

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.

10th Anniversary Speaker Series 2007