Directions in General Relativity

I first met Charles Misner at the genial general relativity meetings that James Anderson and Ralph Schiller organized at Stevens Institute of Technology in the mid-‘50s. His birthday reminds me of our collaboration in topological physics in 1959, when we found the topological spin-statistics connection and gravitational kinks. Misner's contributions to the discovery of the relativistic theory of the black hole are not adequately appreciated. Let me say a little about these matters here.

They all hang on the thread of anomalous spin. The first anomalous spin was the spin ½ of the electron. It was anomalous in that the very possibility of spin ½ was initially overlooked by quantum theorists. Then experiment and Uhlenbeck & Goudsmit forced it to our attention. Wigner explained this spin by examining how the electron wavefunction behaved under the Wigner waltz W: a path in the rotation group describing a continuous rotation of the physical system through 2π. In three dimensions W cannot shrink continuously to a point (W is nontrivial), but W2, a 4π rotation, can (W2 is trivial). It followed that W can change quantum phase by π. This happens for spin ½.

In 1954, fresh out of graduate school, I set out to find a unified theory of the known particles and forces, as I imagined one was supposed to do. As an undergraduate my ambition was to carry out Von Neuman's quantum set theory program. What I describe next began a decade detour from that program, to which I later returned.