  We describe a simple gedanken experiment which illustrates the physical
effects of the QED theta angle, a fundamental parameter of Nature that has yet
to be measured. The effects are manifest in quantum phases analogous to those
in the Aharonov-Bohm effect, although they are not intrinsically topological.
We also derive the quantum phases using a functional Schrodinger approach, and
generalize the results to non-Abelian gauge theories.
