  The conflict between the locality of general relativity, reflected in its
space-time description, and the non-locality of quantum mechanics, contained in
its Hilbert space description, is discussed. Gauge covariant non-local
observables that depend on gauge fields and gravity as well as the wave
function are used in order to try to understand and minimize this conflict
within the frame-work of these two theories. Applications are made to the
Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and
gravity.
