Non-locality of Quantum Mechanics and the Locality of General Relativity

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.Comment: 14 pages, 1 figure. Invited talk at the Meeting on the Interface of Gravitational and Quantum Realms, IUCAA, Pune, India, Dec. 17-21, 2001. To be published in Modern Physics Letters