  Usual quantum mechanics requires a fixed, background, spacetime geometry and
its associated causal structure. A generalization of the usual theory may
therefore be needed at the Planck scale for quantum theories of gravity in
which spacetime geometry is a quantum variable. The elements of generalized
quantum theory are briefly reviewed and illustrated by generalizations of usual
quantum theory that incorporate spacetime alternatives, gauge degrees of
freedom, and histories that move forward and backward in time. A generalized
quantum framework for cosmological spacetime geometry is sketched. This theory
is in fully four-dimensional form and free from the need for a fixed causal
structure. Usual quantum mechanics is recovered as an approximation to this
more general framework that is appropriate in those situations where spacetime
geometry behaves classically.
  (Talk given at the Workshop on Physics at the Planck Scale, Puri, India,
December12-21, 1994. This talk is a precis of the author's 1992 Les Houches
Lectures: Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime,
gr-qc/9304006).

General Relativity and Quantum Cosmology;High Energy Physics - Theory;Quantum Physics