Quantum gravity studies how our ideas of quantum mechanics influence our ideas of spacetime. The subject of this talk is how our evolving ideas of spacetime have changed our ideas of quantum mechanics.
Milestones in the evolution of our concepts of space and time include: the separate space and absolute time of Newtonian physics, Minkowski spacetime with different times in different Lorentz frames, the curved but fixed spacetime of general relativity, the quantum fluctuations of spacetime in quantum gravity, and the idea of string/M-theory that spacetime is an approximation to something more fundamental. The changes in quantum theory that have reflected this evolution will be reviewed. But further changes are necessary in quantum quantum gravity where there is no fixed spacetime through which a state can unitarily evolve. Feynman's 1948 spacetime formulation of quantum mechanics supplies one route to the generalization of quantum mechanics necessary for quantum gravity. The spacetime formulation incorporates both unitary evolution and the reduction of the state vector in a unified way. The spacetime formulation is equivalent to usual Hamiltonian quantum mechanics when the fine grained histories are single valued in a time, (as in Minkowski space quantum field theory) but generalizes usual quantum mechanics when the histories do not have this property. The simple example of alternatives extended over time will be used to illustrate the generalization.