One of the things we’ve been discussing in Metaphysics this term has been the problem of motion through time, and whether or not Russell’s at-at theory sufficiently explains our everyday perception of change as occurring through time. Meanwhile, in Quantum Mechanics, we’ve been talking about the Hamiltonian operator as the generator of translations through time, analogous to the momentum operator generating translations through space.

I’ve got two weird ideas at the moment. First, momentum and position space are Fourier conjugate pairs of each other: you can convert states between them with a symmetric Fourier integral. I wonder if a similar relationship exists between the energy basis (or some other space related to the Hamiltonian) and time.