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.
The other question is whether the perception of change in time really involves any real change at all. Augustine was content to measure the extent of time periods through the duration of his mind, which, I suspect, could be adequately explained as the spatial relationship of neurons in the now. That would sort of eliminate the now as any privileged reference frame, but could retain the important perceptions of the past as having happened.
Oh, final question: if the quantum state evolution is deterministic, what makes the past any different from the future, predictively speaking? Why is it that the past seems to leave traces on the present, whereas we don’t know what the future will be yet?