What if Time Really Exists?

Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.