Abstract
I prove that, if a change happens in a closed quantum system so that its state is perfectly distinguishable from all past or future states, the Hamiltonian is H=-iℏ∂/∂τ. A time operator τ can be defined as its canonical conjugate. This Hamiltonian is usually rejected because it has no ground state, but I show that even a weaker form of irreversibility is inconsistent with a ground state. What is the right choice, that the world's Hamiltonian is -iℏ∂/∂τ, or that changes are reversible?