  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 $\widehat{H}=-i\hbar\frac{\partial\ }{\partial\tau}$. A time
operator $\widehat{\tau}$ 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
$-i\hbar\frac{\partial\ }{\partial\tau}$, or that changes are reversible?
