The Problem of Irreversible Change in Quantum Mechanics

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

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