Origin of the arrow of time in quantum mechanics

We point out that time’s arrow is naturally induced by quantum mechanical evolution, whenever the systems have a very large number Formula: see text of nondegenerate states and a Hamiltonian bounded from below. When Formula: see text is finite, the arrow is imperfect, since evolution can resurrect past states. In the limit Formula: see text the arrow is fixed by the “tooth of time”: the decay of excited states induced by spontaneous emission to the ground state, mediated by interactions and a large number of decay products which carry energy and information to infinity. This applies to individual isolated atoms, and does not require a coupling to a separate large heath bath.