On the Origin of Time's Arrow in Quantum Mechanics

We point out that time's arrow is generated by quantum mechanical evolution, whenever the systems have a very large number ${\cal N}$ of non-degenerate states and a Hamiltonian bounded from below. When ${\cal N}$ is finite, the arrow can be imperfect, since evolution can resurrect past states. In the limit ${\cal N} \rightarrow \infty$ the arrow is fixed by the ``tooth of time": the decay of excited states induced by {\it spontaneous emission} to the ground state, mediated by interactions and a large number of decay products which carry energy and information to infinity.