Origin of the Arrow of Time in Quantum Mechanics

Abstract

We point out that time's arrow is naturally induced 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 is 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. This applies to individual isolated atoms, and does not require a coupling to a separate large heath bath.