Entanglement and the Infrared.

We shall outline some results regarding the infrared catastrophes of quantum electrodynamics and perturbative quantum gravity and their implications for information loss in quantum processes involving electrically or gravitationally charged particles. We will argue that two common approaches to the solution of the infrared problem, using transition probabilities which are inclusive of copious soft photon and graviton production and using dressed states describe fundamentally different quantizations of electrodynamics and low energy gravity which are, in principle, distinguishable by experiments.