Decoherence and the Uncertainty Principle

The uncertainty principle is normally understood as representing a limit on the fundamental accuracy of simultaneous measurements of incompatible observables. In the context of consistent/decoherent histories formulations of quantum theory, we show that it may also be understood as quantifying the degree of course-graining necessary in order for histories of a quantum system to decohere. This follows as a consequence of a new inequality bounding the interference between histories in a consistent histories formulation of quantum theory.