Aoderson1 and Mott2 showed that scattering from a strongly disordered system qualitatively changes the way in which electron waves propagate. It has recently been realized that these changes occur universally for all waves, in particular optical waves3-5. It is also becoming apparent that many important new phenomena previously inferred indirectly for electrons can now be observed directly for photons. Here, we show how the time evolution of the scattered wave due to inelastic phase breaking (dephasing) processes can be followed directly. When coherent light is scattered by a disordered system an image of the emergent wave is obtained in the form of an apparently random intensity alternation known as speckle. From the time evolution of this speckle pattern we have found that multiple scattering greatly reduces the time required for phase breaking. This unexpected result is explained in terms of the extreme fragility of the phases of long trajectories, and appears to have important implications for a wide variety of phenomena.