We elucidate the physics of the dynamical transition via 15 ns long molecular dynamics simulations at a series of temperatures (spanning 160 - 280 K) where the protein retains its native structure. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a cross-over from a piecewise stationary to stationary set of processes that underly the dynamics of protein motions in the water environment.We find that a two-time-scale function captures the non-exponential character of backbone structural relaxations. One is attributed to the collective protein motions and the other to local relaxations. The former is well-defined by a single-exponential, nanosecond decay that is operative at all temperatures. The latter, on the other hand, is described by a large number of single-exponential motions that display a distribution of time-scales. Though their average remains on the order of 10 ps at all temperatures, the distribution markedly contracts with the onset of the dynamical transition. Interestingly, the collective motions are shown to impose bounds on the time-scales spanned by the local dynamical processes, although they are not directly involved in the transition.The piecewise stationary character below the transition implicates the presence of a collection of sub-states whose inter-communication is restricted. The ineffectiveness of these sub-states to influence the overall relaxation time is shown to require a wide distribution of local motion time-scales, extending well beyond that of nanoseconds. At physiological temperatures, on the other hand, local motions are confined to time-scales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate, providing alternative routes for protein functionality.