Molecular dynamics simulation of a united-atom polyethylene model was performed to study the short time dynamics of polymer liquid and glass. Simulation runs lasting up to 5 ns were performed at ten temperatures above and below the estimated glass transition temperature. Quantities evaluated for the purpose of studying the dynamics include : segmental mean square displacement, van Hove space-time correlation function, intermediate scattering function, dynamic structure factor, and velocity autocorrelation function. Many of the features observed agree well with those obtained from quasielastic neutron scattering measurements with polymeric and nonpolymeric liquids. The dynamics in the time scale between 0.01 and 10(3) ps clearly divides itself into two regimes; the fast process, occurring below about 1.5 ps, is Debye-like, while the slower process follows the Kohlrausch-Williams-Watts function. The former probably arises from motion of segments within a cage, and the latter from the a : relaxation involving cooperative motion of groups of segments. The "apparent" glass transition temperature, noted from the behavior of the mean square displacement plotted against temperature, is shifted downward as the observation time is prolonged. The hopping process, seen with small molecule liquids at or below the glass transition temperature, has not been observed here at any temperature. Yet there is no indication that a nonergodicity, or a state of complete structural arrest, sets in even at the lowest of the temperatures studied.