Dynamic heterogeneity, where it is noticed in molecular dynamics (MD) simulations that, for example, conformational transition rates vary greatly from bond to bond, is characteristic of polymeric glasses. The phenomenon can be attributed to the fact that certain local bond sequences are more capable of conformational rearrangement than others. These local sequences become fixed sites when the overall chain trajectory is frozen-in in the glass. Although this is no doubt the case, because of the relatively short times of MD trajectories and the relatively small numbers of transitions it is important to establish that the heterogeneity does evolve in time in the manner expected from the local site picture and is not an artifact of short simulations or small numbers. This is undertaken here using a polyethylene system that has been much studied previously. Long trajectories are generated where the time evolution of heterogeneity can be studied. It is found that both the standard deviation and the mean value of the transitions over the bonds evolve linearly in time. This is consistent with the local fixed site picture and not with a random process involving relatively small numbers of transitions.