  We demonstrate, via numerical simulations, that the relaxation dynamics of
supercooled liquids correlates well with a plastic length scale measuring a
particle's response to impulsive localized perturbations and weakly to measures
of local elasticity. We find that the particle averaged plastic length scale
vanishes linearly in temperature and controls the super-Arrhenius temperature
dependence of the relaxation time. Furthermore, we show that the plastic length
scale of individual particles correlates with their typical displacement at the
relaxation time. In contrast, the local elastic response only correlates with
the dynamics on the vibrational time scale.
