  We define a correlation function that quantifies the spatial correlation of
single-particle displacements in liquids and amorphous materials. We show for
an equilibrium liquid that this function is related to fluctuations in a bulk
dynamical variable. We evaluate this function using computer simulations of an
equilibrium glass-forming liquid, and show that long range spatial correlations
of displacements emerge and grow on cooling toward the mode coupling critical
temperature.
