  Glasses behave as solids on experimental time scales due to their slow
relaxation. Growing dynamic length scales due to cooperative motion of
particles are believed to be central to this slow response. For quiescent
glasses, however, the size of the cooperatively rearranging regions has never
been observed to exceed a few particle diameters, and the observation of
long-range correlations that are signatures of an elastic solid has remained
elusive. Here, we provide direct experimental evidence of long-range
correlations during the deformation of a dense colloidal glass. By imposing an
external stress, we force structural rearrangements that make the glass flow,
and we identify long-range correlations in the fluctuations of microscopic
strain, and elucidate their scaling and spatial symmetry. The applied shear
induces a transition from homogeneous to inhomogeneous flow at a critical shear
rate, and we investigate the role of strain correlations in this transition.
