  Recently there has been a surge in interest in using video-microscopy
techniques to infer the local mechanical properties of disordered solids. One
common approach is to minimize the difference between particle vibrational
displacements in a local coarse-graining volume and the displacements that
would result from a best-fit affine deformation. Effective moduli are then be
inferred under the assumption that the components of this best-fit affine
deformation tensor have a Boltzmann distribution. In this paper, we combine
theoretical arguments with experimental and simulation data to demonstrate that
the above does not reveal information about the true elastic moduli of jammed
packings and colloidal glasses.
