  We demonstrate that the elasticity of jammed solids is nonlocal. By forcing
frictionless soft sphere packings at varying wavelength, we directly access
their transverse and longitudinal compliances without resorting to curve
fitting. The observed wavelength dependence of the compliances is incompatible
with classical (local) elasticity, and hence quantifies the amplitude of
nonlocal effects. Three distinct length scales, two of which diverge, control
the amplitude of both nonlocal effects and fluctuations about the mean
response. Our results identify new, more accurate constitutive relations for
weakly jammed solids, including emulsions, foams, and granulates.
