It is shown, as an exact consequence of the nonrelativistic quantum theory of light scattering, that the dependence of differential cross section on the incident and scattered wave vectors and polarization vectors is the same as it is in the Kramers–Heisenberg approximate result. Combining this result with previous work, we conclude that in systems of randomly oriented scattering molecules (with no external fields) there is a necessary condition for the diagonally polarized elements of the Perrin matrix 〈Pi3〉 and 〈P3i〉 (with i=1,2,4) to be nonzero. The condition is that the molecule be radiatively and/or nonradiatively damped, and/or that retarded multiple scattering is occurring within the molecule. To show observable retardation effects, molecular size need only be comparable to wavelength. The retarded component of the 〈P3i〉 elements has a frequency prefactor of ω6, in contrast to the total intensity prefactor of ω4. Therefore, the bluest possible laser should be used for their measurement.