In several textbooks and papers, like this one for example, a claim like the following is made:
The EDM of a system $\vec{d}$ must be parallel (or antiparallel) to the average angular momentum of the system $\hbar\langle\vec{J}\rangle$.
What is the motivation for making such an assertion? It seems not to make much sense if you consider, for example, two opposite electric charges held apart by a short, rigid massless rod (the usual classical picture of an electric dipole). The system can have zero angular momentum, but still has a nonzero electric dipole moment.
