I understand that pure rotational spectra only exist for molecules which have a permanent dipole moment. The common explanation is "so that they can interact with the E-field of the incoming photons", but I don't think it is clear why photons can only interact with dipoles.
I'm also aware that the answer probably has something to do with the matrix element $\langle\psi_i|x|\psi_j\rangle$ where $\psi_i$ and $\psi_j$ are the initial and final states of the molecule, and $x$ comes from the dipole moment operator. I'm just not sure why we need this matrix element and not something else. And as an extension, why does Raman spectroscopy depend on the polarisability of a molecule, whose operator behaves like $x^2$?