  Given a real reductive group Lie group $G_\mathbb{R}$, the Mackey analogy is
a bijection between the set of irreducible tempered representations of
$G_\mathbb{R}$ and the set of irreducible unitary representations of its Cartan
motion group. We show that this bijection arises naturally from families of
twisted $\mathcal{D}$-modules over the flag variety of $G_\mathbb{R}$.
