  Coupling fermions to gravity necessarily leads to a non-renormalizable,
gravitational four-fermion contact interaction. In this essay, we argue that
augmenting the Einstein-Cartan Lagrangian with suitable kinetic terms quadratic
in the gravitational gauge field strengths (torsion and curvature) gives rise
to new, massive propagating gravitational degrees of freedom. This is to be
seen in close analogy to Fermi's effective four-fermion interaction and its
emergent W and Z bosons.
