  The electric dipole strength distribution in $^{40}$Ca between 5 and 25 MeV
has been determined at RCNP, Osaka, from proton inelastic scattering
experiments at very forward angles. Combined with total photoabsorption data at
higher excitation energy, this enables an extraction of the electric dipole
polarizability $\alpha_\mathrm{D}$($^{40}$Ca) = 1.92(17) fm$^3$. Together with
the measured $\alpha_{\rm D}$ in $^{48}$Ca, it provides a stringent test of
modern theoretical approaches, including coupled cluster calculations with
chiral effective field theory interactions and state-of-the art energy density
functionals. The emerging picture is that for this medium-mass region dipole
polarizabilities are well described theoretically, with important constraints
for the neutron skin in $^{48}$Ca and related equation of state quantities.
