  The electrodynamic response of the organic spin-liquid candidate
$\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ has been measured in an extremely wide
energy range ($10^{-13}$ to 2 eV) as a function of temperature (5 to 300 K).
Below the Mott gap, excitations from the un-gapped spinon continuum cause a
considerable contribution to the infrared conductivity, as suggested by the
U(1) gauge theory. At THz frequencies we can identify a power-law behavior
$\sigma(\omega) \propto \omega^{\beta}$ with two distinct exponents $\beta$
that change from 0.9 to 1.3 at low temperatures. The corresponding crossover
scales with temperature: $\hbar\omega_c \approx k_B T$. The observed exponents
differ by more than a factor of 2 from the theoretically predicted ones. The
findings are compared with those obtained on Herbertsmithites.
