  The motion of electrons in the vast majority of conductors is diffusive,
obeying Ohm's law. However, the recent discovery and growth of high-purity
materials with extremely long electronic mean free paths has sparked interest
in non-ohmic alternatives, including viscous and ballistic flow. Although
non-ohmic transport regimes have been discovered across a range of materials,
including two-dimensional electron gases, graphene, topological semimetals, and
the delafossite metals, determining their nature has proved to be challenging.
Here, we report on a new approach to the problem, employing broadband microwave
spectroscopy of the delafossite metal PdCoO$_{2}$ in three distinct sample
geometries that would be identical for diffusive transport. The observed
differences, which go as far as differing power laws, take advantage of the
hexagonal symmetry of PdCoO$_{2}$. This permits a particularly elegant
symmetry-based diagnostic for non-local electrodynamics, with the result
favouring ballistic over strictly hydrodynamic flow. Furthermore, it uncovers a
new effect for ballistic electron flow, owing to the highly facetted shape of
the hexagonal Fermi surface. We combine our extensive dataset with an analysis
of the Boltzmann equation to characterize the non-local regime in PdCoO$_{2}$.
More broadly, our results highlight the potential of broadband microwave
spectroscopy to play a central role in investigating exotic transport regimes
in the new generation of ultra-high conductivity materials.
