  Emergent $U(1)$ gauge theories and artificial photons in frustrated magnets
are outstanding examples of many-body collective phenomena. The classical and
quantum regimes of these systems provide platforms for classical and quantum
spin liquids, and are the subject of current active theoretical and
experimental investigations. Recently, realizations of rank-2 $U(1)$ (R2-U1)
gauge theories in three-dimensional frustrated magnets have been proposed. Such
systems in the quantum regime may lead to the so-called fracton ordered phases
-- a new class of topological order that has been associated with quantum
stabilizer codes and holography. However, there exist few distinguishing
characteristics of these states for their detection in real materials. Here we
focus on the classical limit, and present the dynamical spin structure factor
for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we
find unique signatures of the R2-U1 state, and we contrast them with the
results obtained from a more conventional $U(1)$ spin liquid. These results
provide a new path of investigation for future inelastic neutron scattering
experiments on candidate materials.
