  Recently, a new class of three-dimensional spin liquid models have been
theoretically discovered, which feature generalized Coulomb phases of emergent
symmetric tensor $U(1)$ gauge theories. These "higher rank" tensor models are
particularly intriguing due to the presence of quasi-particles with restricted
mobility, such as fractons. We investigate universal experimental signatures of
tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids
(both quantum and classical) feature characteristic pinch-point singularities
in their spin-spin correlation functions, accessible via neutron scattering,
which can be readily distinguished from pinch points in conventional $U(1)$
spin liquids. These pinch points can thus serve as a crisp experimental
diagnostic for such phases. We also tabulate the low-temperature heat capacity
of various tensor Coulomb phases, which serves as a useful additional
diagnostic in certain cases.
