  Thermodynamics provides powerful constraints on physical and chemical systems
in equilibrium. However, non-equilibrium dynamics depends explicitly on
microscopic properties, requiring an understanding beyond thermodynamics.
Remarkably, in dilute gases, a set of universal relations is known to connect
thermodynamics directly with microscopic properties. So far, these "contact"
relations have been established only for interactions with $s$-wave symmetry,
i.e., without relative angular momentum. We report measurements of two new
physical quantities, the "$p$-wave contacts", and present evidence that they
encode the universal aspects of $p$-wave interactions through recently proposed
relations. Our experiments use an ultracold Fermi gas of $^{40}$K, in which
$s$-wave interactions are suppressed by polarising the sample, while $p$-wave
interactions are enhanced by working near a scattering resonance. Using
time-resolved spectroscopy, we study how correlations in the system develop
after "quenching" the atoms into an interacting state. Combining
quasi-steady-state measurements with new contact relations, we infer an
attractive $p$-wave interaction energy as large as half the Fermi energy. Our
results reveal new ways to understand and characterise the properties of a
resonant $p$-wave quantum gas.
