  We report the spontaneous decay of a soft, optical phonon in a solid. Using
neutron spectroscopy, we find that specific phonon lifetimes in the relaxor
PbMg$_{1/3}$Nb$_{2/3}$O$_{3}$ are anomalously short within well-defined ranges
of energy and momentum. This behavior is independent of ferroelectric order and
occurs when the optical phonon with a specific energy and momentum can
kinematically decay into two acoustic phonons with lower phase velocity. We
interpret the well-known relaxor "waterfall" effect as a form of quasiparticle
decay analogous to that previously reported in quantum spin liquids and quantum
fluids.
