  Using two-photon Bragg spectroscopy, we study the energy of particle-like
excitations in a strongly interacting homogeneous Bose-Einstein condensate, and
observe dramatic deviations from Bogoliubov theory. In particular, at large
scattering length $a$ the shift of the excitation resonance from the
free-particle energy changes sign from positive to negative. For an excitation
with wavenumber $q$, this sign change occurs at $a \approx 4/(\pi q)$, in
agreement with the Feynman energy relation and the static structure factor
expressed in terms of the two-body contact. For $a \gtrsim 3/q$ we also see a
breakdown of this theory, and better agreement with calculations based on the
Wilson operator product expansion. Neither theory explains our observations
across all interaction regimes, inviting further theoretical efforts.
