  We analyze relativistic quantum scattering in the Schr\"odinger picture. The
suggestive requirement of translational invariance and conservation of the
four-momentum, that the interacting Hamiltonian commute with the four-momentum
$P$ of free particles, is shown to imply the absence of interactions.
  The relaxed requirement, that the interacting Hamiltonian $H'$ commute with
the four-velocity $U= P/M$, $M=\sqrt{P^2}$, allows Poincar\'e covariant
interactions just as in the nonrelativistic case. If the $S$-matrix is Lorentz
invariant, it still commutes with the four-momentum $P$ though $H'$ does not.
  Shifted observers, whose translations are generated by the four-velocity $U$,
just see a shifted superposition of near-mass-degenerate states with unchanged
relative phases, while the four-momentum generates oscillated superpositions
with changed relative phases.
