  If scattering amplitudes are ordinary complex numbers (not quaternions) there
is a universal algebraic relationship between the six coherent cross sections
of any three scatterers (taken singly and pairwise). A violation of this
relationship would indicate either that scattering amplitudes are quaternions,
or that the superposition principle fails. Some possible experimental tests
involve neutron interferometry, K_S-meson regeneration, and low energy
proton-proton scattering.
