  Analysis of the logical foundations of quantum mechanics indicates the
possibility of constructing a theory using quaternionic Hilbert spaces. Whether
this mathematical structure reflects reality is a matter for experiment to
decide. We review the only direct search for quaternionic quantum mechanics yet
carried out and outline a recent proposal by the present authors to look for
quaternionic effects in correlated multi-particle systems. We set out how such
experiments might distinguish between the several quaternionic models proposed
in the literature.
