Quaternionic quantum Hamiltonians describing nonrelativistic spin particles
require the ambient physical space to have five dimensions. The quantum
dynamics of a spin-1/2 particle system characterised by a generic such
Hamiltonian is described. There exists, within the structure of quaternionic
quantum mechanics, a canonical reduction to three spatial dimensions upon
which standard quantum theory is retrieved. In this dimensional reduction,
three of the five dynamical variables oscillate around a cylinder, thus
behaving in a quasi one-dimensional manner at large distances. An analogous
mechanism exists in the case of octavic Hamiltonians, where the ambient
physical space has nine dimensions. Possible experimental tests in search
for the signature of extra dimensions at low energies are briefly discussed.
(Talk based on joint work with Eva-Maria Graefe, Imperial.)