  We give examples illustrating the fact that the different space/time
splittings of the tangent bundle of a semi-Riemannian spin manifold give rise
to non-equivalent norms on the space of compactly supported sections of the
spinor bundle, and as a result, to different completions. We give a necessary
and sufficient condition for two space/time splittings to define equivalent
norms in terms of a generalized Doppler shift between maximal negative definite
subspaces. We explore some consequences for the Noncommutative Geometry
program.
