Of course, there is no need to confine evolution to this fibration. By the introduction of lapse functions and shift
vectors, the evolution may be developed along any other foliation and fibration, respectively. But this does not
change the circumstance that choice of an initial labeling of the world lines of the fibration with the associated
proper times has destroyed diffeomorphism invariance in any but the trivial sense (see next footnote). The
lapse and shift functions merely serve to situate points of space-time with respect to this initial individuating
field.