  Time-reparametrization invariance in general relativistic space-time does not
allow us to single out a time in quantum mechanics in a mechanical way of
measurement. Motivated by this problem, we examine this gauge invariance in the
ground state of the quasi-stationary coarse-grained state of a long-range
interacting closed system of identical or identified, macroscopic, and
spatiotemporally inhomogeneous Bose-Einstein condensates in the thermodynamic
and Newtonian limits. As a result, we find that it is a theoretical
counterexample of this gauge invariance, except for proper-time translational
invariance, at a coarse-grained level.
