Time Parametrizations in Long-Range Interacting Bose-Einstein Condensates.

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 invariance in the ground state of the quasi-stationary state of a long-range interacting closed system of identical and macroscopic spatiotemporally inhomogeneous Bose-Einstein condensates in the thermodynamic and Newtonian limits. As a result, we find that it is a theoretical counterexample of this invariance, except for the proper-time translational invariance.