We observe that quantum indistinguishability is a dynamical effect dependent on measurement duration. We propose a quantitative criterion for observing indistinguishability in quantum fluids and its implications including quantum statistics and derive a viscoelastic function capable of describing both long-time and short-time regimes where indistinguishability and its implications are operative and inactive, respectively. On the basis of this discussion, we propose an experiment to observe a transition between two states where the implications of indistinguishability become inoperative, including a transition between statistics-active and statistics-inactive states.