  The Carr-Purcell Meiboom-Gill (CPMG) experiment has been used for decades to
measure nuclear-spin transverse ($T_2$) relaxation times. In the presence of
magnetic-field inhomogeneities, the limit of short interpulse spacings yields
the intrinsic $T_2$ time. Here we show that the signal decay in such
experiments exhibits fundamentally different behaviors between liquids and
gases. In gases, CPMG unexpectedly fails to eliminate the inhomogeneous
broadening due to the non-Fickian nature of the motional averaging.
