Motivated by the recent debate on whether the Kasevich-Chu atom interferometer can measure the gravitational redshift, we show that in different representations of quantum mechanics chosen for the calculation, the observed phase shift appears as though it originates from different physical phenomena. In particular, we demonstrate that the decomposition of the total phase shift into three dynamical phases, which emerges in a semiclassical approach and is at the very heart of the redshift controversy, does not appear in an exact treatment based on a representation-free analysis. Here only two phenomena determine the phase shift: the difference of the laser phases and the acceleration of the atom. Hence, the Kasevich-Chu interferometer is an accelerometer or gravimeter.