  In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement
of the gravitational redshift by the interference of matter waves, Nature 463,
926-929 (2010)] argued that atom interferometry experiments published a decade
ago did in fact measure the gravitational redshift on the quantum clock
operating at the very high Compton frequency associated with the rest mass of
the Caesium atom. In the present Communication we show that this interpretation
is incorrect.
