  From the principle of equivalence, Einstein predicted that clocks slow down
in a gravitational field. Since the general theory of relativity is based on
the principle of equivalence, it is essential to test this prediction
accurately. Muller, Peters and Chu claim that a reinterpretation of decade old
experiments with atom interferometers leads to a sensitive test of this
gravitational redshift effect at the Compton frequency. Wolf et al dispute this
claim and adduce arguments against it. In this article, we distill these
arguments to a single fundamental objection: an atom is NOT a clock ticking at
the Compton frequency. We conclude that atom interferometry experiments
conducted to date do not yield such sensitive tests of the gravitational
redshift. Finally, we suggest a new interferometric experiment to measure the
gravitational redshift, which realises a quantum version of the classical clock
"paradox".
