  We analyze the nature and performance of clocks formed by stabilizing an
oscillator to the phase difference between two paths of an atom interferometer.
The phase evolution has been modeled as being driven by the proper-time
difference between the two paths, although it has an ambiguous origin in the
non-relativistic limit and it requires a full quantum-field-theory treatment in
the general case. We present conditions for identifying deviations from the
non-relativistic limit as a way of testing the proper-time driven phase
evolution model. We show that the system performance belies the premise that an
atom-interferometer clock is referenced to a divided-down Compton oscillation,
and we suggest that this implies there is no physical oscillation at the
Compton frequency.
