  We investigate the use of a Bose-Einstein condensate trapped on an atom chip
for making interferometric measurements of small energy differences. We measure
and explain the noise in the energy difference of the split condensates, which
derives from statistical noise in the number difference. We also consider
systematic errors. A leading effect is the variation of rf magnetic field in
the trap with distance from the wires on the chip surface. This can produce
energy differences that are comparable with those due to gravity.
