  Recent conjectures that there are mesoscopically ``large'' extra dimensions,
through which gravity propagates have interesting implications for much of
physics. The scenario implies gross departures from Newton's law of gravity at
small length scales. Testing departures from Coulomb's law on sub-millimetre
scales is hard. It is now possible to routinely create Bose-Einstein
condensates with de Broglie wavelengths of order a $\mu m$ and total size of
order $10 \mu m$. BEC condensates move coherently under gravitational
acceleration, and I propose that the transverse fringe shift due to the
acceleration of pair of interfering BECs passing a dense linear mass may be
measurable, and provide direct evidence for anomalous gravitational
acceleration. Ideally such experiments are best carried out in free fall to
maximise the time spent by a BEC in the non-Newtonian regime.
