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An experiment in Low Earth Orbit (LEO) is proposed to measure components ofthe Riemann curvature tensor using atom interferometry. We show that thedifference in the quantum phase $\Delta\phi$ of an atom that can travel alongtwo intersecting geodesics is given by $mR_{0i0j}/\hbar$ times the spacetimevolume contained within the geodesics. Our expression for $\Delta\phi$ alsoholds for gravitational waves in the long wavelength limit.Comment: 7 pages LaTeXed with RevTeX 4.0, 2 figures. Submitted to the 2003  Gravity Research Foundation Essay Contes

QUANTUM INTERFERENCE TO MEASURE SPACETIME CURVATURE: A PROPOSED EXPERIMENT AT THE INTERSECTION OF QUANTUM MECHANICS AND GENERAL RELATIVITY