We are developing an instrument to determine whether a new predicted position uncertainty is compatible with experiment. The prediction is a consequence of the idea that the total holographic information in a system is limited by Planck-scale physics but can have an effect at measurable scales by diffraction over long paths. The instrument consists of a correlated pair of high-bandwidth 40 m Michelson interferometers. It is the first, and at present unique, experiment designed to prepare and measure a coherent quantum state of position over an extended region in space. The sensitivity to transverse position noise, expressed in spectral density units, is smaller than a Planck time. When operating at its design noise limit, it will either detect or rule out some candidate forms of holographic quantum geometry.