Planck scale displacement of a connected mirror pair: an energy measurement in a gravitational field

Reflection of a particle from a mirror pair that is fixed to a platform which falls freely in a gravitational field is shown to infer displacement of the center of mass of this platform of order the Planck length. This displacement and its relationship to the wave and particle nature of reflection in such an energy measurement is elucidated using harmonic motion of the mirror pair.
Comment: 5 pages, 2 figures