We do not know the nature of the quantum system that gives rise to a macroscopic geometry for space and time. In standard physics, a classical geometry is assumed, and quantum theory is applied to spatially extended modes of matter fields. This talk considers the consequences of the opposite approximation: classical matter on a quantum geometry. Although useless for talking about quantum particles, it makes a new prediction: quantum-geometrical uncertainty and noise in transverse positions of massive bodies. Even though the effect originates at the Planck scale, the idea can be tested in interferometers.