  Standard particle theory is based on quantized matter embedded in a classical
geometry. Here, a complementary model is proposed, based on classical matter --
massive bodies, without quantum properties -- embedded in a quantum geometry.
It does not describe elementary particles, but may be a better, fully
consistent quantum description for position states in laboratory-scale systems.
Gravitational theory suggests that the geometrical quantum system has an
information density of about one qubit per Planck length squared. If so, the
model here predicts that the quantum uncertainty of geometry creates a new form
of noise in the position of massive bodies, detectable by interferometers.
