  All existing experimental results are currently interpreted using classical
geometry. However, there are theoretical reasons to suspect that at a deeper
level, geometry emerges as an approximate macroscopic behavior of a quantum
system at the Planck scale. If directions in emergent quantum geometry do not
commute, new quantum-geometrical degrees of freedom can produce detectable
macroscopic deviations from classicality: spatially coherent, transverse
position indeterminacy between any pair of world lines, with a displacement
amplitude much larger than the Planck length. Positions of separate bodies are
entangled with each other, and undergo quantum-geometrical fluctuations that
are not describable as metric fluctuations or gravitational waves. These
fluctuations can either be cleanly identified or ruled out using
interferometers. A Planck-precision test of the classical coherence of
space-time on a laboratory scale is now underway at Fermilab.
