Interferometric Constraints on Spacelike Coherent Rotational Fluctuations
Abstract
Precision measurements are reported of the cross-spectrum of rotationally-induced differential position displacements in a pair of colocated 39 m long, high power Michelson interferometers. One arm of each interferometer is bent 90 near its midpoint to obtain sensitivity to rotations about an axis normal to the plane of the instrument. The instrument achieves quantum-limited sensing of spatially-correlated signals in a broad frequency band extending beyond the 3.9 MHz inverse light travel time of the apparatus. For stationary signals with bandwidth f > 10\;kHz, the sensitivity to rotation-induced strain h of classical or exotic origin surpasses CSDδ h < tP / 2, where tP = 5.39 × 10-44\;s is the Planck time. This measurement is used to constrain a semiclassical model of nonlocally coherent rotational degrees of freedom of spacetime, which have been conjectured to emerge in holographic quantum geometry but are not present in a classical metric.