Interferometric Constraints on Spacelike Coherent Rotational Fluctuations

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 Δ f > 10 kHz , the sensitivity to rotation-induced strain h of classical or exotic origin surpasses CSDδh< t P / 2 , where t P = 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.