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 $90^{\circ}$ 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 $\Delta f > 10\;\mathrm{kHz}$, the sensitivity to rotation-induced strain $h$ of classical or exotic origin surpasses $\mathrm{CSD}_{\delta h} < t_P / 2$, where $t_P = 5.39 \times 10^{-44}\;\mathrm{s}$ 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.