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 $\mathrm{\Delta }f>10\mathrm{kHz}$, 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.

Figure 1

Layout of the dual 40-m interferometer system. In this experiment, the X-arm of each interferometer is bent 90° near its midpoint. Dimensions are as marked, with the horizontal plane of interferometer 1 sitting 0.15 m higher than that of interferometer 2. The vacuum chambers are rendered with transparent tops; red lines indicate the positions of the laser beams, with heavier lines indicating the power-recycled cavity. Two radiofrequency photoreceivers sense the output intensity of each interferometer. A diagram of the post-detection signal flow is shown in Fig. 1 of Ref. [2].

Figure 2

Measured power and cross-spectral densities of the interferometer signals, shown in displacement units (left axis) and in strain units normalized to Planck time (right axis). The spectra are averaged across 1098 hours of dual interferometer time series data, or $3.9\times {10}^{10}$ independent spectral measurements per 9.92-kHz bin. Top panel: spectra magnitudes at 9.92-kHz resolution. The teal and green curves show the power spectral density of each interferometer (IFO). The red curve shows the cross-spectral density (CSD), whose statistical sensitivity is indicated by the black trace. Bottom panels: real and imaginary CSD components, rebinned to 496-kHz resolution. Error bars reflect the combined $1\sigma$ statistical uncertainty and 10% systematic calibration uncertainty [1]. For reference, all panels are overlaid with a semiclassical model spectrum of quantum geometrical fluctuations (purple curves) reproduced from Ref. [7], but adjusted for the actual dimensions of the as-built instrument. Bins showing excess coherence with environmental channels are vetoed (gray shading).