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 $90^{\circ }$ 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.

arXiv comment9 pages, 4 figures. PRL accepted manuscript

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