# Interferometric Constraints on Quantum Geometrical Shear Noise Correlations

## TL;DR

This paper reports on the first experimental search for quantum geometrical shear noise correlations in space-time using the Holometer, setting new constraints that surpass previous limits and probing fundamental quantum space-time models.

## Contribution

It introduces the first measurement of correlated space-time position variations at Planck-scale sensitivities, testing models of quantum space-time geometry with unprecedented precision.

## Key findings

- No detectable shear noise correlations found within sensitivity limits.
- Constraints on models of quantum space-time shear noise exceed previous bounds.
- Experimental limits surpass the Planck-scale holographic bound on position states.

## Abstract

Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.