Measurement of Quantum Fluctuations in Geometry

TL;DR

This paper predicts a fundamental quantum-induced noise in spacetime geometry, called holographic noise, with specific spectral and spatial characteristics, potentially observable in current interferometers like GEO600.

Contribution

It derives a parameter-free prediction of holographic noise's spectrum and spatial signature from quantum limits of measurement, linking quantum indeterminacy to observable interferometer signals.

Findings

Holographic noise has a flat power spectral density at the Planck time scale.

The noise exhibits a distinctive transverse shear signature.

Predicted noise level is comparable to current interferometer measurements in GEO600.

Abstract

A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the limits of measurement possible with Planck wavelength radiation. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ``holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature, and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions, and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometer GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as LIGO, where beam power is much less in the beamsplitter than in the arms.