Statistical Measures of Planck Scale Signal Correlations in Interferometers

TL;DR

This paper develops a statistical framework to analyze interferometer data for detecting Planck scale quantum geometrical correlations, aiming to test deviations from classical spacetime structure at extremely small scales.

Contribution

It introduces a model-independent method to interpret high-precision interferometer measurements of quantum geometrical correlations, connecting them to Planck scale physics.

Findings

Derived frequency-domain power spectra for correlation functions.

Showed consistency of candidate correlation functions with classical causal structure.

Projected experimental sensitivity to constrain Planck scale departures.

Abstract

A model-independent statistical framework is presented to interpret data from systems where the mean time derivative of positional cross correlation between world lines, a measure of spreading in a quantum geometrical wave function, is measured with a precision smaller than the Planck time. The framework provides a general way to constrain possible departures from perfect independence of classical world lines, associated with Planck scale bounds on positional information. A parametrized candidate set of possible correlation functions is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of information suggested by gravity. Frequency-domain power spectra are derived that can be compared with interferometer data. Simple projections of sensitivity for specific experimental set-ups suggests that measurements will directly yield constraints on a universal time derivative of the correlation function, and thereby confirm or rule out a class of Planck scale departures from classical geometry.