Indeterminacy of Holographic Quantum Geometry

TL;DR

This paper models the indeterminacy of position in holographic spacetime using wave optics, predicts observable holographic noise in interferometers, and links it to fundamental quantum gravitational limits.

Contribution

It introduces a wave optics effective theory for holographic spacetime, predicts measurable holographic noise, and connects it to the fundamental Planck scale and gravitational thermodynamics.

Findings

Holographic noise spectrum estimated for GEO600 matches unexplained noise.

Transverse position uncertainty exceeds Planck length for large separations.

The theory provides a fundamental limit on time intervals in a holographic universe.

Abstract

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopically separated positions the transverse uncertainty is much larger than the Planck length, and is predicted to be observable as a "holographic noise" in relative position with a distinctive shear spatial character, and an absolutely normalized frequency spectrum with no parameters once the fundamental wavelength is fixed from the theory of gravitational thermodynamics. The spectrum of holographic noise is estimated for the GEO600 interferometric gravitational-wave detector, and is shown to approximately account for currently unexplained noise between about 300 and 1400Hz. In a holographic world, this result directly and precisely measures the fundamental minimum interval of time.