Measuring the foaminess of space-time with gravity-wave interferometers

TL;DR

This paper proposes that quantum fluctuations cause space-time to be inherently foamy at very small scales, which can be tested by future gravity-wave interferometers like LIGO/VIRGO and LISA.

Contribution

It introduces a new limit on distance measurements due to quantum foaminess and links this to holographic principles, suggesting testable predictions for gravitational wave detectors.

Findings

Distance measurement uncertainty is larger than the Planck scale.

Quantum foaminess affects gravitational wave interferometer noise levels.

Future detectors may test the foaminess of space-time.

Abstract

By analyzing a gedanken experiment designed to measure the distance $l$ between two spatially separated points, we find that this distance cannot be measured with uncertainty less than $(ll_P^2)^{1/3}$, considerably larger than the Planck scale $l_P$ (or the string scale in string theories), the conventional wisdom uncertainty in distance measurements. This limitation to space-time measurements is interpreted as resulting from quantum fluctuations of space-time itself. Thus, at very short distance scales, space-time is "foamy." This intrinsic foaminess of space-time provides another source of noise in the interferometers. The LIGO/VIRGO and LISA generations of gravity-wave interferometers, through future refinements, are expected to reach displacement noise levels low enough to test our proposed degree of foaminess in the structure of space-time. We also point out a simple connection to the holographic principle which asserts that the number of degrees of freedom of a region of space is bounded by the area of the region in Planck units.