Tests of the Gravitational Inverse-Square Law

TL;DR

This paper surveys experimental tests of the gravitational inverse-square law (ISL) at millimeter and submillimeter scales, motivated by theories predicting extra dimensions and new light bosons. It outlines Yukawa-type and other parameterizations to capture deviations and reviews a suite of experiments—torsion balances, microcantilevers, and Casimir-force measurements—along with their backgrounds, calibrations, and constraints on ISL-violating interactions. The work highlights how current data constrain extra-dimensional scenarios and light scalar/vector exchanges while noting remaining viable models and the prospects for substantial sensitivity improvements in the near term. The findings are crucial for guiding searches for new gravitational physics and for testing fundamental ideas about quantum gravity, cosmology, and the structure of spacetime.

Abstract

We review recent experimental tests of the gravitational inverse-square law and the wide variety of theoretical considerations that suggest the law may break down in experimentally accessible regions.

Figures (10)

• Figure 1: Schematic diagram of the 10-hole pendulums and rotating attractors used in the two experiments of Hoyle et al. ho:01ho:01ahe:02. The active components are shaded.
• Figure 2: Top: Torques measured in the first experiment of Hoyle et al. as a function of pendulum/attractor separation. Open circles are data taken with the lower attractor disk removed and show the effect of uncancelled gravity. Smooth curves show the Newtonian fit. Bottom: Residuals for the Newtonian fit. The solid curve shows the expected residual for a Yukawa force with $\alpha=3$ and $\lambda=250~\mu$m.
• Figure 3: Spectral density of the torque signal in the 22-fold symmetric experiment of the Eöt-Wash group. The peaks at 8.5 and 17 $\omega$ are gravitational calibrations; the fundamental and first three overtones of the short-range signal are at 22, 44, 66, and 88 $\omega$. The smooth curve shows the thermal noise computed using Equation \ref{['eq:thermal']}.
• Figure 4: 95%-confidence-level constraints on ISL-violating Yukawa interactions with $\lambda > 1$ cm. The LLR constraint is based on the anomalous perigee precession; the remaining constraints are based on Keplerian tests. This plot is based on Figure 2.13 of Reference fi:99 and updated to include recent LLR results.
• Figure 5: 95%-confidence-level constraints on ISL-violating Yukawa interactions with 1 $\mu{\rm m} < \lambda < 1$ cm. The heavy curves give experimental upper limits (the Lamoreaux constraint was computed in Reference lo:99). Theoretical expectations for extra dimensions Ar:98a, moduli DG:96, dilaton Ka:00a, and radion An:97 are shown as well.