Torsion-balance tests of the weak equivalence principle

TL;DR

This work reviews torsion-balance tests of the weak equivalence principle (WEP), focusing on high-precision Be–Ti and Be–Al differential accelerations that probe possible new Yukawa-type forces. By framing WEP violations as limits on vector or scalar couplings with range $\lambda$ and strength $\tilde{\alpha}$, the study combines lab-based Be–Ti/Be–Al results with lunar laser ranging to constrain long-range interactions and dilaton-like scalars, finding no evidence for WEP violation at the 10^{-13}–10^{-5} level. The results have implications for antimatter gravity and dark matter couplings, and outline pathways for substantial sensitivity improvements in future torsion-balance experiments, including higher-contrast test bodies and lower-noise suspensions. Overall, the paper strengthens limits on beyond-Newtonian forces and outlines the feasibility of tighter constraints with next-generation instrumentation.

Abstract

We briefly summarize motivations for testing the weak equivalence principle and then review recent torsion-balance results that compare the differential accelerations of beryllium-aluminum and beryllium-titanium test body pairs with precisions at the part in $10^{13}$ level. We discuss some implications of these results for the gravitational properties of antimatter and dark matter, and speculate about the prospects for further improvements in experimental sensitivity.

Figures (9)

• Figure 1: Operating principle of the Eötvös torsion balance. This idealized balance consists of two test bodies attached to a rigid, massless frame that is supported by a perfectly flexible torsion fibre. ${\bm F_1}$ and ${\bm F_2}$ denote the external forces on the test bodies. The torque about the fibre axis is $T_z=({\bm F_1} \times {\bm F_2}\cdot {\bm r_{12}}) /|{\bm F_1}+{\bm F_2}|$. The signal is the change in $T_z$ when the instrument is rotated about the fibre axis so that the component of $\bm r_{12}$ along the direction of ${\bm F_1}\times{\bm F_2}$ changes sign.
• Figure 2: Simplified scale drawing of the Eöt-Wash WEP torsion balance.
• Figure 3: [Colour online] Torsion pendulum used in the recent Eöt-Wash WEP test. An Al frame holds 4 mirrors and supports 8 barrel-shaped test bodies, 4 of which are Be and 4 are Ti or Al. The structure underneath the pendulum allows the pendulum to be parked to prevent damage when the apparatus is serviced and catches the pendulum if a small earthquake should break the suspension fibre. The tungsten fibre is just visible at the top.
• Figure 4: [Colour online] Power spectral density of the twist signal. The upper [blue] histogram shows WEP data taken with $\omega_{\rm tt}/\omega_0=2/3$. The curve is the thermal noise predicted by equation \ref{['eq: noise']} for a room-temperature oscillator with $Q=6000$. The peaks at integer multiples of $\omega_{\rm tt}$ arise from reproduceable variations in $\omega_{\rm tt}$ (see equation \ref{['eq: false effect']}). The small peak at $\omega_{\rm tt}/2$ is caused by the turntable leveling system that recomputed the tilt every two turntable rotationshe:08. The lower [green] histogram displays data taken with the turntable stationary and the pendulum resting on a support to show the readout noise. The low-frequency readout noise is ascribed to thermal fluctuations.
• Figure 5: Data collected in the Ti-Be (first 4 runs) and Be-Ti (last 2 runs) configurations of the pendulum. The final result is in the difference between the means of the two configurations (shown as solid lines).