Sub-millimeter Tests of the Gravitational Inverse-square Law

TL;DR

This study directly tests the gravitational inverse-square law at sub-millimeter scales using two 10-hole azimuthally symmetric torsion pendulums and rotating 10-hole attractors. By analyzing high-harmonic torque signals (10ω, 20ω, 30ω) and employing meticulous alignment, shielding, and calibration, the authors find no deviations from Newtonian gravity and place stringent limits on short-range Yukawa and power-law ISL violations. The results translate into robust constraints on large extra dimensions, radion/dilaton couplings, axion exchange, and massive pseudoscalars, significantly advancing the sensitivity of sub-mm gravity tests and informing beyond-Standard-Model theories. The work demonstrates both high-precision experimental technique and meaningful theoretical implications, guiding future searches with enhanced hole counts and smaller-scale probes.

Abstract

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R <= 160 microns, and on two equal-sized large extra dimensions of R <= 130 microns. Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of pseudoscalars with m <= 10 meV/c^2.

Figures (38)

• Figure 1: [color online] 95$\%$ confidence upper limits on a short-range Yukawa violation of the gravitational ISL as of 1999. The region excluded by previous torsion-balance experiments la:97la:98mi:88ho:85 lies above the heavy lines labeled Lamoreaux, Moscow, and Irvine, respectively. The constraints are taken from Ref. lo:99. The dilaton and moduli predictions are taken from Refs. ka:00di:96, respectively. The extra dimensions and radion predictions are based on Eqs. \ref{['eq:R and alpha']}, \ref{['eq:true M_P']} and \ref{['eq:radion']}, assuming $n=2$ and $M_{\ast}=1$ TeV.
• Figure 2: [color online] Torsion pendulums and rotating attractors used in Experiments I (left) and II (right). The active components are shaded. For clarity, we show an unrealistically large vertical separation between the pendulums and attractors, and omit the conducting membranes and attractor drive mechanisms.
• Figure 3: Predicted torques for Experiment I as a function of separation $s$. Solid curves are Newtonian gravity; dotted curves are for a Yukawa interaction with $\alpha=3$, $\lambda=0.25$ mm; dashed curves are for a power-law interaction with $\beta_3=0.05$.
• Figure 4: [color online] Top and side views of the attractor disks. The disks from Experiment I are on the left. The solid circles represent the in-phase upper-plate holes. The open circles show the out-of-phase holes in the upper and lower plates. The three small holes held pins that aligned the upper and lower disks.
• Figure 5: [color online] Schematic diagram of the optical system that measured the pendulum twist.