Experimental Status of Gravitational-Strength Forces in the Sub-Centimeter Regime

TL;DR

This paper surveys experimental constraints on gravitational-strength Yukawa forces at sub-centimeter scales, using a Yukawa-modified potential $V(r) = - G \frac{m_1 m_2}{r} [1 + \alpha e^{-r/\lambda}]$ to map excluded regions in the $\alpha$–$\lambda$ parameter space. It synthesizes limits from classical torsion-balance tests and Casimir-force measurements, and outlines a theoretical landscape where light bosons, moduli, dilatons, axions, and large extra dimensions predict sizable forces at μm–mm ranges. It then proposes a high-frequency (≈1 kHz) mechanical-oscillator experiment with coordinated source and detector masses, deriving explicit expressions for the expected Yukawa torque and the thermal-noise-limited sensitivity, projecting reach down to around $\lambda \approx 50\ \mu\mathrm{m}$ and spanning roughly 10 decades in parameter space. The work underscores the continued motivation to probe sub-centimeter gravity with macroscopic devices, given compelling predictions from string-inspired theories and extra-dimensional scenarios, and highlights the potential for substantial improvements over existing limits.

Abstract

We review the experimental constraints on additional macroscopic Yukawa forces for interaction ranges below 1 cm., and summarize several theoretical predictions of new forces in this region. An experiment using 1 kHz mechanical oscillators as test masses should be sensitive to much of the parameter space covered by the predictions.

Figures (4)

• Figure 1: Parameter space for Yukawa-type forces in which the strength relative to gravity ($\alpha$) is plotted versus the range ($\lambda$). Limit curves from experiments defining the excluded region are shown (bold lines) along with the anticipated sensitivity of the proposed experiment, as well as specific predictions for new long range forces (fine and dashed lines).
• Figure 2: a) principal components of the apparatus; b) cross-section of central region showing dimensions used in calculation of experimental sensitivity.
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