The 2020 HUST torsion-pendulum experiment verified the gravitational inverse-square law down to a Yukawa length scale of 48 μm (violation strength |α| ≤ 1 at 95% confidence), setting the strongest laboratory bound in the 40–350 μm range, but identified the electrostatic environment as the blocking issue for tests at even shorter separations: the measured torque noise grows rapidly as the pendulum–attractor gap shrinks, driven by the coupling of residual vibration of the thin electrostatic shielding membrane to residual surface potentials, and the spatially varying patch potentials on the pendulum and membrane produce a residual electrostatic torque that was difficult to characterize. The problem is to carry out a shorter-range test of the inverse-square law by suppressing this vibration-coupled electrostatic torque noise and by measuring and controlling the patch-potential torque down to the level of the gravitational signal being sought. No published inverse-square-law constraint at shorter range exists, so the problem remains open.

Background

Tests of the gravitational inverse-square law (ISL) at short range search for departures from Newtonian gravity that many theories beyond the Standard Model predict, such as large extra dimensions (the Arkani-Hamed–Dimopoulos–Dvali, or ADD, model) or ultralight dark-sector bosons. The departure is conventionally parametrized as a Yukawa correction to the Newtonian potential, V(r)=−Gm1m2(1+αe−r/λ)/rV(r) = -G m_1 m_2 (1 + \alpha e^{-r/\lambda})/r, where α\alpha is the relative strength and λ\lambda the range of the new interaction; an experiment excludes a region of the (α,λ)(\alpha, \lambda) plane. The leading instruments are torsion pendulums: a suspended pendulum disk or plate responds to the torque from a rotating attractor mass, and a null or compensation geometry suppresses the dominant Newtonian torque so that a non-Newtonian signal would modulate at a characteristic frequency. Because the gravitational signal is extraordinarily weak at submillimeter separations, a thin (tens of micrometers) electrically grounded conducting membrane — the shielding membrane — is inserted between pendulum and attractor to block electrostatic forces, which would otherwise overwhelm gravity by many orders of magnitude. Two electrostatic limitations survive the shield. First, any residual (average) potential difference between pendulum and membrane converts residual vibration — seismic motion of the pendulum and, dominantly, of the membrane — into a fluctuating separation and hence a fluctuating electrostatic torque, so the random torque noise rises steeply as the gap shrinks. Second, real conducting surfaces are not equipotentials: patch potentials, spatially varying surface potentials arising from crystallographic grains, adsorbed contaminants, and work-function differences across the surface, generate a residual electrostatic torque between closely spaced bodies that grows at short separation and is hard to characterize because the potential distribution on the actual machined and coated surfaces is unknown. In that experiment (Tan et al., Phys. Rev. Lett. 124, 051301 (2020), from Huazhong University of Science and Technology, HUST), a torsion pendulum with two tungsten test plates hung from a 25 μm tungsten fiber faced an eight-plate rotating tungsten attractor behind a 30 μm beryllium-copper membrane at a minimum surface-to-surface gap of 210 μm, with capacitive feedback stabilizing the balance; the improvement over the group's 2016 test came precisely from suppressing membrane vibration. The result — the ISL holds with ∣α∣≤1|\alpha| \le 1 down to λ=48\lambda = 48 μm at 95% confidence, the strongest bound over 40–350 μm — was stated by the authors to be limited at short range by the vibration-coupled electrostatic noise and by the uncharacterized patch-potential distribution, which they flagged as the unresolved challenge for testing the law at even shorter scales. In parallel, the Eöt-Wash group (University of Washington) tested the 1/r21/r^2 law at separations down to 52 μm (Lee et al., 2020). Later analyses by the same HUST group additionally identified residual-gas damping as a new noise floor: squeeze-film damping — viscous dissipation by the residual gas film trapped between the closely spaced plates — is predicted to exceed the pendulum's internal thermal noise for gaps below roughly 40 μm, so any substantially shorter-range test must confront that limit as well. The physics of patch forces between conductors goes back to Speake and Trenkel (2003), with limits on short-separation force sensing derived by Behunin et al. (2014), and torsion-pendulum scanning-probe measurements of surface-potential variations by Yin et al. (2014).

Problem Statement

Extend the laboratory test of the gravitational inverse-square law to separations shorter than the 210 μm minimum gap of the 2020 HUST torsion-pendulum experiment — and thereby strengthen or extend the exclusion of Yukawa-type violations below the current frontier of ∣α∣≤1|\alpha| \le 1 at λ=48\lambda = 48 μm — by overcoming the two electrostatic limitations that the 2020 experiment identified as blocking progress: (1) the random torque noise that grows rapidly as the separation decreases, produced by the coupling of residual vibration of the torsion pendulum and, dominantly, of the electrostatic shielding membrane to the residual surface potential, requiring vibration isolation or common-mode suspension of pendulum and membrane (or equivalent) such that this coupled noise falls below the gravitational signal to be measured; and (2) the residual electrostatic torque from the spatially varying patch potentials on the pendulum and the shielding membrane, requiring the surface-potential distribution on the actual interacting surfaces to be measured or bounded — together with its temporal drift — so that the patch-induced torque at the operating separations is quantified and demonstrated to be subdominant. A complete answer is a new experimental constraint on deviations from the inverse-square law at shorter range, in which both electrostatic noise channels are measured, modeled, and shown not to limit the reported bound.

References

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