The Eöt-Wash torsion-balance experiment of Lee et al. (Phys. Rev. Lett. 124, 101101 (2020)) tested Newton's inverse-square law at detector–attractor separations down to 52 μm and set the still-current laboratory frontier: any gravitational-strength Yukawa-type deviation must have a range λ < 38.6 μm (95% confidence). Reaching smaller separations was blocked by environmental and seismic vibrations coupling to electrostatic patch fields below ~30 μm pendulum–shield-foil gaps, by dust particles, by the metrology of reproducible sub-micron face-to-face separations (whose zero-point includes shield-foil and glue-film thicknesses), and by magnetic-susceptibility torques of the platinum test bodies. The open problem is to extend direct laboratory inverse-square-law tests below this 52 μm separation frontier, on the torsion-balance platform or another, so as to push the exclusion region in the (|α|, λ) plane of Yukawa-type new interactions to shorter ranges and smaller coupling strengths.

Background

Short-range tests of Newtonian gravity are usually parametrized by adding a Yukawa correction to the Newtonian potential between point masses m1m_1 and m2m_2, V(r)=−Gm1m2r[1+α e−r/λ],V(r) = -\frac{G m_1 m_2}{r}\left[1 + \alpha\, e^{-r/\lambda}\right], where α\alpha is the strength of a hypothetical new interaction relative to ordinary gravity and λ\lambda is its range. Many extensions of general relativity — compact large extra dimensions, dilatons or massive gravitons, radion unification, and recent micron-scale 'dark dimension' scenarios — predict such terms at micrometer-to-millimeter scales, so each laboratory exclusion curve in the (∣α∣,λ)(|\alpha|, \lambda) plane directly bounds new-physics parameter space that colliders cannot reach.

The leading instrument is the torsion balance: a pendulum disk hanging from a thin fiber is suspended above a rotating 'attractor' whose azimuthal density pattern — in the 2020 University of Washington (Eöt-Wash) experiment, superposed 18-fold and 120-fold hole patterns in 54 μm and 99 μm thick platinum disks of 5.5 cm diameter — exerts harmonic torques at multiples nωn\omega of the rotation frequency. A deviation from the 1/r21/r^2 law changes the separation-dependence of these torques. A 10 μm thick, gold-coated beryllium-copper membrane stretched between pendulum and attractor provides electrostatic shielding; the face-to-face separation is inferred from electrical capacitances plus the measured thicknesses of this foil and of the glue films that mount the test-body foils, and the pendulum's free-oscillation frequency ω0≈0.0184 s−1\omega_0 \approx 0.0184\ \mathrm{s^{-1}} must be tracked because stray electrostatic 'patch' fields (spatially varying surface potentials on the coated surfaces) shift it at small gaps.

Lee et al. (2020) took data at separations between 52 μm and 3.0 mm. Newtonian gravity fit the data well, giving 95%-confidence limits: any gravitational-strength (∣α∣=1|\alpha| = 1) Yukawa interaction must have range λ<38.6 μm\lambda < 38.6\ \mu\mathrm{m}, the largest toroidal extra dimension must be smaller than 30 μm, and dilaton/heavy-graviton and radion-unification mass scales must exceed 5.1 meV and 7.1 TeV respectively — at the time the tightest existing laboratory constraints on such 'string-inspired' phenomena. Going to smaller separations was blocked by four instrumental effects, identified explicitly in the paper: (1) environmental and seismic vibrations, which couple to patch electrostatic fields, sharply increased the noise once the pendulum–foil gap fell below ~30 μm and prevented data below 52 μm altogether (the authors were implementing an active vertical-vibration-reduction system); (2) dust particles, which can disturb the gap and prevent data-taking at small separations; (3) the difficulty of establishing and measuring reproducible sub-micron face-to-face separations, since the separation zero-point sums the shield-foil thickness and glue-film thicknesses; and (4) torques from the magnetic susceptibility of the platinum test bodies in residual magnetic fields, which in 2020 was characterized with shield-removal runs and subtracted as a roughly 1% systematic of the 120ω\omega torque.

For context on the neighboring landscape: microcantilever and torsional-oscillator experiments (Geraci et al., 2008; Sushkov et al., 2011) constrained only much stronger couplings at the ~10 μm scale; the Huazhong University of Science and Technology (HUST) torsion pendulum (Tan et al., 2020) operates at gaps of 210 μm or larger; and below ~1 μm the best limits come from Casimir-force experiments, which are sensitive only to couplings many orders of magnitude above gravitational strength. No laboratory experiment has yet reported a competitive measurement below 52 μm: the levitated-microsphere search at ~6 μm separation reaches only |α| ≈ 10^6–10^7, about six orders of magnitude above gravitational strength, and micro-fabricated torsion-resonator platforms have not yet yielded a measurement. The regime below λ≈38.6 μm\lambda \approx 38.6\ \mu\mathrm{m} at gravitational strength is therefore currently unconstrained by direct laboratory tests, and reaching it requires exactly the instrumental advances the source experiment names.

Problem Statement

Extend direct laboratory tests of the gravitational inverse-square law to test-mass separations below 52 μm — the minimum detector–attractor separation reached by Lee et al. (2020) — with sensitivity at or approaching gravitational strength, thereby moving the 95%-confidence exclusion region in the (∣α∣,λ)(|\alpha|, \lambda) plane of Yukawa-type new interactions (where α\alpha is the strength of a Yukawa correction αe−r/λ\alpha e^{-r/\lambda} to the Newtonian potential and λ\lambda is its range) beyond the Lee et al. (2020) curve — to ranges λ<38.6 μm\lambda < 38.6\ \mu\mathrm{m} at ∣α∣=1|\alpha| = 1 and/or to smaller ∣α∣|\alpha| at accessible ranges — or detecting a statistically significant deviation from Newtonian gravity with the harmonic content and separation dependence predicted for the apparatus geometry.

The source experiment identifies the obstacles that any such extension must overcome, and a complete answer must show they are controlled rather than merely assumed away: (i) environmental and seismic vibration coupling to electrostatic patch fields, which dominated the noise for pendulum–shield-foil gaps below ~30 μm and set the 52 μm floor; (ii) dust particles, and the achievement of reproducible, sub-micron-accuracy face-to-face separations whose zero-point includes the shield-foil and glue-film thicknesses; and (iii) magnetic-susceptibility-related torques of the dense test bodies, which must be bounded or suppressed at the smaller separations. The problem is platform-agnostic: it may be answered with an improved torsion balance (for example with active vertical-vibration reduction) or with another technique such as levitated microsensors or micro-fabricated resonators, provided the measurement is direct, reaches separations below 52 μm, carries a quantified systematic-error budget addressing the above effects, and supersedes the published exclusion curve at short ranges (or reports a validated detection). A quantified design — a direct measurement, or a design of one, that reaches separations below 52 μm, carries the required noise and systematic-error budget, and yields a projected 95%-confidence exclusion curve lying below the Lee et al. (2020) curve at short ranges (λ < 38.6 μm at |α| = 1 and/or smaller |α| at accessible ranges), or a validated detection — resolves the task; executed data are not required.

References

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