A new analytical framework proposes a common way to read torsion-balance data in gravity experiments: treat a possible signal as a known torque pattern, or treat unexplained fluctuations as additional random torque noise. The manuscript says calibrated spectra can be turned into bounds for both cases, giving researchers a shared measurement interface for weak-field tests. It is an arXiv version-1 preprint dated 26 August 2026.
Those two routes are deliberately separate. For a deterministic signal—one with a specified time or frequency pattern—the analysis uses a matched filter, a calculation that weights the data against that template, and derives a finite-time Cramér–Rao amplitude bound. The method fixes one-sided spectrum conventions, a linear calibrated angle-equivalent noise budget and the angle-to-torque conversion needed to put the result in physical units.
For a stochastic model, the procedure starts with the observed angle spectrum. It subtracts the standard calibrated noise budget, turns whatever remains into equivalent torque units and uses that residual to bound extra stationary torque noise. A single diffusion parameter, Dτ, is allowed only for Markovian white torque noise—the case treated as having no relevant time memory; colored or non-Markovian noise must be compared with the full frequency-dependent residual.
The benchmark gap is large
The numbers illustrate why the distinction matters. In a representative room-temperature Cavendish benchmark, the resonant measurement-added standard quantum limit, or SQL, for angle noise is 3.25 × 10−12 rad/√Hz. The same calculation puts resonant thermal angle noise at 1.36 × 10−4 rad/√Hz. Both are angle amplitude spectral densities, or ASDs, meaning noise levels quoted per square-root hertz. The thermal value is about 4.2 × 10⁷ times the SQL, and the benchmark’s viscous thermal white-diffusion scale is Dτ ≃ 1.9 × 10−30 N² m² s.
That gap is not being offered as a universal limitation of torsion balances. The authors label the Cavendish values illustrative and use the diffusion figure only to set a scale; it is not an experimental semiclassical-gravity limit. The benchmark is therefore a way to organize the noise scale, not a new apparatus-independent bound.
A public sensitivity point, recast
The paper then works through a public sensitivity point from Yan et al. The reported angle sensitivity is 0.3 µrad/√Hz at 2.5 mHz. Using the calibrated susceptibility, the example converts that point to an equivalent torque ASD of about 9.77 × 10−12 N m/√Hz. Treating the quoted floor as white noise gives DτYan ≃ 2.38 × 10−23 N² m² s.
But this is a reference calculation, not a full reanalysis of the Yan spectrum. The value uses a single public sensitivity point and the total observed floor, rather than a fully subtracted residual. The paper therefore presents it as a conservative observed-floor estimate, not as a fully subtracted constraint on semiclassical noise.
From noise bounds to branch tests
One possible use is to compare competing deterministic torque patterns. In its discussion of Page–Geilker and Fedida–Kent-style MEP tests, the paper treats them as physically distinct interpretive applications of the template formalism. A representative branch-discrimination calculation produces a torque threshold of approximately 9 × 10−18 N m.
That threshold is a benchmark calculation, not a demonstrated feasible experiment. The same caution applies to the broader white-noise figures: Dτ is meaningful as a one-number summary only under the Markovian-white assumption. If the residual is colored or non-Markovian, the relevant object is the full frequency-dependent spectrum, not a single diffusion scale.
The result is a measurement language more than a verdict about gravity. It tells analysts where to place a proposed signal—against a calibrated torque template or into an equivalent-torque residual—and how to connect a quoted limit to the assumptions behind it.
Paper data and sources
Original title: Torsion balances as operational probes of semiclassical gravity: Matched-filter bounds, torque-diffusion constraints, and quantum-noise benchmarks
Authors: Jyotirmaya Mohanta, Yutaka Shikano
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text