Atmospheric pressure fluctuations are unlikely to be the factor limiting current torsion-balance measurements of the gravitational constant, G, according to a new modeling study. Under the study’s benchmark assumptions, the environmental contribution stays below a current reference relative uncertainty of 2.2 × 10−5. But the analysis also points to a harder problem ahead: experiments seeking uncertainties of one part in a million or one part in ten million would need much tighter control of the gravity gradients linked to pressure fluctuations.
The work is an arXiv version-1 preprint dated 26 Aug 2026. It develops a framework for carrying atmospheric Newtonian noise—the gravitational effect associated with changing pressure or surface density—through the calculation used to estimate the experiment’s torque and into its uncertainty budget.
Turning pressure into a measurement uncertainty
The calculation begins with a first-order GUM propagation. In practical terms, the estimate treats the measured torque and the geometry-dependent response coefficient as the key inputs, then follows how their uncertainties contribute to the final result. For stationary, correlated noise, the model uses the estimator’s transfer function to evaluate uncertainty at different frequencies. It treats that stationary environmental noise separately from slow, non-stationary baseline drift.
To build its atmospheric input, the study uses global low- and high-noise ambient-pressure spectra compiled from an infrasound network. It converts pressure changes into an effective surface density through hydrostatic balance, then brackets the link between time variations and spatial patterns with two phase-velocity benchmarks: 340 metres per second for acoustic propagation and about 10 metres per second for slow advection.
That conversion is a benchmark closure, not a universal description of every laboratory. The study’s pressure-to-gravity treatment is two-dimensional and does not capture all altitude weighting, non-hydrostatic fluctuations, boundary-layer turbulence or building-specific pressure patterns. Outdoor global envelopes may also differ from indoor fields shaped by ventilation, building acoustics and local flows.
Geometry changes the environmental coupling
The authors compare two idealized layouts to show how geometry can change the environmental channel. A two-mass dumbbell is used as an upper-coupling reference, while a perfectly symmetric cross represents an idealized rejection limit. These are analytical bounds, not complete reconstructions of historical G experiments.
For long-wavelength disturbances, the symmetric-cross baseline factor has a leading coefficient of 1/1152 and scales with the sixth power of kl. That steep scaling indicates substantially stronger suppression than a simple low-order coupling benchmark as the disturbance wavelength grows relative to the apparatus baseline.
There is an important trade-off. If the desired source-mass signal and the environmental field occupy the same quadrupole channel, reducing that channel suppresses both. The perfectly symmetric cross therefore cannot be treated as a complete G-measurement geometry or as a free way to remove noise.
A small present contribution with a wider uncertainty envelope
Across the atmospheric benchmarks, simple-mean propagation gives an equivalent gravity-gradient range of about 4 × 10−18 to 1 × 10−13 s−2, with a more central envelope around 10−16 to 10−14 s−2. The width reflects assumptions about pressure level, integration duration and the mapping between temporal frequency and spatial wavenumber.
Within that comparison, the standard atmospheric background is not expected to be a limiting contributor at the current reference scale. The conclusion is conditional: local fields and the transfer functions of a particular apparatus could differ substantially from the analytical benchmarks.
The design margin narrows as the target improves. For a relative uncertainty of 10−6, the benchmark signal-gradient range implies an environmental-gradient bound of roughly 10−13 to 10−12 s−2. At 10−7, the corresponding bound is roughly 10−14 to 10−13 s−2. The figures are rounded internal benchmarks, not apparatus-specific measurements.
A possible route to monitoring and subtraction
The study also tests whether a surrounding array of pressure sensors could help estimate and subtract the environmental field. In its dimensionless toy simulation, the authors used 50 independent random-field realizations, with 120 modes in each realization, wavenumbers from 0.05 to 20 in units of 1/l, a relative-noise parameter of 0.05, sensor-radius ratios of 0.5, 1.0 and 2.0, and sensor counts from 2 through 32.
In that broad-band model, arrays with sensor radii of about one arm length to a few arm lengths performed better than the most compact arrangement, with the 2l case comparable to or slightly better than l when the number of sensors was larger. The result is qualitative: the simulation omits atmospheric altitude weighting and site-specific spatio-temporal spectra, so it is not a universal prescription for where to place barometers.
The paper’s practical message is that atmospheric gravity gradients can be included in future torsion-balance uncertainty budgets and should be bounded and monitored as measurements move toward and below the part-per-million regime. It does not reanalyze an individual G experiment, explain historical scatter, establish a universal laboratory phase velocity or solve non-stationary instrument drift. The Ornstein–Uhlenbeck process used in the study is only a stationary benchmark; baseline wandering remains a separate metrological contribution.
The work was partially supported by JST ASPIRE and the JST SPRING Program, identified in the report as JPMJAP2339 and JPMJSP2124.
Paper data and sources
Original title: Atmospheric Newtonian noise in torsion-balance measurements of the gravitational constant $G$
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