Covariance scaling and a dual-mode torque diagnostic in measurements of the gravitational constant
Abstract
Laboratory determinations of the Newtonian gravitational constant G disagree by more than their quoted uncertainties allow. We examine the sixteen determinations comprising the CODATA-2018 archive using a proportional covariance-scale model that retains the full reported covariance matrix. Because the 2026 NIST torsion-balance redetermination shares apparatus lineage with the BIPM Mark II balance, our primary historical fit excludes the BIPM-14 determination, giving λ̂ = 2.967 for the remaining fifteen measurements. Evaluated against this historical model under the declared uniform covariance-scaling convention, the correlated four-configuration NIST result is highly unlikely under the archive's reported, unscaled covariance but is statistically unremarkable once the historically inferred extra dispersion is applied (Qλ= 4.840; finite-sample F tail p = 0.382); a mean-only scaling sensitivity leaves the vector discrepant. Retaining the complete archive also gives a comparable result. We further examine four matched free-minus-servo torque differences reported by NIST. They are consistent with a single common absolute torque offset across the four tested configurations, ΔN̂ = 1.918 ± 0.215 pN m, and poorly described by an equally simple fractional-scale alternative under the stated independent-Type-A treatment, with a chi-square contrast of Δχ2 = 11.041 between the two torque models. The paper provides a covariance audit of the historical archive, a lineage-qualified consistency check, and an experimentally testable diagnostic for dual-mode torsion balances, without proposing a revised value of G.
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BibTeX
@misc{kumar2026covariance,
title = {{Covariance scaling and a dual-mode torque diagnostic in measurements of the gravitational constant}},
author = {Vineet Kumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04707},
eprint = {2610.04707},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04707},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Covariance scaling and a dual-mode torque diagnostic in measurements of the gravitational constant
AU - Vineet Kumar
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04707
UR - https://arxiv.org/abs/2610.04707
AB - Laboratory determinations of the Newtonian gravitational constant G disagree by more than their quoted uncertainties allow. We examine the sixteen determinations comprising the CODATA-2018 archive using a proportional covariance-scale model that retains the full reported covariance matrix. Because the 2026 NIST torsion-balance redetermination shares apparatus lineage with the BIPM Mark II balance, our primary historical fit excludes the BIPM-14 determination, giving λ̂ = 2.967 for the remaining fifteen measurements. Evaluated against this historical model under the declared uniform covariance-scaling convention, the correlated four-configuration NIST result is highly unlikely under the archive's reported, unscaled covariance but is statistically unremarkable once the historically inferred extra dispersion is applied (Q_λ= 4.840; finite-sample F tail p = 0.382); a mean-only scaling sensitivity leaves the vector discrepant. Retaining the complete archive also gives a comparable result. We further examine four matched free-minus-servo torque differences reported by NIST. They are consistent with a single common absolute torque offset across the four tested configurations, ΔN̂ = 1.918 ± 0.215 pN m, and poorly described by an equally simple fractional-scale alternative under the stated independent-Type-A treatment, with a chi-square contrast of Δχ^2 = 11.041 between the two torque models. The paper provides a covariance audit of the historical archive, a lineage-qualified consistency check, and an experimentally testable diagnostic for dual-mode torsion balances, without proposing a revised value of G.
ER -