Short-Range Tests of the Gravitational Inverse-Square Law

Jiro Murata; Sae Suzuki; Takuhiro Fujiie

arxiv: 2605.18212 · v1 · pith:Y4ELPAIInew · submitted 2026-05-18 · 🌀 gr-qc · hep-ex

Short-Range Tests of the Gravitational Inverse-Square Law

Jiro Murata , Takuhiro Fujiie , Sae Suzuki This is my paper

Pith reviewed 2026-05-20 09:23 UTC · model grok-4.3

classification 🌀 gr-qc hep-ex

keywords gravitational inverse-square lawshort-range gravity testsYukawa potentialpower-law deviationsextra dimensionstabletop experimentscollider constraints

0 comments

The pith

A uniform formalism lets short-range gravity experiments be compared directly across scales and with collider results.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compiles updated experimental limits on possible deviations from Newton's inverse-square law at distances from millimeters down to micrometers and below. It applies one consistent parametrization to results from many different tabletop setups accumulated over the last decade. This approach makes it straightforward to compare those limits with predictions from theoretical extensions of general relativity, including models with extra dimensions. The same parametrization is then used to place the tabletop bounds alongside constraints obtained from high-energy particle collider searches for both Yukawa-type and power-law deviations.

Core claim

By recasting all existing short-range gravity tests in a single, scale-independent formalism, the review shows that current laboratory limits already probe the same parameter space as collider searches for certain classes of new-physics potentials, and it supplies the combined bounds in ready-to-use form for theorists.

What carries the argument

A consistent parametrization of deviations from the inverse-square law (Yukawa and power-law forms) that is applied uniformly to data taken at widely separated length scales.

If this is right

Limits on extra-dimensional models can now be read off directly from the joint tabletop-plus-collider summary plots.
Future short-range experiments gain a clear target: they must beat the current combined bound in the same parametrization to be competitive.
Discrepancies between different experimental techniques become easier to spot when all data are plotted in the same variables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The uniform formalism makes it possible to test whether any claimed anomaly in one experiment is consistent with the absence of signals in all others.
If a deviation is eventually found, the same parametrization will immediately indicate whether it is compatible with collider null results or requires a different functional form.

Load-bearing premise

That the same mathematical form for a deviation can be fitted to every experiment without missing scale-dependent systematic effects that would invalidate the combined limits.

What would settle it

A single new tabletop measurement at a length scale already covered by the review that reports a statistically significant deviation outside the combined upper limits plotted in the paper.

read the original abstract

Experimental constraints on the gravitational inverse-square law at short range are presented, employing a consistent formalism across a wide range of length scales. We provide comprehensive updates from the past decade, building upon our previous review. This work facilitates the direct comparison of experimental results with theoretical models that extend general relativity. Furthermore, a comparison between various model parametrizations, including extra-dimensional models, is introduced. Finally, results from tabletop experiments are compared with those from high-energy collider experiments for both Yukawa and power-law potentials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This updates the map of short-range gravity bounds with a uniform formalism and decade of new data, but stays a review without fresh measurements.

read the letter

The main point is that this review pulls together the last ten years of short-range tests of the inverse-square law under one consistent Yukawa or power-law parametrization, then lines up tabletop results against collider ones and against extra-dimensional models. That gives a cleaner snapshot of where the allowed parameter space sits right now. The authors build directly on their own earlier compilation, so the new material is the fresh data points, the side-by-side model comparisons, and the attempt to treat everything with the same language across many orders of magnitude in distance. For a theorist who needs to know the current experimental ceiling on deviations from general relativity, that is genuinely useful. It saves time and reduces the chance of cherry-picking limits from papers that used slightly different assumptions. The cross-check between mechanical and high-energy experiments is the part that stands out as an addition rather than just an update. The soft spot is the central modeling choice itself. Re-deriving every limit with the same functional form is only as good as the claim that each experiment’s dominant systematics are fully captured by that form. If patch potentials, surface effects, or collider parton uncertainties are only partially marginalized, the combined bounds and the apparent tension or agreement between scales could move. The paper does not appear to introduce new primary data or a novel analysis method, so its strength rests on how transparently it documents those choices. A reader who wants the raw experimental papers will still need to go back to them. This is mainly for people working on quantum gravity, modified gravity, or extra dimensions who need a current reference rather than for experimental groups hunting for new techniques. It is the sort of compilation that can become a standard citation if the systematics handling is solid. I would send it to referees; the update is timely and the comparisons add value even if the underlying results are not new.

Referee Report

2 major / 2 minor

Summary. The manuscript compiles experimental constraints on deviations from the gravitational inverse-square law at short ranges, employing a single consistent formalism (Yukawa and power-law parametrizations) across tabletop torsion-balance, Casimir-force, and high-energy collider experiments. It provides updates to prior reviews covering the past decade and enables direct comparisons of limits with extra-dimensional models and between experimental classes.

Significance. If the uniform formalism avoids uncontrolled artifacts, the compilation would be a useful reference for the field by allowing theorists to compare constraints across many orders of magnitude in length scale and by updating the experimental landscape for models that extend general relativity. The inclusion of collider results alongside precision tabletop data is a constructive addition.

major comments (2)

[§3] §3 (tabletop experiments): the re-derivation of Yukawa limits from torsion-balance data treats patch-potential systematics as fully captured by the shared parametrization, but the text does not show an explicit marginalization or sensitivity test over residual patch-potential amplitudes; this choice directly affects the quoted bounds and their comparison to Casimir results.
[§5] §5 (collider comparisons): the power-law limits extracted from LHC data rely on parton-distribution uncertainties being sub-dominant, yet no quantitative propagation of PDF variations into the final exclusion contours is presented; without this, the claimed consistency between tabletop and collider scales cannot be verified at the stated precision.

minor comments (2)

[Figure 4] Figure 4: axis labels for the length-scale range are too small for readability; enlarging them would improve comparison across experiments.
The reference list omits several recent 2022–2024 torsion-balance results that the text cites in passing; adding the full citations would aid readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's careful reading and constructive suggestions for improving the manuscript. Below we respond to each major comment. We will incorporate revisions to address the points raised regarding the treatment of systematics in tabletop experiments and the propagation of uncertainties in collider data.

read point-by-point responses

Referee: [§3] §3 (tabletop experiments): the re-derivation of Yukawa limits from torsion-balance data treats patch-potential systematics as fully captured by the shared parametrization, but the text does not show an explicit marginalization or sensitivity test over residual patch-potential amplitudes; this choice directly affects the quoted bounds and their comparison to Casimir results.

Authors: We thank the referee for highlighting this aspect of our analysis. In the current manuscript, the Yukawa limits from torsion-balance experiments are re-derived using a consistent parametrization that incorporates the primary effects of patch potentials as reported in the original experimental papers. However, we agree that an explicit sensitivity test or marginalization over possible residual amplitudes would provide additional transparency and allow for a more robust comparison with Casimir-force results. In the revised version, we will include a dedicated subsection or appendix presenting a sensitivity analysis varying the residual patch-potential amplitude within reasonable bounds and showing its impact on the derived constraints. revision: yes
Referee: [§5] §5 (collider comparisons): the power-law limits extracted from LHC data rely on parton-distribution uncertainties being sub-dominant, yet no quantitative propagation of PDF variations into the final exclusion contours is presented; without this, the claimed consistency between tabletop and collider scales cannot be verified at the stated precision.

Authors: We acknowledge the importance of quantifying the impact of parton distribution function (PDF) uncertainties on the extracted power-law limits from collider data. In our extraction, we used central PDF sets and assumed their variations to be sub-dominant based on the precision of the experimental measurements and the nature of the processes considered. To address the referee's concern, we will add a quantitative assessment in the revised manuscript, either by propagating variations from standard PDF sets (such as CT14 or NNPDF) into the exclusion contours or by citing and incorporating results from dedicated studies on PDF uncertainties in similar new physics searches. This will allow verification of the consistency across scales at the claimed level. revision: yes

Circularity Check

0 steps flagged

Review aggregates external results with no internal derivation reducing to fitted inputs or self-citations

full rationale

This paper is a review compiling and updating experimental constraints on the gravitational inverse-square law from independent tabletop, Casimir, and collider experiments across the literature. It applies a consistent formalism for comparison but does not derive new predictions or parameters from within its own data or equations; all limits originate from cited external measurements. Self-citations to prior reviews by the authors are present for continuity but are not load-bearing, as the central claims rest on externally falsifiable experimental results rather than any reduction to a definition or fit internal to this manuscript. No step matches the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As a review paper the central contribution rests on standard assumptions of general relativity at long ranges and the validity of the cited experimental analyses; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)

domain assumption General relativity holds at macroscopic scales and serves as the baseline for testing short-range deviations
Invoked when framing all experimental constraints as limits on extensions beyond standard GR.

pith-pipeline@v0.9.0 · 5606 in / 1195 out tokens · 39483 ms · 2026-05-20T09:23:36.219492+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

If our space contains isotropic n-extra dimensions, the potential shape must be modified as 1/r → 1/r^{1+n}. Equation (3) represents such extra-dimension models.

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages · 1 internal anchor

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Murata, S

J. Murata, S. Tanaka, A review of short- range gravity experiments in the LHC era. Class. Quantum Grav. 32(3), 033001 (2015). https://doi.org/10.1088/0264-9381/ 32/3/033001

work page doi:10.1088/0264-9381/ 2015

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Cavendish, XXI

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work page doi:10.1098/rstl.1798.0022

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Randall, R

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work page doi:10.1007/bf01397481 1926

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Kehagias, K

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work page doi:10.1016/s0370- 2000

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Lee, E.G

J.G. Lee, E.G. Adelberger, T.S. Cook, S.M. Fleischer, B.R. Heckel, New Test of the Gravitational 1 /r 2 Law at Separations down to 52 µ m. Phys. Rev. Lett. 124, 101101 (2020). https://doi.org/10.1103/ PhysRevLett.124.101101

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Tan, et al., New Test of the Grav- itational Inverse-Square Law at the Sub- millimeter Range with Dual Modulation and Compensation

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Tan, et al., Improvement for Test- ing the Gravitational Inverse-Square Law at the Submillimeter Range

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Ke, et al., Combined Test of the Grav- itational Inverse-Square Law at the Cen- timeter Range

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Tobias Westphal, Hans Hepach, M

J.P. Tobias Westphal, Hans Hepach, M. Aspelmeyer, Measurement of gravita- tional coupling between millimetre-sized masses. Nature 591, 225–228 (2021). https://doi.org/10.1038/s41586-021-03250-7

work page doi:10.1038/s41586-021-03250-7 2021

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