Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
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We conducted three torsion-balance experiments to test the gravitational inverse-square law at separations between 9.53 mm and $55\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, probing distances less than the dark-energy length scale ${\ensuremath{\lambda}}_{d}=\sqrt[4]{\ensuremath{\hbar}c/{\ensuremath{\rho}}_{d}}\ensuremath{\approx}85\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. We find with 95% confidence that the inverse-square law holds ($|\ensuremath{\alpha}|\ensuremath{\le}1$) down to a length scale $\ensuremath{\lambda}=56\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and that an extra dimension must have a size $R\ensuremath{\le}44\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$.
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The ten-dimensional Planck scale takes the range M_D=10p ∼ 10 keV - 10 TeV, assuming an upper bound on the size of any compact dimension of roughly order microns (or eV) from gravitational bounds to approximately 10^-18 m (or a TeV) from collider bounds, and six compact dimensions.
“If we assume an upper bound on the size of any compact dimension of roughly order microns, or equivalently eV, from gravitational bounds [29] to approximately 10 -18 m or a TeV from collider bounds [30], and six compact dimensions then the ten-dimensional Planck scale takes the range M D =10 p ∼ 10 keV -10 TeV.”
From Gravitational memory and compact extra dimensions (2022) · cites this paper as [29]
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- Authors
- Kapner, D. J., Cook, T. S., Adelberger, E. G., Gundlach, J. H., Heckel, B. R., Hoyle, C. D., & Swanson, H. E.
- Affiliations
- University of Washington (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-01-08
- Volume
- 98
- Issue
- 2
- Pages
- 021101-021101
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2102660738
- Cited by
- 984
- References
- 3
- Citations by year
- 2026: 36 · 2025: 44 · 2024: 56 · 2023: 47 · 2022: 42 · 2021: 46 · 2020: 49 · 2019: 50 · 2018: 65 · 2017: 40 · 2016: 44 · 2015: 43 · 2014: 66 · 2013: 38 · 2012: 53
- FWCI
- 39.82
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy
- Office of Science
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- gravitational inverse-square law, torsion balance, dark energy, extra dimensions, modified gravity, fifth force
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