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Cited by 445Cosmology and Gravitation TheoriesNoncommutative and Quantum Gravity TheoriesRelativity and Gravitational Theory

Photon and graviton mass limits

Open access
Goldhaber, Alfred Scharff, Nieto, Michael Martin·2010·Reviews of Modern Physics
DOI 10.1103/revmodphys.82.939
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Abstract

Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) testing the power in the inverse-square laws of Newton and Coulomb, (2) seeking a nonzero value for the rest mass of photon or graviton, and (3) considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since the previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. ``Cold dark matter'' (slow, invisible classical particles) fits well at large scales. ``Modified Newtonian dynamics'' provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. ``Dark energy'' might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. Significant mass limits are summarized in a table.

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Crossref · 10.1103/revmodphys.82.939

Cites

295 of 295 references verified0 citation errors · 0 not checkable

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Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • m_A ≡ ξ^{1/2} can be interpreted as the rest mass of photons.

    “When ξ is positive, this equation is equivalent to the Proca equation [34-36] and m A ≡ ξ 1 / 2 can be interpreted as the rest mass of photons.”

    From Electrodynamics on cosmological scales (2016) · cites this paper as [36]

    “Photon mass from the Proca equation” (pp. 5–6) says that Proca’s modification can give the photon a nonzero rest mass. The passages do not define ξ or establish that √ξ is that mass, so the specific identification is not supported by our copy. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • When ξ is positive, equation (10) is equivalent to the Proca equation.

    “When ξ is positive, this equation is equivalent to the Proca equation [34-36] and m A ≡ ξ 1 / 2 can be interpreted as the rest mass of photons.”

    From Electrodynamics on cosmological scales (2016) · cites this paper as [36]

    Section B (p. 5) describes the Proca modification of Maxwell’s equations as giving the photon a nonzero rest mass. The equations in our copy are not decoded, however, and the text does not identify the citing paper’s equation (10) or its parameter ξ. It therefore supports the general Proca–photon-mass connection, but not the stated equivalence under ξ > 0. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • If longitudinal photons interact with matter sufficiently weakly or do not interact with matter at all, we still get g = 2 and the Stephan-Boltzmann law remains valid.

    “If they interact with matter sufficiently weak or do not interact with matter at all, we still get g = 2 and the Stephan-Boltzmann law remains valid [35, 36, 58].”

    From Electrodynamics on cosmological scales (2016) · cites this paper as [36]

    Section II.F (p. 12) says that, with local charge conservation, longitudinal-photon coupling is suppressed as photon mass approaches zero and observable electromagnetic phenomena remain continuous in that limit. This supports the weak-interaction premise, but the paper also says a photon with nonzero mass has three polarization degrees of freedom; it does not state that g = 2 or address the Stefan–Boltzmann law. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • There is no observational or experimental evidence for gauge invariance of electromagnetic fields in a curved spacetime with a nonvanishing Ricci curvature.

    “We also remark that there is no observational or experimental evidence for gauge invariance of electromagnetic fields in a curved spacetime with a nonvanishing Ricci curvature.”

    From Electrodynamics on cosmological scales (2016) · cites this paper as [36]

    The discussion of gauge invariance (p. 9) calls the symmetry unobservable, but does not assess observational or experimental evidence for electromagnetic gauge invariance in curved spacetime. Searches for Ricci curvature and tests in curved spacetime found no passage addressing the claim’s specific setting. (LLM, conf=0.73)

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Cites

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Research works printed but not linked: 10

  1. [10][10] C. Amsler et al., The Particle Data Group, '2009 Review of Particle Properties,' Phys. Lett. B 667 , 1-1340 (2008). See pp. 385-386 for the photon and graviton masses. -
  2. [13][13] A. A. Tseytlin, 'Born-Infeld action, Supersymmetry and String Theory,' in: The Many Faces of the Superworld: Yuri Golfand Memorial Volume ,' ed. M. A. Shifman (World Scientific, Singapore, 2000), pp. 417452. Ar Xiv: hep-th/9908105. - · arXiv
  3. [14][14] G. W. Gibbons, 'Aspects of Born-Infield Theory and String/M-Theory,' Rev. Mex. Fis. 49-S1 , 19-29 (2003). ArXiv: hep-th/0106059. - · arXiv
  4. [26][26] L. de Broglie, La M´ echanique Undulatoire du Photon, Une Novelle Th´ eorie de la Lumi` ere (Hermann, Paris, 1940), pp. 39-40. -
  5. [30][30] E. Schr¨ odinger, 'On the Solutions of Wave Equations for Non-Vanishing Rest-Mass Including A Source Function,' Proc. Roy. Irish Acad. A 47 , 1-23 (1941). -
  6. [31][31] E. Schr¨ odinger, 'The General Unitary Theory of the Physical Fields,' Proc. Roy. Irish Acad. A 49 , 43-58 (1943). -
  7. [32][32] E. Schr¨ odinger, 'The Earth's and the Sun's Permanent Magnetic Fields in the Unitary Field Theory,' Proc. Roy. Irish Acad. A 49 , 135-148 (1943). -
  8. [172][172] J. Stachel, 'Einstein's Search for General Covariance,' in Einstein and the History of General Relativity , Einstein Studies, D. Howard and J. Stachel, eds., Vol. I (Birkh¨ auser, Berlin, 1989) pp. 63-100; reprinted in J. Stachel, Einstein from 'B' to 'Z' , (Birkh¨ auser, Berlin, 2002) pp. 301-337. -
  9. [197][197] P. S. (Marquis de) Laplace and N. Bowditch (trans,), Celestial Mechanics, v. 4, (Chelsea Pub. Bronx, NY, 1966). Book 10, Chap. 7, § 22, pp. 612-615. Original French edition: Trait´ e de M´ ecanique C´ eleste , 1799-1825. This voluve 4 was published in Paris by Courcier and our article is livre x, chap. vii, § 22. This is also contained in Œuvres Compl` etes de Laplace , 14 vol. (Gauthier-Villars, Paris, 1978-1912) -
  10. [234][234] M. Milgrom, 'MOND -A Pedagogical Review,' Acta Phys. Polon. B 32 , 3613 (2001). ArXiv: astro-ph/0112069. - · arXiv

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Related

Authors
Goldhaber, A. S., & Nieto, M. M.
Affiliations
State University of New York (US)
ORCID
Nieto, Michael Martin
Venue
Reviews of Modern Physics
Publisher
American Physical Society (APS)
Published
2010-03-23
Volume
82
Issue
1
Pages
939-979
ISSN
  • 0034-6861 (ISSN-L)
  • 1539-0756
DOI
10.1103/revmodphys.82.939
OpenAlex
W2076997212
Cited by
445
References
295
Citations by year
2026: 14 · 2025: 33 · 2024: 22 · 2023: 25 · 2022: 20 · 2021: 16 · 2020: 19 · 2019: 28 · 2018: 28 · 2017: 35 · 2016: 50 · 2015: 30 · 2014: 29 · 2013: 30 · 2012: 24
FWCI
15.19
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Reviews of Modern Physics (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • arXiv (Cornell University)
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
photon mass, graviton mass, modified gravity, Compton wavelength, dark matter, MOND, dark energy, gauge invariance, general coordinate invariance, cosmological constraints

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