Cited by 303Quantum and Classical ElectrodynamicsRelativity and Gravitational TheoryParticle physics theoretical and experimental studies

The DOI matches its Crossref record; 204 of the 205 references it cites were found in a registry or an index.

The mass of the photon

Tu, Liang-Cheng, Luo, Jun, Gillies, George T·2005·Reports on Progress in Physics

DOI 10.1088/0034-4885/68/1/r02

Open this paper in CoChat — free account

Abstract

Because classical Maxwellian electromagnetism has been one of the cornerstones of physics during the past century, experimental tests of its foundations are always of considerable interest. Within that context, one of the most important efforts of this type has historically been the search for a rest mass of the photon. The effects of a nonzero photon rest mass can be incorporated into electromagnetism straightforwardly through the Proca equations, which are the simplest relativistic generalization of Maxwell's equations. Using them, it is possible to consider some far-reaching implications of a massive photon, such as variation of the speed of light, deviations in the behaviour of static electromagnetic fields, longitudinal electromagnetic radiation and even questions of gravitational deflection. All of these have been studied carefully using a number of different approaches over the past several decades. This review attempts to assess the status of our current knowledge and understanding of the photon rest mass, with particular emphasis on a discussion of the various experimental methods that have been used to set upper limits on it. All such tests can be most easily categorized in terms of terrestrial and extra-terrestrial approaches, and the review classifies them as such. Up to now, there has been no conclusive evidence of a finite mass for the photon, with the results instead yielding ever more stringent upper bounds on the size of it, thus confirming the related aspects of Maxwellian electromagnetism with concomitant precision. Of course, failure to find a finite photon mass in any one experiment or class of experiments is not proof that it is identically zero and, even as the experimental limits move more closely towards the fundamental bounds of measurement uncertainty, new conceptual approaches to the task continue to appear. The intrinsic importance of the question and the lure of what might be revealed by attaining the next decimal place are as strong a draw on this question as they are in any other aspect of precise tests of physical laws.

Integrity signals

Registry

Crossref · 10.1088/0034-4885/68/1/r02

Cites

204 of 204 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

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

Classical Electrodynamics
(2020) · Princeton University Press eBooks · doi:10.2307/j.ctv131bv37.5 · Cited by 22,595
A treatise on electricity and magnetism
(1954) · Journal of the Franklin Institute · doi:10.1016/0016-0032(54)90053-8 · Cited by 9,134
Significance of Electromagnetic Potentials in the Quantum Theory
Aharonov, Y., & Bohm, D. (1959) · Physical Review · doi:10.1103/physrev.115.485 · Cited by 6,996
The hierarchy problem and new dimensions at a millimeter
Arkani–Hamed, N., Dimopoulos, S., & Dvali, G. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00466-3 · Cited by 6,563
Review of Particle Physics
Particle Data Group, Workman, R., Burkert, V., Credé, V., Klempt, E., Thoma, U., Tiator, L., Agashe, K., Aielli, G., Allanach, B. C., et al. (2022) · Progress of Theoretical and Experimental Physics · doi:10.1093/ptep/ptac097 · Cited by 6,080
A Treatise on Electricity and Magnetism
(1873) · Nature · doi:10.1038/007478a0 · Cited by 4,538
Review of particle properties
Yost, G. P., Barnett, R. M., Hinchliffe, I., Lynch, G., Rittenberg, A., Ross, R. R., Suzuki, M., TRIPPE, T. G., Wohl, C. G., Armstrong, B., et al. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)90505-9 · Cited by 4,401
The work function of the elements and its periodicity
Michaelson, H. B. (1977) · Journal of Applied Physics · doi:10.1063/1.323539 · Cited by 4,304
Quantised singularities in the electromagnetic field,
Dirac, P. A. M. (1931) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1931.0130 · Cited by 3,701
Review of Particle Properties
Hagiwara, K., Hikasa, K., Nakamura, K., Tanabashi, M., Aguilar-Benitez, M., Amsler, C., Barnett, R. M., Burchat, P. R., Carone, C. D., Caso, C., et al. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.010001 · Cited by 3,354

Show all 205 references

Research works printed but not linked: 26

Al'pert Y L, 1941, Zh. Tech. Fiz., 11, 7
Alfvén H, 1968, Ann. Geophys., 24, 341
Bartlett D F, 1969, Bull. Am. Phys. Soc., 14, 17
Binney J, 1987, Galactic Dynamics, 211
Casimir H B G, 1948, Proc. K. Ned. Akad. Wet., 51, 793
Clear J, 1987, Astron. Astrophys., 174, 85
Cochran G D, 1968, Bull. Am. Phys. Soc., 13, 1379
Elliott R S, 1966, Electromagnetics
Gintsburg M A, 1963, Astron. Zh., 40, 703
Gintsburg M A, 1964, Sov. Astron.-AJ, 7, 536
Lehnert B, 2000, J. New Energy, 5, 81
Norman T, 1987, The Atomic Constants Light and Time
Proca A, 1930, Compt. Rend., 190, 1377
Proca A, 1930, Compt. Rend., 191, 26
Proca A, 1931, Compt. Rend., 193, 832
Proca A, 1936, Compt. Rend., 202, 1366
Proca A, 1936, Compt. Rend., 202, 1490
Proca A, 1936, Compt. Rend., 203, 709
Proca A, 1938, J. Physique Ser. VII, 9, 61
Schrödinger E, 1943, Proc. R. Ir. Acad., 49, 135
Schrödinger E, 1943, Proc. R. Ir. Acad., 49, 43
Stueckelberg E C G, 1941, Helv. Phys. Acta, 14, 51
Stueckelberg E C G, 1957, Helv. Phys. Acta, 30, 209
Wilkie T, 1983, New Sci., 100, 258
Williams E R, 1970, Bull. Am. Phys. Soc., 15, 586
Zhang Y Z, 1998, Speical Relativity and its Experimental Foundations, 245

Sorted by citations

Instability of the massive Klein-Gordon field on the Kerr spacetime
Dolan, S. R. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.084001 · Cited by 562
“For comparison, the (lab-based) experimental upper bound on the photon’s mass is currently around ∼ 10 eV [49].”
Background
Photon and graviton mass limits
Goldhaber, A. S., & Nieto, M. M. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.939 · Cited by 445
“In particular, Byrne (3) concentrated on astrophysical limits, Tu and Luo (6) on laboratory limits based on tests of Coulomb’s Law, and, joined by Gillies, on all experimental tests (7).”
Dark photon limits: A handbook
Caputo, A., Millar, A. J., O’Hare, C. A. J., & Vitagliano, E. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.095029 · Cited by 356
Feebly-interacting particles: FIPs 2022 Workshop Report
Antel, C., Battaglieri, M., Beacham, J. B., Bœhm, C., Buchmueller, O. L., Calore, F., Carenza, P., Chauhan, B., Cladé, P., Coloma, P., et al. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-12168-5 · Cited by 191
Happy centenary, photon
Zeilinger, A., Weihs, G., Jennewein, T. D., & Aspelmeyer, M. (2005) · Nature · doi:10.1038/nature03280 · Cited by 145
Photon mass limits from fast radio bursts
Bonetti, L., Ellis, J. R., Mavromatos, N. E., Sakharov, A., Sarkisyan, E. K. G., & Spallicci, A. D. A. M. (2016) · Physics Letters B · doi:10.1016/j.physletb.2016.04.035 · Cited by 110
CONSTRAINTS ON THE PHOTON MASS WITH FAST RADIO BURSTS
Wu, X.-F., Zhang, S., Gao, H., Wei, J.-J., Zou, Y.-C., Lei, W.-H., Zhang, B., Dai, Z.-G., & Mészáros, P. (2016) · The Astrophysical Journal Letters · doi:10.3847/2041-8205/822/1/l15 · Cited by 97
“All of these effects have been employed to derive increasingly restrictive constraints on the photon rest mass, either through laboratory experiments or astrophysical and cosmological observations (Goldhaber & Nieto 1971; Tu et al. 2005; Pani et al. 2012).”
Background
Using plasma physics to weigh the photon
Ryutov, D. D. (2007) · Plasma Physics and Controlled Fusion · doi:10.1088/0741-3335/49/12b/s40 · Cited by 102
Biophoton emissions from cell cultures: biochemical evidence for the plasma membrane as the primary source.
Dotta, B. T., Buckner, C. A., Cameron, D., Lafrenie, R. M., & Persinger, M. A. (2011) · PubMed · doi:10.4149/gpb_2011_03_301 · Cited by 79
FRB 121102 casts new light on the photon mass
Bonetti, L., Ellis, J. R., Mavromatos, N. E., Sakharov, A., Sarkisyan, E. K. G., & Spallicci, A. D. A. M. (2017) · Physics Letters B · doi:10.1016/j.physletb.2017.03.014 · Cited by 71
Constraining the range of Yukawa gravity interaction from S2 star orbits III: improvement expectations for graviton mass bounds
ZAKHAROV, A. F., Jovanović, P., Borka, D., & Jovanović, V. B. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/04/050 · Cited by 59
“Different ways to evaluate photon mass are discussed in couple of reviews [63, 70, 71] and original papers [72–77].”
Photon emissions from human brain and cell culture exposed to distally rotating magnetic fields shared by separate light-stimulated brains and cells
Dotta, B. T., Buckner, C. A., Lafrenie, R. M., & Persinger, M. A. (2011) · Brain Research · doi:10.1016/j.brainres.2011.03.001 · Cited by 55
“Considering the inferential evidence that photons may not be massless (Tu et al., 2005) and the results of several experiments logy, Laurentian Universi a (M.A. Persinger). hed by Elsevier B.V. l., Photon emissions fro -stimulate..., Brain Res. by physicists demonstrating entanglement between…”
BackgroundInfluential
“Doubling” of local photon emissions when two simultaneous, spatially-separated, chemiluminescent reactions share the same magnetic field configurations
Dotta, B. T., & Persinger, M. A. (2012) · Journal of Biophysical Chemistry · doi:10.4236/jbpc.2012.31009 · Cited by 54
“We employed the terminology from Tu and his colleagues [17] who described that one of the implications of the photon displaying a nonzero mass would be to produce a difference between group velocity and phase velocity.”
BackgroundMethodInfluential
Path integral quantization of generalized quantum electrodynamics
Bufalo, R., Pimentel, B. M., & Zambrano, G. E. R. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.045007 · Cited by 53
Testing fundamental physics with astrophysical transients
Wei, J.-J., & Wu, X.-F. (2021) · Frontiers of Physics · doi:10.1007/s11467-021-1049-x · Cited by 52
Massive photon and dark energy
Kouwn, S., Oh, P., & Park, C. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.083012 · Cited by 48
“ntum electrodynamics breaks gauge invariance and might spoil the renormalizability, which renders the theory quantum mechanically inconsistent. However, the consideration of non-vanishing photon mass [9] has a long history, and theoretically, it is well known that Maxwell theory with abelian gauge symmetry can be exte…”
Background
Solar wind test of the de Broglie-Proca massive photon with Cluster multi-spacecraft data
Retinò, A., Spallicci, A. D. A. M., & Vaivads, A. (2016) · Astroparticle Physics · doi:10.1016/j.astropartphys.2016.05.006 · Cited by 46
How to explain the non-zero mass of electromagnetic radiation consisting of zero-mass photons
Gabovich, A. M., & Gabovich, N. A. (2007) · European Journal of Physics · doi:10.1088/0143-0807/28/4/004 · Cited by 46
Thermodynamic Properties in Higher-Derivative Electrodynamics
Filho, A. A. A., & Maluf, R. V. (2021) · Brazilian Journal of Physics · doi:10.1007/s13538-021-00880-0 · Cited by 42
“As a result, since the electromagnetic interactions are described in terms of the symmetry group, namely U(1), the quantum electrodynamics should be reexamined whether massive modes were taken into account [5].”
Background
Theoretical and Experimental Evidence of Macroscopic Entanglement Between Human Brain Activity and Photon Emissions: Implications for Quantum Consciousness and Future Applications
Persinger, M. A., & Lavallee, C. F. (2010) · Journal of consciousness exploration & research · Cited by 41
Electromagnetic fields as structure-function zeitgebers in biological systems: environmental orchestrations of morphogenesis and consciousness
Rouleau, N., & Dotta, B. T. (2014) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2014.00084 · Cited by 39
“This value constitutes a threshold energy bordering rest-mass of a photon or ∼ 10−52 kg (Tu et al., 2005).”
Background
Limits on the Weak Equivalence Principle and Photon Mass with FRB 121102 Subpulses
Xing, N., Gao, H., Wei, J.-J., Li, Z., Wang, W., Zhang, B., Wu, X.-F., & Mészáros, P. (2019) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ab3c5f · Cited by 40
“Such effects could be applied to make restrictive constraints on the photon rest mass (Goldhaber & Nieto 1971, 2010; Tu et al. 2005; Pani et al. 2012).”
Background
A survey of existing and proposed classical and quantum approaches to the photon mass
Spavieri, G., Quintero, J., Gillies, G. T., & Rodriguez, M. (2011) · The European Physical Journal D · doi:10.1140/epjd/e2011-10508-7 · Cited by 37
Self-citation
Gravitomagnetic London moment and the graviton mass inside a superconductor
de Matos, C. J., & Tajmar, M. (2005) · Physica C Superconductivity · doi:10.1016/j.physc.2005.08.004 · Cited by 35
Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang–Mills and Gravitational Theories
Pitts, J. B. (2010) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axq014 · Cited by 36
“Electromagnetism can be unified with an SU(2) Yang–Mills field describing the weak nuclear force into the electroweak theory (see, for example, (Weinberg [1996])).”
Background
Electrodynamics in superconductors explained by Proca equations
Tajmar, M. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.10.070 · Cited by 33
Dispersion by pulsars, magnetars, fast radio bursts and massive electromagnetism at very low radio frequencies
Bentum, M., Bonetti, L., & Spallicci, A. D. A. M. (2016) · Advances in Space Research · doi:10.1016/j.asr.2016.10.018 · Cited by 34
Infrared Lorentz Violation and Slowly Instantaneous Electricity
Dvali, G., Papucci, M., & Schwartz, M. D. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.191602 · Cited by 33
Dirac star in the presence of Maxwell and Proca fields
Джумакадырович, Д. В., & Folomeev, V. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.104066 · Cited by 32
Induced electric dipole in a quantum ring
Dantas, L., & Furtado, C. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.09.002 · Cited by 32
Probing Minicharged Particles with Tests of Coulomb’s Law
Jaeckel, J. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.080402 · Cited by 33
Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect
Belokogne, A., & Folacci, A. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.044063 · Cited by 32
Robust limits on photon mass from statistical samples of extragalactic radio pulsars
Wei, J.-J., & Wu, X.-F. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2018/07/045 · Cited by 31
How Stable is the Photon?
Heeck, J. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.021801 · Cited by 35
Quantum mechanics of Proca fields
Zamani, F., & Mostafazadeh, A. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3116164 · Cited by 29
Counting photons in static electric and magnetic fields
Mück, W. M. (2013) · The European Physical Journal C · doi:10.1140/epjc/s10052-013-2679-0 · Cited by 30
“For recent reviews on this subject, see [24, 25].”
Background
Increased Photon Emissions from the Right But Not the Left Hemisphere While Imagining White Light in the Dark: The Potential Connection Between Consciousness and Cerebral Light
Dotta, B. T., & Persinger, M. A. (2011) · Journal of consciousness exploration & research · Cited by 28
Massive photons in magnetic materials from nonlocal quantization
El‐Nabulsi, R. A. (2018) · Journal of Magnetism and Magnetic Materials · doi:10.1016/j.jmmm.2018.03.012 · Cited by 28
Bounding the photon mass with cosmological propagation of fast radio bursts
Wang, H., Miao, X., & Shao, L. (2021) · Physics Letters B · doi:10.1016/j.physletb.2021.136596 · Cited by 30
LIMITS ON THE COUPLING CONSTANT OF HIGHER-DERIVATIVE ELECTROMAGNETISM
Accioly, A. J., & Scatena, E. (2010) · Modern Physics Letters A · doi:10.1142/s0217732310031610 · Cited by 27
Axiomatic derivation of coincident general relativity and its premetric extension
Koivisto, T., Hohmann, M., & Marzola, L. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.103.064041 · Cited by 26
New limits on the photon mass with radio pulsars in the Magellanic clouds
Wei, J.-J., Zhang, E.-K., Zhang, S., & Wu, X.-F. (2017) · Research in Astronomy and Astrophysics · doi:10.1088/1674-4527/17/2/13 · Cited by 25
“Considering an age of the Universe of about1010 years, the ultimate upper limit on the rest mass of the photon can be estimated to bemγ ≈ ~/(∆t)c2 ≈ 10−66 g on the basis of the Heisenberg uncertainty principle, where~ is the Plank constant (Tu et al. 2005).”
Background
Cerebral Biophoton Emission as a Potential Factor in Non-Local Human-Machine Interaction
Caswell, J. M., Dotta, B. T., & Persinger, M. A. (2013) · NeuroQuantology · doi:10.14704/nq.2014.12.1.713 · Cited by 24
“Although traditionally thought to possess no mass, recent evidence has suggested a non-zero rest mass for the photon (upper limit ~10-52 kg; Tu et al., 2005).”
Background
Congruence of Energies for Cerebral Photon Emissions, Quantitative EEG Activities and ~5 nT Changes in the Proximal Geomagnetic Field Support Spin-based Hypothesis of Consciousness
Persinger, M. A., Dotta, B. T., Saroka, K. S., & Scott, M. A. (2013) · Journal of consciousness exploration & research · Cited by 24
Tight Constraint on Photon Mass from Pulsar Spindown
Yang, Y.-P., & Zhang, B. (2017) · The Astrophysical Journal · doi:10.3847/1538-4357/aa74de · Cited by 23
“…prove that the photon rest mass is exactly zero via experiments, the only experimental strategy is to place ever tighter upper limits on photon rest mass. Due to the uncertainty principle, there is an ultimate upper limit of photon rest mass (e.g. Goldhaber & Nieto 1971; Tu et al. 2005), i.e., mγ .”
Background
Schrödinger–Poisson systems in the 3-sphere
Hebey, E., & Wei, J. (2012) · Calculus of Variations and Partial Differential Equations · doi:10.1007/s00526-012-0509-0 · Cited by 24
Dirac star with SU(2) Yang-Mills and Proca fields
Джумакадырович, Д. В., & Folomeev, V. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.024023 · Cited by 23
Brain electromagnetic activity and lightning: potentially congruent scale-invariant quantitative properties
Persinger, M. A. (2012) · Frontiers in Integrative Neuroscience · doi:10.3389/fnint.2012.00019 · Cited by 22
“Phase shift can be obtained by time divided by the square root of v2/c2.”
BackgroundInfluential
Evidence for Maxwell’s equations, fields, force laws and alternative theories of classical electrodynamics
Tran, M. M. (2018) · European Journal of Physics · doi:10.1088/1361-6404/aadf9b · Cited by 22
OCTONIC GRAVITATIONAL FIELD EQUATIONS
Demi̇r, S., Tanışlı, M., & Tolan, T. (2013) · International Journal of Modern Physics A · doi:10.1142/s0217751x13501121 · Cited by 22
Dimensional Analyses of Geometric Products and the Boundary Conditions of the Universe: Implications for a Quantitative Value for the Latency to Display Entanglement
Persinger, M. A. (2013) · The Open Astronomy Journal · doi:10.2174/1874381101306010010 · Cited by 21
“[11] the phase and group velocities of the applied fields were not dissociated or if the optimal sequence of the patterns were reversed.”
Background
Constraining hidden photons via atomic force microscope measurements and the Plimpton-Lawton experiment
Kroff, D., & Malta, P. C. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.095015 · Cited by 22
“7, in which we also include the exclusion limits from Cavendish-like experiments [10, 19–21].”
BackgroundMethodInfluential
Resonant states for the static Klein–Gordon–Maxwell–Proca system
Hebey, E., & Wei, J. (2012) · Mathematical Research Letters · doi:10.4310/mrl.2012.v19.n4.a18 · Cited by 21
“[10], and Ruegg and Ruiz–Altaba [13] for very complete references on the Proca approach.”
Background
The canonical structure of Podolsky's generalized electrodynamics on the null-plane
Bertin, M. C., Pimentel, B. M., & Zambrano, G. E. R. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3653510 · Cited by 21
Corrections to Reissner-Nordström black hole solution due to exponential nonlinear electrodynamics
Kruglov, S. I. (2016) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/115/60006 · Cited by 21
Proca Metamaterials, Massive Electromagnetism, and Spatial Dispersion
Mikki, S. M. (2021) · Annalen der Physik · doi:10.1002/andp.202000625 · Cited by 20
Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects
Movilla, J. L., Planelles, J., & Climente, J. I. (2023) · Nanoscale Advances · doi:10.1039/d3na00592e · Cited by 20
Potential Origins of a Quantitative Equivalence Between Gravity and Light
Persinger, M. A. (2012) · The Open Astronomy Journal · doi:10.2174/1874381101205010041 · Cited by 20
“[6] the upper limit for the rest mass of a photon may be ~10 -52 kg.”
Background
Upper bounds on the photon mass
Accioly, A. J., Helayël-Neto, J. A., & Scatena, E. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.065026 · Cited by 23
Constraining the mass of the photon with gamma-ray bursts
Zhang, B., Chai, Y., Zou, Y.-C., & Wu, X.-F. (2016) · Journal of High Energy Astrophysics · doi:10.1016/j.jheap.2016.07.001 · Cited by 20
“The mass of photon can be measured via two types of approaches, laboratory experiments and astronomical observations (Tu et al. 2005, and references therein).”
Method
Can there be massive photons? A pedagogical glance at the origin of mass
Robles, P., & Claro, F. H. (2012) · European Journal of Physics · doi:10.1088/0143-0807/33/5/1217 · Cited by 19
Testing Nonclassical Theories of Electromagnetism with Ion Interferometry
Neyenhuis, B., Christensen, D., & Durfee, D. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.200401 · Cited by 21
Test of local gauge invariance in Proca electrodynamics
Tu, L., Shao, C.-G., Luo, J., & Luo, J. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.12.017 · Cited by 18
Self-citation
Testing Einstein's equivalence principle with short gamma-ray bursts: Table 1.
Sang, Y., Lin, H.-N., & Chang, Z. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw1136 · Cited by 19
“∆tspe is proportional to the square of the photon rest mass (Gao et al. 2015), while the latter has proved to be very close to zero (Tu et al. 2005; Wu et al. 2016b).”
Background
Extended electrodynamics and its consequences
Arbab, A. I. (2017) · Modern Physics Letters B · doi:10.1142/s0217984917500993 · Cited by 19
Combined limit on the photon mass with nine localized fast radio bursts
Wei, J.-J., & Wu, X.-F. (2020) · Research in Astronomy and Astrophysics · doi:10.1088/1674-4527/20/12/206 · Cited by 22
Thixotropic Phenomena in Water: Quantitative Indicators of Casimir-Magnetic Transformations from Vacuum Oscillations (Virtual Particles)
Persinger, M. A. (2015) · Entropy · doi:10.3390/e17096200 · Cited by 17
“If the upper limit of the rest mass photon is ~2 × 10−52 kg [21], and it is considered imaginary (i) and the diffusivity velocity of 2.”
Background
Excessive correlated shifts in pH within distal solutions sharing phase-uncoupled angular accelerating magnetic fields: Macro-entanglement and information transfer
Dotta, B. T., Murugan, N. J., Karbowski, L. M., & Persinger, M. A. (2013) · International Journal of the Physical Sciences · doi:10.5897/ijps2013.3961 · Cited by 17
A framework for the next generation of stationary cosmological models
Sanejouand, Y. (2022) · International Journal of Modern Physics D · doi:10.1142/s0218271822500845 · Cited by 14
“[41, 42, 43, 44, 45, 46, 47]), the speed of light is constant and that delays, due for instance to the Shapiro effect [48], can be neglected in such a way that:”
Background
Gauge Invariant Massive Long Range and Long Lived Photons
Nyambuya, G. G. (2014) · Journal of Modern Physics · doi:10.4236/jmp.2014.517185 · Cited by 12
“[7]’s excellent review article diligently touches on the many efforts that have been conducted to measure the mass of the photon.”
BackgroundInfluential
Are Photons Massless or Massive?
Nyambuya, G. G. (2014) · Journal of Modern Physics · doi:10.4236/jmp.2014.518207 · Cited by 13
Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds. II
Druet, O., Hebey, E., & Vétois, J. (2014) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crelle-2013-0125 · Cited by 16
“considerable importance and intensively studied in modern physics (see for instance Adelberger, Dvali and Gruzinov [1], Byrne [13], Goldhaber and Nieto [25, 26], Luo and Tu [38], Luo, Gillies and Tu [37] and the references in these papers). When n= 3, the KGMP equations consist in the nonlinear Klein-Gordon matter equ…”
Background
Axially symmetric Proca-Higgs boson stars
Джумакадырович, Д. В., & Folomeev, V. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.104024 · Cited by 13
“Introduction of such fields is motivated by the fact that if one regards Proca theory as the generalization of Maxwell’s theory, it permits one to take into account various effects related to the possible presence of the rest mass of a photon [19], to describe the massive Z and W± particles in the Standard Model of pa…”
Background
Gauge Invariance of Sedeonic Equations for Massive and Massless Fields
Mironov, V. L., & Mironov, S. V. (2016) · International Journal of Theoretical Physics · doi:10.1007/s10773-016-2941-y · Cited by 13
Photon mass and quantum effects of the Aharonov-Bohm type
Spavieri, G., & Rodriguez, M. (2007) · Physical Review A · doi:10.1103/physreva.75.052113 · Cited by 13
Local Electromagnetic Fields Exhibit Temporally Non-Linear, East-West Oriented 1 - 5 nT Diminishments within a Toroid: Empirical Measurement and Quantitative Solutions Indicating a Potential Mechanism for Excess Correlation
Rouleau, N., & Persinger, M. A. (2015) · Journal of Electromagnetic Analysis and Application · doi:10.4236/jemaa.2015.72003 · Cited by 12
“[5] that photons may exhibit non-zero rest masses and hence would display a dissociation between group and phase velocities, Dotta et al.”
Background
Dreams, Time Distortion and the Experience of Future Events: A Relativistic, Neuroquantal Perspective
Dotta, B. T., & Persinger, M. A. (2009) · Cited by 12
Revisiting constraints on the photon rest mass with cosmological fast radio bursts
Wang, B., Wei, J.-J., Wu, X.-F., & López-Corredoira, M. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/09/025 · Cited by 17
“The ultimate upper bound on the photon rest mass would be mγ ≤ ~/(∆tc2) ≈ 10−69 kg with the age of the Universe ∆t ≈ 1010 years [8, 9].”
Photon in the Earth-ionosphere cavity: Schumann resonances
Sucu, Y., & Tekincay, C. (2019) · Astrophysics and Space Science · doi:10.1007/s10509-019-3547-7 · Cited by 10
Proca balls with angular momentum or flux of electric field
Джумакадырович, Д. В., & Folomeev, V. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.016022 · Cited by 12
“2 dark matter [12, 13], processes at cosmological scales [14], various effects related to the possible presence of the rest mass of a photon [15], as well as flux tube configurations filled with electric and magnetic fields [16–18].”
Background
Limits to differences in active and passive charges
Lämmerzahl, C., Macı́as, A., & Müller, H. (2007) · Physical Review A · doi:10.1103/physreva.75.052104 · Cited by 12
Reduced Order Podolsky Model
Thibes, R. (2016) · Brazilian Journal of Physics · doi:10.1007/s13538-016-0475-7 · Cited by 12
Graviton mass due to dark energy as a superconducting medium-theoretical and phenomenological aspects
Inan, N. A., Ali, A. F., Jusufi, K., & Yasser, A. (2024) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2024/08/012 · Cited by 11
“2 See [31] for various limits on measured photon mass as well as other physical implications of a massive photon.”
Testing the Ampère–Maxwell law on the photon mass and Lorentz symmetry violation with MMS multi-spacecraft data
Spallicci, A. D. A. M., Sarracino, G., Randriamboarison, O. C., Helayël-Neto, J. A., & Dib, A. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-024-05200-4 · Cited by 12
Coherence behaviors of an atom immersing in a massive scalar field
Huang, Z. (2022) · The European Physical Journal D · doi:10.1140/epjd/s10053-022-00399-2 · Cited by 11
“There is also report that massive scalar fields can serve as components of the massive photon field [23,24].”
Background
Listening for dark photon radio signals from the Galactic Center
Hardy, E., & Song, N. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.115035 · Cited by 17
“[65] Liang-Cheng Tu, Jun Luo, and George T Gillies, “The mass of the photon,” Reports on Progress in Physics 68, 77 (2004).”
Background
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F. D., & Plastino, A. R. (2016) · The European Physical Journal C · doi:10.1140/epjc/s10052-016-4196-4 · Cited by 11
Noncommutative Einstein-Proca spacetime
González, A., Linares, R., Maceda, M., & Sánchez-Santos, O. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.124085 · Cited by 11
Electronic Maxwell’s equations
Li, M., Shi, P., Du, L., & Yuan, X. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abc853 · Cited by 11
The Harribance Effect as Pervasive Out-of-Body Experiences: NeuroQuantal Evidence with More Precise Measurements
Persinger, M. A. (2010) · NeuroQuantology · doi:10.14704/nq.2010.8.4.301 · Cited by 11
THE EXTENDED GAUGE TRANSFORMATIONS
Arbab, A. I. (2014) · Progress In Electromagnetics Research M · doi:10.2528/pierm14090503 · Cited by 10
“Equation (35) is the energy conservation equation obtained for Proca equations [10].”
Gravitational Lensing Time Delays with Massive Photons
Glicenstein, J. F. (2017) · The Astrophysical Journal · doi:10.3847/1538-4357/aa9439 · Cited by 10
“Conclusion The bound on the photon mass derived in Section 4 is several orders of magnitude less constraining than the best limits available (Tu et al. 2005), but comparable to the limit obtained with the gravitational deflection of radio waves by the Sun (Accioly et al. 2010).”
Background
Gravitational and quantum bounds on the photon mass
Accioly, A. J., Helayël-Neto, J. A., Turcati, R., Morais, J., & Scatena, E. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/20/205010 · Cited by 9
Predicting Quantum Random Events from Background Photon Density Two Days Previously: Implications for Virtual-to-Matter Determinism and Changing the Future
Vares, D. A. E., & Persinger, M. A. (2013) · Cited by 9
General relativistic electromagnetic and massive vector field effects with gamma-ray burst production
Tamburini, F., Laurentis, M. D., Amati, L., & Thidé, B. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.104003 · Cited by 9
Bounding the photon mass with the dedispersed pulses of the Crab pulsar and FRB 180916B
Chang, C.-M., Wei, J.-J., Zhang, S., & Wu, X.-F. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/01/010 · Cited by 11
“According to the uncertainty principle, the ultimate upper limit on the photon rest mass would be mγ ≤ ~/∆tc2 ≈ 10−69 kg, using the age of the universe of about 1010 years [1, 2].”
Momentum work and the energetic foundations of physics. III. The unification of mechanics and electrodynamics
Kalies, G., & Do, D. D. (2023) · AIP Advances · doi:10.1063/5.0166847 · Cited by 9
Atomic spectroscopy and the photon mass: Effects on the 21 cm radiation
Caccavano, A., & Leung, P. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.08.011 · Cited by 9
Casimir-Polder interactions with massive photons: Implications for BSM physics
Mattioli, L., Frassino, A. M., & Panella, O. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.100.116023 · Cited by 9
A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach
Christianto, V., & Rahul, B. (2014) · Bulletin of Mathematical Sciences and Applications · doi:10.18052/www.scipress.com/bmsa.10.48 · Cited by 8

Authors: Tu, L.-C., Luo, J., & Gillies, G. T.
Affiliations: Huazhong University of Science and Technology (CN)
University of Virginia (US)
Corresponding author: Gillies, George T
ORCID: Luo, Jun
Gillies, George T
Venue: Reports on Progress in Physics
Publisher: IOP Publishing
Published: 2004-11-24
Volume: 68
Issue: 1
Pages: 77-130
ISSN: 0034-4885 (ISSN-L)
1361-6633
DOI: 10.1088/0034-4885/68/1/r02
OpenAlex: W2153158728
Cited by: 303
References: 205
Citations by year: 2026: 13 · 2025: 17 · 2024: 23 · 2023: 32 · 2022: 14 · 2021: 12 · 2020: 9 · 2019: 10 · 2018: 13 · 2017: 10 · 2016: 28 · 2015: 17 · 2014: 17 · 2013: 19 · 2012: 9
FWCI: 4.50
Type: journal article
Language: en
Open access: closed
Locations: Reports on Progress in Physics (publishedVersion)
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
Keywords: photon mass, Proca equation, modified Maxwell equations, variable speed of light, gravitational deflection

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

The mass of the photon

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks