User:WillowW/Mass of the photon

Experimental limits on mass[edit]

Since the photon is a gauge boson, most physicists believe that its intrinsic mass is exactly zero. All experimental data hitherto are consistent with the photon having zero mass^[1]^[2]^[3]^[4]^[5]^[6]^[7]. However, physicists continue to tighten the error bars on the photon mass, in the hopes of discovering discrepancies with the Standard Model.

If the photon were to have a mass, electromagnetism would be described by the Proca theory instead of Maxwell's equations. This has two measurable consequences:

Coulomb's law would be invalid. Since Gauss's law would also be invalid, electric fields inside a charged hollow conductor would not be zero. An experiment searching for this effect yielded an upper limit on the photon mass of 10^-14 eV (1.8x10^-50 kg)^[8].

The energy density of the electromagnetic field would contain an additional term $m^{2}A_{\mu }A^{\mu }\!$ , where m is the mass of the photon and $A_{\mu }\!$ is the Proca vector potential. Since the magnetic field is given by $\mathbf {B} ={\boldsymbol {\nabla }}\times \mathbf {A} \!$ , large-scale magnetic fields should be dominated by this term; the magnitude of $\mathbf {A}$ should be roughly equal to $\left|\mathbf {B} \right|R\!$ , where B is the "ambient" magnetic field strength and R the length scale over which it exists. The strongest upper limits on the photon mass have been derived from the potential effects of planetary and galactic vector potentials.

Satellite measurements of planetary magnetic fields were carried out by the Charge Composition Explorer spacecraft and used to derive an upper limit of 6x10^-16 eV (1.1x10^-51 kg) on the mass of the photon. An improved upper limit of 2x10^-16 eV (3.6x10^-52 kg) was obtained in 1998 by Roderic Lakes ^[9]. A slightly stronger upper limit is given by the Particle Data Group, based on the magnetohydrodynamics of the solar wind.^[10]. Studies of galactic magnetic fields suggest an even better upper limit of 3x10^-27 eV (5.3x10^-63 kg), but the validity of this method has been questioned.

It has been argued^[11] that, if the mass of the photon is generated via a Higgs mechanism, these limits imposed by large-scale magnetic fields are invalid. If so, the strongest upper limit on the photon mass is 10^-14 eV (1.8x10^-50 kg), determined from the experimental limit on deviations of Coulomb's Law, as described above^[8].

This experiment exploited the fact that the energy of a magnetised ring depends on its orientatation with respect to the galactic vector potential $A_{\mbox{gal}}$ , due to the $A_{\mbox{ring}}\cdot A_{\mbox{gal}}$ component of the energy term $m^{2}A_{\mu }A^{\mu }\!$ . This produces a torque on the ring that can be measured using a Cavendish balance.

Notes[edit]

^ Goldhaber AS and Nieto MM (1971) "Terrestrial and Extraterrestrial Limits on The Photon Mass", Reviews of Modern Physics, 43, 277–296. [1]
^ Fischbach E, Kloor H, Langel RA, Lui ATY, and Peredo M (1994) "New Geomagnetic Limits on the Photon Mass and on Long-Range Forces Coexisting with Electromagnetism", Physical Review Letters, 73, 514–517.
^ Official particle table http://pdg.lbl.gov/2005/tables/gxxx.pdf
^ Davis L, Goldhaber AS, and Nieto MM (1975) "Limit on Photon Mass Deduced from Pioneer-10 Observations of Jupiter's Magnetic Field", Physical Review Letters, 35, 1402-1405.
^ Luo J, Shao CG, Liu ZZ, and Hu ZK (1999) "Determination of the limit of photon mass and cosmic magnetic vector with rotating torsion balance", Physical Review A, 270, 288-292.
^ Schaefer BE (1999) "Severe limits on variations of the speed of light with frequency", Physical Review Letters, 82, 4964-4966.
^ Luo J, Tu LC, Hu ZK, and Luan EJ (2003) "New experimental limit on the photon rest mass with a rotating torsion balance", Physical Review Letters, 90, Art. No. 081801.
^ ^a ^b Williams ER, Faller JE and Hill HA (1971) "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass", Physical Review Letters, 26, 721–724. article
^ Lakes R (1998) "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential", Physical Review Letters, 80, 1826 (1998) [2]. This experiment exploited the fact that the energy of a magnetised ring depends on its orientatation with respect to the galactic vector potential $A_{\mbox{gal}}$ , due to the $A_{\mbox{ring}}\cdot A_{\mbox{gal}}$ component of the energy term $m^{2}A_{\mu }A^{\mu }\!$ . This produces a torque on the ring that can be measured using a Cavendish balance.
^ 2006 PDG listing for photon
^ Adelberger E, Dvali G, and Gruzinov A, Photon Mass Bound Destroyed by Vortices, preprint

[1] Goldhaber AS and Nieto MM (1971) "Terrestrial and Extraterrestrial Limits on The Photon Mass", Reviews of Modern Physics, 43, 277–296. [1]

[2] Fischbach E, Kloor H, Langel RA, Lui ATY, and Peredo M (1994) "New Geomagnetic Limits on the Photon Mass and on Long-Range Forces Coexisting with Electromagnetism", Physical Review Letters, 73, 514–517.

[3] Official particle table http://pdg.lbl.gov/2005/tables/gxxx.pdf

[4] Davis L, Goldhaber AS, and Nieto MM (1975) "Limit on Photon Mass Deduced from Pioneer-10 Observations of Jupiter's Magnetic Field", Physical Review Letters, 35, 1402-1405.

[5] Luo J, Shao CG, Liu ZZ, and Hu ZK (1999) "Determination of the limit of photon mass and cosmic magnetic vector with rotating torsion balance", Physical Review A, 270, 288-292.

[6] Schaefer BE (1999) "Severe limits on variations of the speed of light with frequency", Physical Review Letters, 82, 4964-4966.

[7] Luo J, Tu LC, Hu ZK, and Luan EJ (2003) "New experimental limit on the photon rest mass with a rotating torsion balance", Physical Review Letters, 90, Art. No. 081801.

[will-8] Williams ER, Faller JE and Hill HA (1971) "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass", Physical Review Letters, 26, 721–724. article

[9] Lakes R (1998) "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential", Physical Review Letters, 80, 1826 (1998) [2]. This experiment exploited the fact that the energy of a magnetised ring depends on its orientatation with respect to the galactic vector potential $A_{\mbox{gal}}$ , due to the $A_{\mbox{ring}}\cdot A_{\mbox{gal}}$ component of the energy term $m^{2}A_{\mu }A^{\mu }\!$ . This produces a torque on the ring that can be measured using a Cavendish balance.

[10] 2006 PDG listing for photon

[adel-11] Adelberger E, Dvali G, and Gruzinov A, Photon Mass Bound Destroyed by Vortices, preprint

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