Is the photon necessarily massless?
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No. Astronomical observations only pose an upper bound of currently
2 10^{-25} eV (approx. 3.6 10^{-61} kg)
on the photon mass, and all known experimental data seem
to be in agreement with the assumption that the mass of the photon is
exactly zero, as in the standard model. Thus this is the default
until experiments find a positive lower bound on the mass.
(Neutrinos were considered massless also until a few years ago,
when experiments had become accurate enough to detect differences to
the predictions derived from a zero neutrino mass.)
A thorough analysis of the problems involved in determining the mass of
the photon is given in the paper
L.-C. Tu, J. Luo, and G.T. Gillies,
The mass of the photon
Rep. Prog. Phys. 68 (2005), 77--130.
See also
AS Goldhaber, MM Nieto
Photon and graviton mass limits
Reviews of Modern Physics, 2010
arxiv:0809.1003
and the old paper
L. Bass, E. Schroedinger
Must the Photon Mass be Zero?
Proc. Roy. Soc. London A 232 (1955), 1-6.
A recent paper is
A.S. Goldhaber and M.M. Nieto
Photon and graviton mass limits
Rev. Mod. Phys. 82, 939-979 (2010)
Observations are never exact, so sufficiently small deviations
(and hence a sufficiently small mass of the photon) cannot
be observed. The point of experiments testing for a nonzero photon mass
is precisely to improve the limit on how small these deviations must be.
If actual deviations would be found by an accurate enough
experiment, it would make a (tiny) difference to physics.
Maxwell's equations would have to be replaced by Proca's equations
(though for very high accuracy predictions only), Coulomb's
inverse-square law would look slightly different, and quantum
electrodynamics would have to be modified to account for the photon
mass. (Massive QED is still renormalizable, so nothing serious would
happen to the current foundations.)
Experiments abundantly confirm the fact (usually called causality
and/or locality) that there is a limit speed that cannot be exceeded
by traveling matter, energy, or information. This speed is usually
denoted by c and called the ''speed of light'', since (until contrary
evidence forces us to give this up) photons are regarded as massless
particles.
Would the photon be found to have a slight mass, this speed would
simply be renamed to ''limit speed'' or something like that,
photons would have a rest frame, but not much else would change.
One would just have to adjust to the inconvenience that discussions of
concepts such as inertial frames, that are currently linked to
properties of light, could no longer be tested directly by truly
massless particles - since then light no longer travels with the limit
speed, and the behavior of light depends on the reference frame.
A conceptual difference between the massless and the massive case is
that massive fields have transverse modes, massless fields cannot have
them. However, for almost massless particles, the transverse mode is
suppressed by a huge factor (proportional to the inverse of its mass,
or even mass square - I'd need to check; haven't done such calculations
for a long time.)
This can be seen by writing the massive representation in the
Jacob-Wick helicity form, where the massless limit can be taken.
Jacob M & Wick G C.
On the general theory of collisions for particles with spin.
Ann.Phys. 7:404-428, 1959.
The massless case is just a conventional limit of the massive case,
without any discontinuity when the mass approaches zero.
Thus an extremely small positive mass of the photon will go unnoticed
forever.
Note that photons are slower in transparent media than in vacuum, but
this is not because they would become massive (they are still massless
and heve only transversal modes) but because photons in a medium are
''effective photons'' only, i.e., no longer the same objects as in
vacuum, since the medium has a dressing effect on light particles.
This dressing reduces the speed of light.
A recent paper in arxiv:1005.3480 discusses nonrenormalizable field
theories that admit a massive photon.