Photon Mass: Empirical Limits & Implications

[A. Neumaier]

We used to think neutrinos were massless, and therefore traveled at c. Now we know that at least some types of neutrinos have mass, and travel at less than c. What about the photon?

Do massive photons produce any technical problems in QED?

This is discussed with a number of important and/or very recent references in the section ''Is the photon necessarily massless?'' of Chapter B2 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#photonmass
Some quotes from there:

''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.)''

The speed of light ''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.

 

[A. Neumaier]

In the massless case, a constant A has an energy density of zero. When the photon has mass, the energy density becomes [E^2+H^2+\mu^2(A^2+V^2)]/8\pi, so even if A's derivatives vanish (so that E and H vanish), you still have an energy density.

Not really. This would yield a constant contribution to the energy density, which is removed again by renormalization.