Photon-Mass Bound Destroyed by Vortices

The Particle Data Group gives an upper bound on the photon mass $m<2\times {10}^{-16}\mathrm{eV}$ from a laboratory experiment and lists, but does not adopt, an astronomical bound $m<3\times {10}^{-27}\mathrm{eV}$, both of which are based on the plausible assumption of large galactic vector potential. We argue that the interpretations of these experiments should be changed, which alters significantly the bounds on $m$. If $m$ arises from a Higgs effect, both limits are invalid because the Proca vector potential of the galactic magnetic field may be neutralized by vortices giving a large-scale magnetic field that is effectively Maxwellian. If, on the other hand, the galactic magnetic field is in the Proca regime, the very existence of the observed large-scale magnetic field gives $m^{-1}\gtrsim 1\mathrm{kpc}$, or $m\lesssim {10}^{-26}\mathrm{eV}$.