If the photon has a finite rest mass $m$, a filament of magnetic flux sustained by a partially ionized gas decays exponentially at a rate proportional to $m^2$. Arguing from assumptions regarding the galactic magnetic field that are plausible though not yet rigorously established, we find an upper limit $m<~3\times {10}^{-56\mathrm{}}$ gm, corresponding to a Compton wavelength of 6 lt yr.

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