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 m². Arguing from assumptions regarding the galactic magnetic field that are plausible though not yet rigorously established, we find an upper limit m<~3×10^-56 gm, corresponding to a Compton wavelength of 6 lt yr.
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Williams et al. (1971) studied this question.
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