  We point out that data collected by the Event Horizon Telescope or a similar
project might yield new information about the photon rest mass $m_\gamma$, in
the form of evidence that $m_\gamma\ne 0$ together with a lower bound on
$m_\gamma$ or a new upper bound on $m_\gamma$. Using Sgr A*, there is scope to
improve on the best upper bound obtained via laboratory tests of Coulomb's law
by up to nineteen orders of magnitude.
