We apply positivity bounds directly to a $U(1)$ gauge theory with charged scalars and fermions, i.e., QED, minimally coupled gravity. Assuming that the massless $t$-channel pole may be discarded, we show improved are violated unless new physics is introduced at parametrically low scale ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{new}}\ensuremath{\sim}(em{M}_{\mathrm{Pl}}{)}^{1/2}$, consistent sim...