Ellerman bombs are transient brightenings of the wings of the Balmer lines that uniquely mark reconnection in the solar photosphere. They are also bright in strong Ca II and ultraviolet lines and in ultraviolet continua, but they are not visible in the optical continuum and the Na I D and Mg I b lines. These discordant visibilities invalidate all published Ellerman bomb modeling. I argue that the assumption of Saha-Boltzmann lower-level populations is informative to estimate bomb-onset opacities for these diverse diagnostics, even and especially for Hα, and employ such estimates to gauge the visibilities of Ellerman bomb onsets in all of them. They constrain Ellerman bomb formation to temperatures 10 000-20 000 K and hydrogen densities around 1015 cm-3. Similar arguments likely hold for Hα visibility in other transient phenomena with hot and dense onsets.