Comments on the CKN Bound

Cohen, Kaplan, and Nelson (CKN) conjectured that the UV and IR cutoffs of effective quantum field theories coupled to gravity are not independent, but are connected by the physics of black holes. We interpret the CKN bound as a scale-dependent depletion of the QFT density of states and discuss various aspects of the bound on small and large scales. For laboratory experiments, we argue that the bound provides small corrections to ordinary quantum field theory, which we estimate to be of order $m_e/M_p$ for $g-2$ of the electron. On large scales, we suggest a modification of the CKN bound due to the presence of cosmological horizons and discuss the connection with entropy bounds.