  We provide a simple new argument for a lower bound on the coupling of a
$U(1)$ gauge interaction in an effective field theory (EFT), originally
obtained from the Weak Gravity Conjecture. Our argument employs basic
principles of quantum mechanical energy-time uncertainty and Lorentz
invariance, plus Bekenstein's entropy bound on the ultraviolet (UV) and
infrared (IR) scales of an EFT. We show that using an alternative UV-IR
relation based on the Cohen-Kaplan-Nelson (CKN) bound results in a stronger
lower bound on the $U(1)$ coupling, consistent with the more stringent nature
of the CKN relation. Applicability of our reasoning to other interactions is
briefly discussed. We also slightly extend the CKN bound, by accounting for the
effective degrees of freedom, and examine some of its phenomenological
implications.
