Remarks on the averaged null energy condition in quantum field theory

I propose a simple generalization of the ANEC (averaged null energy condition), in which the right-hand side of the ANEC inequality is replaced by a finite (but in general negative) state-independent lower bound. It is plausible that unlike the original ANEC this version might hold generally in four-dimensional curved spacetime. I study some of the implications of the generalized ANEC, and show, in particular, that if it holds in static traversable wormhole spacetimes (which is likely but remains to be shown), then the generalized ANEC rules out macroscopic (but not necessarily microscopic, Planck-size) static wormholes.