  Within the low-energy effective field theories of QED and gravity, the
low-energy speed of light or that of gravitational waves can typically be
mildly superluminal in curved spacetimes. Related to this, small scattering
time advances relative to the curved background can emerge from known effective
field theory coefficients for photons or gravitons. We clarify why these
results are not in contradiction with causality, analyticity or Lorentz
invariance, and highlight various subtleties that arise when dealing with
superluminalities and time advances in the gravitational context. Consistent
low-energy effective theories are shown to self-protect by ensuring that any
time advance and superluminality calculated within the regime of validity of
the effective theory is necessarily unresolvable, and cannot be argued to lead
to a macroscopically larger lightcone. Such considerations are particularly
relevant for putting constraints on cosmological and gravitational effective
field theories and we provide explicit criteria to be satisfied so as to ensure
causality.
