  It is widely believed that combining the uncertainty principle with gravity
will lead to an effective minimum length scale. A particular challenge is to
specify this scale in a coordinate-independent manner so that covariance is not
broken. Here we examine a class of Lorentz-covariant generalizations of the
uncertainty principle which aim to provide an effective low-energy model for a
Lorentz-invariant minimum length. We show how this modification leads to a
covariant bandlimitation of quantum field theory. However, we argue that this
does not yield an adequate regulator for many quantities of interest, e.g., the
entanglement entropy between spatial regions. The possibility remains open that
it could aid in regulating interactions.
