  In a previous paper, the authors with Ann Nelson proposed that the UV and IR
applicability of effective quantum field theories should be constrained by
requiring that strong gravitational effects are nowhere encountered in a
theory's domain of validity [Phys. Rev. Lett. 82, 4971 (1999)]. The constraint
was proposed to delineate the boundary beyond which conventional quantum field
theory, viewed as an effective theory excluding quantum gravitational effects,
might be expected to break down. In this Letter we revisit this idea and show
that quantum gravitational effects could lead to a deviation of size
$(\alpha/2\pi)\sqrt{m_e/M_p}$ from the Standard Model calculation for the
electron magnetic moment. This is the same size as QED and hadronic
uncertainties in the theory of $a_e$, and a little more than one order of
magnitude smaller than both the dominant uncertainty in its Standard Model
value arising from the accuracy with which $\alpha$ is measured, as well as the
experimental uncertainty in measurement of $a_e$.
