Theories of scalars and gravity, with an Einstein-Hilbert term and
non-minimal interactions, $M^2R/2 -\alpha\phi^2R/12 $, have graviton exchange
induced contact interactions. These modify the renormalization group, leading
to a discrepancy between the conventional calculations in the Jordan frame that
ignore this effect (and are found to be incorrect), and the Einstein frame in
which $\alpha$ does not exist. Thus, the calculation of quantum effects in the
Jordan and Einstein frames does not generally commute with the transition from
the Jordan to the Einstein frame. In the Einstein frame, though $\alpha$ is
absent, for small steps in scale $\delta\mu/\mu$ infinitesimal contact terms
$\sim \delta\alpha$ are induced, that are then absorbed back into other
couplings by the contact terms. This modifies the $\beta$-functions in the
Einstein frame. We show how correct results can be obtained in a simple model
by including this effect.
