  We consider the full effective theory for quantum gravity at second order in
curvature including non-local terms. We show that the theory contains two new
degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost
and a massive scalar field. Furthermore, we show that it is impossible to
fine-tune the parameters of the effective action to eliminate completely the
classical spin-2 ghost because of the non-local terms in the effective action.
Being a classical field, it is not clear anyway that this ghost is problematic.
It simply implies a repulsive contribution to Newton's potential. We then
consider how to extract the parameters of the effective action and show that it
is possible to measure, at least in principle, the parameters of the local
terms independently of each other using a combination of observations of
gravitational waves and measurements performed by pendulum type experiments
searching for deviations of Newton's potential.
