higher derivatives, i.e. terms such as $R^2$ or $R_{\mu\nu}R^{\mu\nu}$. Indeed there is a power counting theorem that says that each gravitational loop always brings in two more powers of the energy. The content of the renormalization group within effective field theory has been explored by Weinberg and others [@weinberg]. While the technique is useful at predicting some leading and subleading logarithmic kinematic dependence, it does not involve the running of the leading order coupling, and in gravity does not predict the running of $G$. Efforts to define a running coupling in the perturbative regime must attempt something outside of the usual application of the renormalization group.

The purpose of this paper is to explore explicit physical calculations in Lorentzian spacetime to see if there is a definition of running gravitational coupling which is physically useful and universal in the regime where we can maintain control of our calculations. Our answer is negative - no such definition is both useful and universal.

Gravitational corrections to coupling constants
===============================================

Ultraviolet divergences in field theories correspond to counterterms in a local Lagrangian. In a theory with a dimensional coupling constant with an inverse mass dimension, such as general relativity, these local terms are 