undiscovered symmetry principles that constrain the parameters and reduce them to a finite set. This is the route taken by string theory, where all of the excitations of the string essentially manifest themselves as new symmetries. Quantum gravity as an effective field theory In an effective field theory, not all but the first few of the infinite set of parameters in a nonrenormalizable theory are suppressed by huge energy scales and hence can be neglected when computing low-energy effects. Thus, at least in the low-energy regime, the model is a predictive quantum field theory. Furthermore, many theorists argue that the Standard Model should be regarded as an effective field theory itself, with "nonrenormalizable" interactions suppressed by large energy scales and whose effects have consequently not been observed experimentally. Works pioneered by Barvinsky and Vilkovisky suggest as a starting point up to second order in curvature the following action, consisting of local and non-local terms: where is an energy scale. The exact values of the coefficients are unknown, as they depend on the nature of the ultra-violet theory of quantum gravity. is an operator with the integral representation By treating general relativity as an effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomena. An example is the well-known calculation of the tiny first-order quantum-mechanical correction to the classical Newtonian gravitational potential between two masses. Moreover, one can compute the quantum gravitational corrections to classical thermodynamic properties of black holes, most importantly the entropy. A rigorous derivation of the quantum gravitational corrections to the entropy of Schwarzschild black holes was provided by Calmet and Kuipers. A generalisation for charged (Reissner–Nordström) black holes was subsequently carried out by Campos Delgado. Spacetime background dependence A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in Newtonian mechanics and special relativity; the spacetime geometry is dynamic. While simple to grasp in principle, this is a complex idea to understand about general relativity, and its consequences are profound and not fully explored, even at the classical level. To a certain extent, general relativity can be seen to be a relational theory, in which the only physically relevant information is the relationship between different events in space-time. On the other hand, quantum mechanics has depended since its inception on a fixed background (non-dynamic) structure. In the case of quantum mechanics, it is time