General relativity is astonishingly good at making accurate predictions in its domain. And as we see here with Gravity Probe B, those predictions are being measured to a remarkable level of precision. So any future replacement to it will have to essentially reduce to making the same predictions as general relativity in all the cases we've been able to test so far, just as general relativity itself reduces to Newtonian mechanics in most cases. Even today we still teach classical mechanics and electrodynamics to students learning physics before we start in on relativity and quantum theory. I suspect that even if someday we find a discrepancy between general relativity and experiment that requires us to modify or replace relativity, we'll still teach it, and probably continue to use it for the intermediate cases where Newtonian gravity isn't quite precise enough, but we don't need a full treatment of neo-hyper-relativistic gravity (or whatever).
Originally Posted by wd40
There have been a number of competitors to Einstein's general relativity that still start with the basic premise of the equivalence principle, but differ in a few of the particulars. They're all pretty similar to general relativity, so using one of those models instead wouldn't really upset physics significantly. So far, to my knowledge, all of them either make the same predictions as general relativity for all measurements made so far, or they've been ruled out by experiment. The results from Gravity Probe B might rule out a few more of them; I'm not sure.
Conserve energy. Commute with the Hamiltonian.