Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?PeterDonis said:My personal view on GR is closer to that of the Cuifolini and Wheeler textbook I referenced, whose tag line is "mass there governs inertia here", i.e., GR is Machian to the extent that such a question even matters. The Einstein Field Equation says that the spacetime geometry at any event is determined by the distribution of stress-energy in the past light cone of that event. That seems pretty Machian to me.
No. A more precise phrasing would be that mass there governs inertial motion here. Mass there determines the spacetime geometry here, and the spacetime geometry here determines which worldlines here are inertial, and what the path curvature is of worldlines here are not inertial. But path curvature is only proper acceleration; what you feel as weight is proper acceleration times inertial mass. The spacetime geometry does not determine what the inertial mass of a body is.timmdeeg said:Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?
Yes this way it makes sense to me and I would prefer to call it just Einsteinian.PeterDonis said:No. A more precise phrasing would be that mass there governs inertial motion here.