Does the Earth move around the Sun?

by Sean Carroll


...But now comes along Einstein and general relativity (GR). What’s the situation there? It actually cuts both ways. Most importantly, in GR the concept of a global reference frame and the more restrictive concept of an inertial frame simply do not exist. You cannot take your locally-defined axes and stretch them uniquely throughout space, there’s just no way to do it. (In particular, if you tried, you would find that the coordinates defined by traveling along two different paths gave you two different values for the same point in space.) Instead, all we have are coordinate systems of various types. Even in Newtonian absolute space (or for that matter in special relativity, which in this matter is just the same as Newtonian mechanics) we always have the freedom to choose elaborate coordinate systems, but in GR that’s all we have. And if we can choose all sorts of different coordinates, there is nothing to stop us from choosing one with the Earth at the center and the Sun moving around in circles (or ellipses) around it. It would be kind of perverse, but it is no less “natural” than anything else, since there is no notion of a globally inertial coordinate system that is somehow more natural. That is the sense in which, in GR, it is equally true to say that the Sun moves around the Earth as vice-versa...