Does the Earth "really" go around the Sun?
I had once this discussion with a fellow physics student. It lasted about 5 hours, getting more and more intricate all the time. The issue of whether "all motion is really relative" in General Relativity is a lot more trickier than most popularizations make it seem.
My present position is this one: All coodinate systems are equivalent in the sense that one could describe all facts equally well adopting any of them, and the laws of Nature are the same in all of them (this is at the core of GR). In the case of the solar system, the coordinate system in which the Sun is at rest has the feature that the spacetime metric (which encodes the gravitational field) becomes assymptotically Minkowskian at large distances from the solar system (the Minkowski metric is the metric of flat spacetime, where there is no gravity present). By contrast, using the coordinate system in which the Earth is at rest the metric does not become Minkowskian at large distances, but includes constant terms related to the relative rotation of the Earth and Sun. The physical and absolute (not coordinate dependent) fact that the gravitational field of the Sun decreases with distance is therefore better "captured" using the first system. It's up to your philosophy of physics whether you view this as merely a "pragmatical convenience" of the first system or a license to say "the Earth really goes around the Sun". I prefer to say the latter.
Posted by: Alejandro February 9, 2006 04:20 PM
Another way of explaining it, perhaps clearer. If one goes at far distances where the physical gravitational field is too weak to be noticed, one can remain at rest relative to the Sun without any rockets turned on. The reference frame of the Sun becomes assymptotically inertial. The reference frame of the Earth does not; if you try to stay at rest relative to the Earth at large distances of the Solar System, one needs to turn on the rockets and make the spaceship go in circles (from the point of view of an external, inertial observer). I take this as meaning that the Earth "really" moves, while others will (bringing up the valid point that one can use either system to describe the situation) regard it as a convenient, pragmatically useful fact of the Sun-centered system.
Of course all this discussion neglects effects of other stars, the motion of the Sun around the galactic center, the relative motions of the galaxies and the expansion of the Universe. But the essential points remain valid.
Posted by: Alejandro February 9, 2006 04:32 PM
To make the second comment clearer: the important thing is not that to stay at rest relative to the Earth one has to go in circles, because this is a coordinate system dependent fact (in the Earth-centered system one is at rest). The important thing is that to stay at rest in the Earth-centered system one needs the rockets turned on, and in the other one not. This shows that relative to a distant, inertial observer it is the Earth that moves and not the Sun.