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My understanding was that relativistic physics can be expressed in any inertial coordinate system, but not arbitrary systems. That is, no experiment can determine if we are "still" or "moving" at a constant velocity; but we can determine if we are accelerating, or moving in a circle (which by definition involves constant acceleration perpendicular to the current velocity).

Thus, we can clearly state that the Earth is orbiting, and can't view it as relativisticly stationary.

But, to my shock, I recently came across this text http://books.google.com/books?id=lWEmNBaHCJMC&pg=PA211&dq=einstein+infeld+physics+ptolemy+copernicus&hl=en&ei=dWZ_TubbKqn20gH8hNjSDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA#v=onepage&q&f=false (which has Einstein as a coauthor) which, on page 212, seems to say that although special relativity requires an inertial coordinate system, general relativity does not! And that therefore we can state that the Earth is stationary and the Sun orbits it! I would reject this as pseudoscientific bunk, if not for the authors of the book.

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"on page 212, seems to say that although special relativity requires an inertial coordinate system, general relativity does not! And that therefore we can state that the Earth is stationary and the Sun orbits it!" - Your deduction (...therefore...) is incorrect. The fact that GR does not assume inertial coordinates does not mean what you write. – mtrencseni Sep 26 '11 at 14:27

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It is special relativity which only works in inertial frames. General relativity is more general exactly because it can handle accelerated frames.

You can really work in any reference frame you like, but transforming into a frame where the earth is stationary and the sun orbits it would result in all sorts of weird virtual forces. You could do it, but it would make thing complicated!

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Please elaborate. – Robert James Sep 25 '11 at 20:53
@RobertJames: The point is that in GR there is no reference system at all with respect to which one can say "this is stationary"; e.g. in the case of Sun-Earth system you can say that they orbit each other, but it makes no sense to say that either of them is stationary or moving on its own. Only relations between objects are "invariant" under general coordinate transforms. A possibly enlightening thought experiment is to stick yourself in a closed box, and ask if that's gravity you're feeling or just the box accelerating upwards --- this is the Equivalence principle. – genneth Sep 26 '11 at 13:45

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