As in, if I'm accelerating away from the Earth, then does the Earth also appear to be accelerating away from me at the same rate? Or is there something to "break" this type of symmetry?
My question is inspired by the below discussions:
http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity
Kinematically, yes. In terms of describing the positions of objects, it is equivalent to say "A is accelerating away from B" and "B is accelerating away from A". However, it is an observed fact that the universe treats these two situations differently. A and B can check whether they feel artificial gravity in their reference frame. If so, it's accelerating. As far as I know, the "way the universe decides" to break this symmetry is a topic of continuing speculation.
Check out some related questions:
Is acceleration an absolute quantity?
Is rotational motion relative to space?
This boils down to the question of how inertial reference frames are defined in GR. GR defines them differently than Newtonian mechanics does. In GR, a frame is inertial if it's defined by a free-falling particle. The earth is essentially a free-falling particle, so its center defines an inertial frame of reference. A person in a rocket ship accelerating away from the earth is not free-falling. One way to tell the difference is that an accelerometer at the center of the earth will read zero, while one in the ship reads a nonzero value.
If you are in a rocket, you will see the Earth accelerating from you away. But everything on the Earth will occur in a regular way. In particular an accelerometer on the Earth will register zero acceleration and you may see it in your window. Your accelerator will show some acceleration and you will also feel it yourself. So accelerated RFs are different.
