GR: Using Earth as a Reference Frame - Q&A

[Emanphys]

I'm trying to get my head around GR. As I understand it, any frame of reference is as valid as any other for modeling the universe. Therefore, it is valid to use a non-rotating Earth as a frame of reference, and try to model the movement that is seen from this frame.

But if that is true, I would view the Sun as rotating around the Earth once a day. That would that mean that the Sun would be moving at approximately 11,000 Km/s if you do the math. That doesn't seem very reasonable, but even worse is if you start thinking about stars that are further away. If you calculate their speed, they must be moving faster than the speed of light, in order to orbit the Earth in a single day. How can this be possible?

Can anyone please explain how to resolve this?

 

[PeterDonis]

How can this be possible?

Because you are using a non-inertial frame, and non-inertial frames work differently from inertial frames. If you want to impose the "nothing travels faster than light" rule in GR generally, you have to generalize it from the rule you are used to for inertial frames. The generalized rule is, heuristically, that nothing can go faster than a light ray that is co-located with it; but that light rays themselves can move at coordinate speeds that exceed $c$, if you are using non-inertial coordinates. So in the case of distant stars in the "Earth rest frame", where the stars are moving and the Earth is not rotating, the stars could be moving faster than $c$ in coordinate terms--but the light being emitted by those stars would be moving even faster in coordinate terms, at least when it was co-located with the stars. (As the light from the stars travels towards Earth, it would slow down, in coordinate terms--so in non-inertial frames the coordinate speed of light is also not the same everywhere, it varies with location.)

 

[pixel]

See a similar question in this thread: https://www.physicsforums.com/threa...under-what-circumstances.842872/#post-5289521

 

[Emanphys]

Thanks for the responses. You've given me more directions to pursue.

 

[PeroK]

Thanks for the responses. You've given me more directions to pursue.

I wouldn't get too excited about the meaning of "valid". You can analyse any situation from any reference frame. In fact, as we sit here on Earth we are effectively obliged to view the rest of the universe rotating around us.