Time dilation of a rotating disk

[Chris Miller]

Would I be right in saying that in the original question, none of the observers are actually moving in any of the other observers' frames of reference except the guy not standing on the disc? They are all accelerating at different amounts, but if you take any of their instantaneous frames of reference none of the other people on the disc are moving at all. They have always been the same distance away in the same direction.

I'd say, no. Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.

 

[PeterDonis]

Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.

What do you consider to be "Earth's FOR"? If a satellite in geosynchronous orbit is directly above you, standing on the equator of the rotating Earth, and you remain still, motionless on the rotating Earth, the satellite remains directly above you: it doesn't move at all relative to you. Doesn't that count as not moving in "Earth's FOR"?

 

[A.T.]

I'd say, no. Or else a satellite in geosynchronous orbit isn't moving relative Earth's FOR, which I'm pretty sure isn't the case.

What do you mean by "earth's FOR"? The non-rotating frame where only the Earth’s centre is at rest? Or the rotating frame where the entire Earth and geostationary satellites are at rest?

 

[John Morrell]

Yeah, the thing about FOR's is that they are essentially coordinate systems. You relate distances, times, velocities, etc in relation to an arbitrarily chosen point or observer. In the frame of reference of a person on earth, the satellite never changes position. The same position vector points from you to the satellite at any time. Likewise, all the people on the disk do not move in relation to each other.

 

[Chris Miller]

I guess I see Earth's FOR as including a vast region of space at which it is at the center and not moving relative to, whereas the satellite, which is far from the center, is.

 

[PeterDonis]

I guess I see Earth's FOR as including a vast region of space at which it is at the center and not moving relative to

Is this frame rotating or not? You can pick either answer: both are valid. But you have to be clear about which you are using. And then you have to realize that answers to other questions can depend on which you pick. If you pick the non-rotating frame (which is often called an "Earth-Centered Inertial" frame in the literature), then yes, the satellite is moving relative to this frame. But if you pick the rotating frame (which is often called "Earth-Centered Earth-Fixed"), the satellite is not moving. So whether the satellite is moving depends on which one you pick: there is no unique answer to the question.