Due to earth's rotation, aren't the stars 'relatively' moving way faster than light?

[sergeidave]

I know this may be a stupid question, at least for us, mere mortals. But I searched for it and didn't find it anywhere on this forum, and couldn't help to ask it myself. I mean, according to Einstein's relativity, any object in a state of movement can actually be at rest relative to another object and viceversa. So, at least in concept, the earth might as well be the one resting and the rest of the universe the one going around the earth once every single day, or am I missing something? If so, practically the whole universe would be moving exponentially faster than the speed of light. What's the explanation to this??

Please forgive my ignorance and I thank you all for any comments that can help me clear this in my mind.

Cheers!!

 

Sergeidave

[insane_alien]

the earths frame is not an inertial frame. so no, they are not moving faster than the speed of light relative to us.

 

it is us on earth that are accelerating round and round and not the universe. if there is an acceleration then we can tell who is accelerating.

 

and it is us on earth and not the rest of the universe.

[JPGreco]

well, putting aside the theory that nothing can move faster than the speed of light, then yes, it would be possible.

You have a planet and everything seen from the planet orbits it in a single day. The further away something is from the planet, the faster it must be moving in order to orbit the planet in a day (relatively speaking). So if an object had a large enough orbit, then yes, its speed would be greater than the speed of light.

However, this doesn't work backwards. If you have a set universe, an object in the middle that is rotating will repeat what is seen once a day. Even if a star is far enough away that its orbit would be greater than the speed of light, it doesn't appear to be any farther away than, say, the moon is from earth, since it is seen every day. Its true distance doesn't account for its relative orbit. Now, regardless of how far something is from earth, its "speed" is the same as something that is half the distance, twice the distance, or any other distance from the earth.

[Mr Skeptic]

In earth's rotating reference frame, yes. It does not violate the laws of physics because you have to restate them all in earth's rotating frame. I do hope you realize that the stars aren't actually orbiting earth.

 

Incidentally, relativity does not apply to acceleration. No matter the inertial frame, you can tell when you are accelerating. In a rotating frame, everything would be accelerating toward you if they were at a fixed angle and distance.

[Severian]

I do hope you realize that the stars aren't actually orbiting earth.

 

In what sense are they not? GR tells us that all frames (whether inertial or not) are equivalent. Therefore, the frame of reference in which the stars are orbiting Earth is perfectly acceptable.

 

In fact, I always find it amusing that Galileo reputedly made such a fuss rejecting the claim that the sun orbits the Earth, when in actuality, it does!

 

Being slightly less flippant, I think this question is deeper than you guys give credit for. As I already mentioned, it is a valid frame, so I don't think you can just say it doesn't count. Your frame compensates for the acceleration by having an additional gravitational field (ie curvature) so I think the answer is probably something to do with the weird curvature of spacetime you get in this frame. Any GR experts around?

[swansont]

But a valid frame is not the same as an inertial frame. If you are in a non-inertial frame, you have to add (fictitious) forces in order to have Newton's laws hold, and you lose the restrictions related to the speed of light.

[Severian]

Hmmmm. I posted another reply about this earlier, but it is not there now. I was in a bit of a rush, so maybe I didn't hit the submit button. Silly me!

 

Anyway, I was wanting to point out that in Einstein's original 1916 GR paper, he doesn't talk about elevators at all, but talks about a relativistic spinning disk. This is directly analogous to the OP's post since you can think of the distant stars as the rim of the disk with us at the centre (although you should take the mass of the disk to zero to eliminate the stress tensor over its body).

 

It is also intimately linked to the Ehrenfest paradox