A question about relativity.?

Question

Okay. So two clocks are synchronized on Earth and set to t=0. One clock is left behind and the other is put on spaceship that travels at 0.5c for 100 light years, turns around then comes back. Ignoring all the acceleration nonsense while the ship turned around to head back to Earth, when the ship gets back, how much time would have passed on the clock that was always on Earth, and how much time would have passed on the clock that traveled through space?

I know that time dilation is:

t = t0 * (Gamma) or t = t0 / Sqrt(1-(v/c)^2)

But I don't fully understand which clock is described by which variable, t or t0. Any help that would assist me in understanding this would be great. :)

Yep. I meant the ship travels across 100 light years. Sorry for not making that clear. :)

Yeah, I know that the acceleration is what determines whose clock is slower when they meet up on Earth. I just said that so we can neglect the amount of time it took for the spaceship to turn around.

I'm just trying to figure out which clock is t0 and which is t. And futhermore, which one is assigned the value 400 years.

So if I assume that t is the clock on Earth, then would t = 400 years, giving t0 = 346 years?

Answer 1

The variable 't0' is time shown on the clock aboard the spaceship. Variable 't' is time shown on the stationary clock.

You said that "...One clock is left behind and the other is put on spaceship that travels at 0.5c for 100 light years,.." Do you mean 100 years instead of 100 light years? For example, traveling at .5 c for a distance of 100 light years would require a flight time of about 200 years.

Answer 2

The problem is that depending on your point of view the answer of which clock is going slower while the two clocks are getting farther apart is different. It is the acceleration nonsense that results in the clocks getting back together. It is the returning to the same location that results in the possibility of agreement on which clock ran faster and which ran slower.

Try the twin paradox on wikipedia