When discussing time dilation, how do you determine which time is slowing down?

Question

I just saw a question about time dilation, and thought I could ask a similar question I never really found an answer for on my own, hoping that some of you bright heads here might be able to provide an answer.

Since speed is relative, how does one determine which time is slowing down?

Let’s take a very simplified example, and make this assumption:
– Assume that it is possible to move away from earth in an arbitrary direction in 0.1 c (relative to earth) for a given time or distance, then turn around and travel back for the same time or distance, and arrive back at earth. (effectively ignoring that earth is experiencing acceleration during this time, or assuming that the spaceship experiences the same).

If my brother leaves on a spaceship and travels for 1 hour (in his time) away from the earth at 0.1 c, then turns around and travels back to earth for 1 hour at 0.1 c, while I remain at earth, will our experienced time differ in this scenario?

And how is this affected by the relativity of speed? Does it change if we instead assume that earth is travelling at 0.1 c through space, and my brothers spaceship decelerates essentially to a “stop”, then accelerates up to 0.2 c in order to “catch up” to earth again?

If my assumption in this question is absurd, I am sorry for that, I just don’t really know how to properly set up an example that describes my question good enough.

In: Physics

Answer 1

If you could observe each other, you would indeed both think the other is slowing down as you fly away from each other. However, velocity isn’t the only thing that causes time dilation. Acceleration also slows down time. When the brother in the rocket slows down, turns around, and speeds up towards home, they are the ones who accelerate.

Unlike velocity, acceleration isn’t relative. Both brothers will agree that during the period of acceleration, time slows down for the brother in the rocket. 

So, both brothers observe the other as slowing down while they are moving at a constant speed, but the brother who is accelerating gets some extra additional slow down which then makes for the age difference both can agree on.