# But what happens going back - time dilation

• B
I've read many explanations of time dilation and relativity, that describe things from the point of an observer, and then some other object moves away from it at some fraction of light speed. i.e. say a spacecraft moves away from an observer at 0.1c for 1 year ship time. Then presumably, to an observer, it really appears to take 1.1 years, and presumably appears to have a speed of 0.1/1.1 (I know some of this maths, is possibly slightly off - I'm trying to state this in general).

But, then I always wonder, what happens when it comes back. I'm really unsure of how to describe the maths of this, but wouldn't it look faster coming back, somewhat like the doppler effect. It seems symmetric, if total ship time for ship occupant's is 2 years, and it seemed like it took 1.1 to go out, it seems like it would - from the observers point of view - that it would take 0.9 to come back.

What am I missing?

What am I missing?
Yes on the way back you would see the doppler effect just as on the way out (blue-shift to the front(ish), red shift behind). On the other hand, the return journey itself is just the outward journey in reverse, so all times (and distances) are the same!

You also need to be more specific about what you mean by "time", because there is more than one "time" involved. This video shows a two-way journey (accelerated/decelerated, not constant speed). Gaze at the pretty pictures if you must, but then concentrate on the clock display at the top left (view in HD to see properly). The red clock is the coordinate or "scene" time on the nearest clock to you (all the red dots are actually synchronized across the whole scene, but you don't see that because of light travel time delay). The yellow dot is a clock on the place that you leave and return to (as if seen through a telescope, including the doppler shift). The green clock is your "proper" or wristwatch time. At the end of the journey, the red and yellow clocks are identical, but your wristwatch time is lagging them because you went somewhere and came back to your starting point.

phinds
Gold Member
2021 Award
At the end of the journey, the red and yellow clocks are identical, but your wristwatch time is lagging them because you went somewhere and came back to your starting point.
While it is true that the statement "...because you went somewhere and came back to your starting point" is correct, it really is not in any way explanatory. Much better is to say " ... because you took a path through space-time that used less time". That is, the statement as you made it seems to imply that only space is involved whereas the actual reason is because space-time is involved.

Ibix