Okay, let's say that there is nothing else in this universe and we know Zorg's ship is the one that is fine and Viola is the one racing away at .5c. Viola travels a full year (her time) before she fixes her ship. Then she returns directly to Zorg at .5c. Will Zorg have aged twice as much as Viola or vice versa? and why?
Two points:
One minor; you'd have to travel at near .99c to have time slow down by half. It is not linear and it is not time moving at half speed if you do half light speed. Doesn't really matter to the overall question it is just a nit.
There is a difference between Zorg and Viola or the shuttle and the earth.
Once the trip out and back is complete you can distinguish between the two. One of them has undergone accelerations and decelerations. That is the one whose clock will show up as slow.
That is when the shuttle returns (at some speed so that it's clock runs at half the rate when observed from earth) then it will show less time passing.
I don't actually know if this is a purely special relativisitc effect (which I think is the case) or if general relativity is involved.
The reason I wonder about that is because time is dilated in a gravitational field as well as by speed. And GR says that acceleration is exactly equivalent to a gravitational field. For this reason the clocks on the shuttle will be slowed by the accelerations. What I don't know is whether the numbers work out.
Remember that the shuttle would have to undergo very large accelerations or very long times accelerating to get to .5 (or more correctly .99c). That would definitely have a general relatavistic effect. Does anyone know if the numbers work out?