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?
Put another way,
Let's say we launched a space shuttle from earth and it traveled away from earth at .5c and there was an atomic clock on board originally synchronized with an atomic clock on earth. Let's say the shuttle returns a year later (earth time), the atomic clock on the shuttle would only have half a year elapsed time, right? But who's to say that the shuttle's clock should not be the standard? If a year had passed on the shuttle's clock, would half a year have passed on the earth clock?
If both observers do believe that time is moving slower for the other one, why do atomic clocks tell us which one is moving and which one is stationary? This question is really confusing to me.
Many times I've heard people explain how a space ship traveling at close to the speed of light for many years (ship time) and returning to the earth would find that many many more years had passed on earth. I had no problem with this, but how can this happen if both observers believe time is moving slower for the other one????
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