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Question about Time Dilation..

I have a question about special relativity which was bothering me for a while now. I know that as one approaches the speed of light, time moves slower for him. So, if I start moving as fast as 99% of the speed of light and travel away from Earth for 1 day and come back, I'll see that (suppose) about 1 year has passed on Earth.

But my question is, if everything is relative, then how can we say that I was the one moving and Earth was the one staying? I mean if I consider myself as the center o the coordinate system, then I can say that Earth went on a travel with the speed of light and came back. So why is that the time slows down for me and not for the Earth? How do we distinguish between the moving and the static object according to relativity?

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marked as duplicate by David Z May 21 '11 at 2:12

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Possibly related: – Qmechanic May 20 '11 at 15:56
In short: Acceleration. By turning around, you had to slow down and speed up again. This means that you have changed inertial frames. – Lagerbaer May 20 '11 at 15:58
ok, that clears the issue to some degree. What about the far far galaxies which are traveling relatively with a very high speed (I guess in some cases with half the speed of light). How can we determine if we are experiencing time slower or them? – Ahmad3D May 20 '11 at 17:15
Both experience the same thing, and this is no problem because someone would have to accelerate to meet to compare clocks. – Phira May 20 '11 at 17:18
That's the thing, distant galaxies aren't necessarily traveling any faster than we are. That's just how it appears because space itself is expanding between us. – voithos May 20 '11 at 17:21

This is known as the Twin Paradox. It isn't really a paradox, and as stated above, this is because only one of the frames is accelerating. The point of view of the guy on the rocket isn't an inertial frame of reference.

Here is a Wikipedia link with more information:

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the guy on the rocket can live in an inertial reference frame most of the time, but crucially the frame is not the same before and after the (possibly infinitesimal) moment of acceleration. this is illustrated nicely in the image at – BjornW May 20 '11 at 22:50

It is the Twin Paradox. Browse the net and almost always the return home phase is said to clear the issue.
But there is no need to return home, nor ...
They can comunicate using light signaling. They will receive the signals (encoding a message with their own local time ;-) equally red shifted and they can not decide wich one is older, except if they decode the message.
In this way I think that the problem is undecidable under the light of Einstein Special Relativity.

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