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Let's say I have a twin who is at rest relative to myself and ten light years away from me, we are both in rocket ships. We have agreed that I will send a laser pulse and that when he receives it we will both accelerate to 80 percent speed of light (quickly) towards each other.

I fire off my laser pulse and wait ten years for my twin to receive it and then fire up my engines. Time dilation and length contraction are experienced during the trip. We underwent the same acceleration and time is going slower for my twin relative to me, and likewise from my twin's viewpoint time is going slower for me.

When we pass each other and look through our windows, who will have aged more?

Thanks in advance far any considerations.

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Careful with comments like "when he receives it"--simultaneity is relative, different frames will disagree about which reading on your clock happens "at the same time" that he receives the pulse. If he is 10 light years away in the frame where you were initially at rest, and you wait 10 years after sending the signal to fire your rockets, then you fire your rockets simultaneously with him relative to this frame, but not others.

That being said, given the conditions of your thought-experiment, you will both have aged the same amount. Although your ages at the time of passing can be calculated in any frame, this is easiest to see if we look at things from the perspective of the frame where you were both initially at rest--in this frame you both accelerate simultaneously, and both travel at the same speed towards each other, so in this frame your clocks will be ticking at the same rate at every moment in time (both before and after you accelerate). In other frames your clocks will tick at different rates after accelerating, but in a given frame the twin whose clock ticks faster after accelerating also accelerated later than the other twin due to the relativity of simultaneity, and in such a frame the twins' ages were actually different before either one accelerated towards the other, so it can still work out that both twins have reached the same age when they pass in such a frame.

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    $\begingroup$ Although this answer is already perfect, let me just add that any relativity "paradox" is easy to resolve if you just take a minute to draw the spacetime diagram. In this case, the diagram would have revealed the symmetry of the situation and you'd have said "Oh, of course!". $\endgroup$ – WillO Dec 19 '14 at 22:49

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