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In every book the solution of twin paradox is that one have to accelerate thus two observer does not trace parallel lorentz vectors thus can't be compared. Through GR we get the one who accelerate will sufer time dilation. But what if the other guy is not accelerating but just moving away with rel. velocity and they use EM waves to send the photos of each other isn't still there is Paradox? Think about that.

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To observers can only directly compare their clocks if they are located at the same point in spacetime. So in the traditional twin paradox the twins compare their clocks twice, once when they part then a second time when they meet again.

If two clocks are not at the same point then the Lorentz transformation will change the times on the two clocks differently. That is because the transformation for time is:

$$ t' = \gamma\left(t - \frac{vx}{c^2}\right) $$

Note that the clock position $x$ appears on the right hand side, so clocks at different $x$ will transform differently.

In the case where the twins part then just continue at constant velocity in a straight line there is no paradox. When the twins do their Lorentz transformations they each get the same result i.e. that the other twins clock is running slow.

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  • $\begingroup$ Thats fine, you quoted that time depends on position co-ordinate too, but what about difference in two successive ticks isn't that independent of position co-ordinate and that's what whole twin paradox is based on. Still I'm not able to solve the paradox. Let's talk about us you are my twin and we synchronized our clock and then you go to spaceship and travel at relativistic velocity. Now after sometime I take my selfie and on that selfie time date everything is written and send that to you. Now if I look from your frame then on your MMS my photo should look younger. But if it is viewed from m $\endgroup$ – user87555 Aug 7 '15 at 5:45

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