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What happens if the twin in the spaceship doesn't return? Would he still be younger than his other twin? Is the symmetry broken simply by accelerating out of earth? If it is still symmetrical when he doesn't return, why do satellites have a different time than the time on earth if they didn't return?

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What happens if the twin in the spaceship doesn't return? Would he still be younger than his other twin?

It's really a moot point, because you can't compare clocks. There is no absolute time! You can't say, "What's each twin's age at this instant?" because "this instant" depends on the observer.

Is the symmetry broken simply by accelerating out of earth?

That and accelerating back.

If it is still symmetrical when he doesn't return, why do satellites have a different time than the time on earth if they didn't return?

Satellites have a different time than on earth because of weaker gravity. They also experience orbital acceleration which breaks symmetry from us.

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    $\begingroup$ Also we receive time signals from the satellites, not the other way around, so even without gravity and acceleration there is still a broken symmetry. $\endgroup$ – user10851 Dec 9 '14 at 22:42
  • $\begingroup$ Good point - we can never know what time it is at a satellite "right now", only what time it was when it sent the signal we just received. $\endgroup$ – Señor O Dec 9 '14 at 22:55
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    $\begingroup$ If the twin looks through a telescope that lets him see the twin though, would he see the old twin or the new one? Also, why does accelerate break symmetry? Doesn't earth accelerate the other way for him? Sorry for the basic questions, I'm still learning. $\endgroup$ – Protoless Dec 9 '14 at 22:58
  • $\begingroup$ "Why does acceleration break symmetry?". Because the twins experience different things. The travelling twin experiences acceleration - just as you do when a car accelerates or breaks - but the stay at home twin does not. Every observer - including the stay at home twin, the travelling twin, and visiting Klingon spaceships whizzing by - will see one twin as having accelerated at some point and the other twin as not accelerating. $\endgroup$ – Peter Webb Mar 1 '15 at 17:37

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