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It's a question that was bothering me for some time. In special relativity one can consider the "twin paradox", where one twins leaves earth and returns, staying young while the twin left behind grows older. This is not a paradox because the twin in the spaceship accelerates to change his direction when turning back- therefore he is not in an inertial frame.

However, in a universe with the geometry of a flat torus, one can go "around" the universe and return to earth without accelerating or experiencing any intrinsic curvature of the universe. In this situation the paradox rises again: which twin is older and which one is younger, considering that both twins' frames of reference are valid?

Nim413
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  • https://physics.stackexchange.com/questions/361/symmetrical-twin-paradox – Slereah Apr 24 '17 at 13:09
  • The twin who follows the path with the shorter proper length will (of course) be younger. There is nothing paradoxical about this. – WillO Apr 24 '17 at 14:26
  • You seem to be imagining that at every moment, Twin A has an opinion about how fast Twin B's clocks are running. But unlike in Minkowski space, Twin A's coordinate system cannot be extended to all of spacetime --- so when Twin B leaves that coordinate system, Twin A no longer attributes any particular speed to Twin B's clock. – WillO Apr 24 '17 at 14:34

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