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I'll keep it simple as this is a very simple twist on the famous twin paradox. The twin paradox is resolved by the fact that for the clocks to actually meet up again one of them has necessarily undergone acceleration, so the assumed symmetry of the 2 observers isn't correct.

However, imagine a finite universe with a periodic metric. You can easily have 2 observers that will cross each other at some point to initially sync clocks, then do a round trip around the universe, then meet up again. You now have the 2 initially synced clocks back at the same location, with each now seemingly correctly assuming time dilation for the other clock. There is no hidden acceleration to save us here.

So what gives ? Is there a GR effect of curved metrics I'm not seeing here that would perfectly cancel out the SR time dilation ?

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    $\begingroup$ Nothing gives. There would be no difference between the ages of the twins if they had undergone entirely symmetrical journeys. $\endgroup$
    – Professor Sushing
    Commented Nov 17 at 21:20
  • $\begingroup$ Yes, but they both would have computed that there should be one given SR time dilation. $\endgroup$
    – ticster
    Commented Nov 17 at 21:22
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    $\begingroup$ I think this is the clearest previous answer: physics.stackexchange.com/a/353230/180843 $\endgroup$
    – Sten
    Commented Nov 17 at 21:38

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