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It is a common exercise while learning special relativity to work out the resolution to the twin paradox. As an extension, I have looked at the twin paradox with compact dimensions, i.e. having an equivalence such as: $$(t,x_0,x_1, \cdots ) \sim (t,x_0+nL,x_1, \cdots ),$$ where $n\in \mathbb{Z}$ and $L$ is the length of the compact dimension. This is commonly done in string theory to resolve the dimensional requirement on ghost-free hilbert spaces. Using this compactification one can associate a single reference frame with each of the twins in which they are always at rest and periodically meet (orbit).

Interestingly, the resolution to the compact twin paradox lies in broken lorentz invariance and consequential emergence of preferred frames of reference.

I understand that string theory is done fully covariantly even if it requires compactifications, how is this paradox resolved there?

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    $\begingroup$ Homotopy classes: arxiv.org/pdf/0910.5847.pdf $\endgroup$ – JEB Sep 11 '19 at 22:56
  • $\begingroup$ @JEB Do I understand correctly that the issue I raise is resolved - within the framework of string theory - by making all symmetries local and not dealing with any global symmetries? $\endgroup$ – Akerai Sep 23 '19 at 12:46

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