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Some known relativistic paradoxes are reconsidered for closed spaces, using asimple geometric model. For two twins in a closed space, a real paradox seemsto emerge when the traveling twin is moving uniformly along a geodesic andreturns to the starting point without turning back. Accordingly, the referenceframes (RF) of both twins seem to be equivalent, which makes the twin paradoxirresolvable: each twin can claim to be at rest and therefore to have aged morethan the partner upon their reunion. In reality, the paradox has the resolutionin this case as well. Apart from distinction between the two RF with respect toactual forces in play, they can be distinguished by clock synchronization. Aclosed space singles out a truly stationary RF with single-valued global time;in all other frames, time is not a single-valued parameter. This implies thateven uniform motion along a spatial geodesic in a compact space is not trulyinertial, and there is an effective force on an object in such motion.Therefore, the traveling twin will age less upon circumnavigation than thestationary one, just as in flat space-time. Ironically, Relativity in this caseemerges free of paradoxes at the price of bringing back the pre-Galileanconcept of absolute rest.  An example showing the absence of paradoxes is also considered for a morerealistic case of a time-evolving closed space.

Relativistic Paradoxes and Lack of Relativity in Closed Spaces