I thought of an interesting paradox on my way home today. Suppose you have one-dimensional, finite universe without boundary. A circle. Special relativity seems to fail on this small world. Take two objects in relative motion. As they pass by each other, they synch their clocks. Stop their clocks when they pass around a second time (after "the other" goes a full cycle around the circle). What do their clocks say? According to SR, the one in motion should have the slowed clock. On a flat world, this isn't a problem, because one or both has to accelerate before they can reconvene. But on a circular world, they will eventually meet again without ever leaving their frame. So does SR not work in such a world? Or does it generalizer in a less-than-obvious way? (Or maybe I just missed something subtle).