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Dec 11, 2018 at 10:38 comment added Eelco Hoogendoorn As I briefly mentioned, the spherical topology isn't essential; its just the most symmetric and easiest to mentally visualise; like a circular wave travelling over a water-planet; just with an extra dimension thrown in. Maybe the universe is spherical and just really huge? Or toroidal and perfectly flat? It's really the topology that would allow triangulation of a special frame, not the curvature.
Dec 11, 2018 at 9:36 comment added Luaan Spherical spacetime would indeed give us some interesting new possibilities (though not necessarily practical). But we're pretty sure spacetime is almost perfectly flat, with the only significant distortions being near large concentrations of energy. But whatever spacetime topology you imagine, you need to do the math. Any topology that isn't nearly perfectly flat gives you at least a theoretical possibility of shortcuts, but our observable universe doesn't seem to be that way - all we get are roundabouts like swinging close to a black hole :)
Dec 9, 2018 at 21:21 history answered Eelco Hoogendoorn CC BY-SA 4.0