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If the universe is compact then there is a twin paradox that is resolvable only by selecting a preferred inertial reference frame (arXiv). I was under the impression that the lack of a preferred inertial reference frame was an empirical result (e.g. from early experiments designed to measure Earth's movement against the aether).

But if I've understood these first points correctly then we should not still be entertaining the notion of a compact universe at all, as in the top voted answer to this question.

So: Is a compact universe theory still viable? If so, what might account for the lack of evidence supporting a preferred inertial reference frame (or is there actually now evidence of a preferred frame)?

Community
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Aaron Golden
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2 Answers2

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If the universe is compact then its scale is at least 100 times greater than the observable universe (because according to experiment the observable universe is flat to within 1%). No experiment of a length scale much shorter than this scale would be able to detect the compact topology, so the Michelson Morley experiment is not incompatible with a compact universe. It just means the universe is locally non-compact, which of course we already know just by looking around.

Even if the universe is compact its scale is increasing as the universe expands, and indeed the expansion is probably exponential due to dark energy. If so, no experiment we can ever do will show the universe to be compact.

John Rennie
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The problem topological compactness poses to Lorentz invariance only shows up globally. That is to say, a preferred frame induced by having a compact universe only shows up when you perform a global experiment (as in the Twin Paradox problem linked to by Qmechanic). Local experiments like Michaelson-Morley only tell you about local properties and they can be perfectly compatible with full Lorentz invariance - they wouldn't tell you anything about global properties unless your apparatus were large enough to see the topology.

James
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