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With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and the actually travelling twin again reached earth after completing the loop, then no such information would have biased the actually travelling twin, and the paradox will still remain (?).

And universe thus can't be a loop, it must have an end point?

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marked as duplicate by John Rennie, Waffle's Crazy Peanut, Emilio Pisanty, Qmechanic May 13 '13 at 19:53

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Well for that you always can have a window in the space-ship . –  nonagon May 13 '13 at 10:13
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@Manishearth why do you say that? It's not what happens in our (probably) non-wrap-around universe. I think this is a good question - at least, the answer doesn't seem trivial. –  Nathaniel May 13 '13 at 10:20
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@Nathaniel: Sure, I'm not saying the question is trivial. And I just realized my blunder; I somehow mixed "age" with "rate of aging". Silly me. –  Manishearth May 13 '13 at 10:21
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Possible duplicate of Symmetrical twin paradox. –  John Rennie May 13 '13 at 12:05
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@Qmechanic please see my comment above. I agree that this is mostly a duplicate of that question, but one subtle and non-obvious difference is that the other question asks about a situation in which there is curvature, so it can only be answered with GR, whereas (I think) this one can be answered using SR alone. I don't know whether I'll have time to post such an answer, but would you consider re-opening it if I did? –  Nathaniel May 14 '13 at 1:06

1 Answer 1

If I'm understanding the question correctly, it's referring to a universe that (1) has a spatial topology that wraps around, and (2) has cosmological conditions such that a timelike curve can circumnavigate the universe (in the sense of reuniting with a geodesic that has been at rest relative to the CMB). I assume that "looped" doesn't refer to closed timelike curves (CTCs), which are timelike and whose existence violates causality.

In answer to zhermes's question posed in a comment, no, this would not theoretically require curvature. Analogously, a piece of paper wrapped into a cylinder has no intrinsic curvature. However, the actual cosmological conditions of our universe can and probably do have nonzero intrinsic spatial curvature.

The mathematically simplest cosmology that has loops in the sense defined above is one in which the intrinsic curvature vanishes everywhere, the universe is static, and one or more spatial dimensions are topologically wrapped around. This is essentially a cylinder. In a cylindrical universe, there is a globally preferred frame of reference, which is the one in which the Lorentz contraction of the universe's circumference is minimized, i.e., the circumference is maximized. This does not contradict the foundations of GR, which only say that there can be no preferred frame locally. The existence of the preferred frame means that you can have a non-null result from the twin paradox even if both twins move inertially.

In a realistic, closed cosmology, I don't think condition #2 above is satisfied.

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