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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?

John Rennie
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  • I have attempted to clarify the question, please let me know if this is not what you meant. – Manishearth May 13 '13 at 10:05
  • AFAICT here the acceleration would be replaced with gravitational time dilation. But I'm not sure if there would be a net effect. Also: to compare ages the moving twin would have to stop(decelerate) anyway. – Manishearth May 13 '13 at 10:08
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    Well for that you always can have a window in the space-ship . –  May 13 '13 at 10:13
  • How would you measure age so that it is consistent for both frames? For example, lets say that Earth has a big counter on it, and so does the spaceship. The counters start at arbitrary values, and increment every second.When the spaceship passes the Earth, the ship will note down a different set of counter values (for both counters), than the Earth. – Manishearth May 13 '13 at 10:18
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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. – N. Virgo 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
  • For example your clock had a counter that measured no. of oscillations of a light pulse between two mirrors , now the space-ship twin's counter showed a number less than the earth twin's or the opposite ?. The counter numbers are displayed on the window such that they can see without anyone having to stop . –  May 13 '13 at 10:21
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    Possible duplicate of Symmetrical twin paradox. – John Rennie May 13 '13 at 12:05
  • I've wondered the same thing as this question. The conclusion looks half correct. I think it demonstrates that the universe can't be a loop, but not that it must have an end point. Basically, this disproves a special relativity version of wormholes. I think the harder question is if you can formulate a general relativity metric that loops and doesn't violate causality. My current belief is that answer is "no", in spite of the fact that people like Michio Kaku publicly argue otherwise. I do not understand how a space loop can avoid violating causality. – Alan Rominger May 13 '13 at 13:35
  • @AlanSE How would looped spacetime violate causality? It seems like this just involves comparisons of measurements – DilithiumMatrix May 13 '13 at 14:57
  • If the universe were spatially cyclic ('looped'), would that require curvature, or can one just 'map' the $x\rightarrow +\infty$ side to the $x\rightarrow -\infty$ side? – DilithiumMatrix May 13 '13 at 14:59
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    @zhermes no, it doesn't need curvature, at least if it only "loops" in one dimension. It's analogous to rolling a piece of paper into a tube - you don't need to stretch it. – N. Virgo May 13 '13 at 15:12
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    Personally, I think the resolution is that creating a "looped" universe in this way necessarily creates a preferred frame of reference that breaks the symmetry. One twin sees a lorenz-contracted universe that's smaller than the one the other twin sees. If I get time I'll write that up as an answer. – N. Virgo May 13 '13 at 15:13
  • @Nathaniel What is a preferred frame ? Aren't all inertial frames equal ? –  May 13 '13 at 17:43
  • Possible duplicate: http://physics.stackexchange.com/q/1787/2451 and links therein. – Qmechanic May 13 '13 at 19:51
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    @nonagon in a non-wraparound universe, all frames are equal. But, I think, in a wrap around universe they are not, because there is one frame in which the universe has a maximum size, and it's smaller in all other frames. Unfortunately it's hard to explain this without the aid of a diagram, and this question has been closed, which means I can't post one. (And unfortunately the "duplicate" question is actually different enough to this one that such a diagram would make no sense as an answer to that question.) – N. Virgo May 14 '13 at 01:04
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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? – N. Virgo May 14 '13 at 01:06
  • @Nathaniel: The linked paper in the answer actually already only uses SR, so your project seems to amount to splitting hair. As a minimum to consider re-opening, you (or somebody else?) should phrase and focus the question and title much better than now, and duplicate questions about e.g. topology of space-time must be deleted. – Qmechanic May 14 '13 at 15:23
  • @Qmechanic ok, fair enough, I didn't follow the link in the answer to the other question. – N. Virgo May 14 '13 at 15:26
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    Related: http://physics.stackexchange.com/questions/24731/does-the-current-acceleration-of-universe-imply-that-our-universe-is-open \ – Abhimanyu Pallavi Sudhir Aug 02 '13 at 14:22

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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.