Closed Universe Twins Paradox: No Acceleration?

[infinitus]

If the universe was closed and such that if one continued in a straight line they would arrive where they began eventually. Wouldn't the twins paradox still be a paradox as neither party is accelerating (are they?) and this would prove that such a universe doesn't exist?

 

[the blob inc]

hmmmmm time dilation, well who is to say that the universe is finite in the first place. considering that we know it is currently expanding(because the gallixys are moving apart) its not to hard to fathom the fact that it may be infinitely big in porportion and that it is getting biger even as we speak.

 

[infinitus]

As long as it isn't expanding faster then the traveller they will still met again if the universe is as suggested in my original post.

 

[Integral]

As long as it isn't expanding faster then the traveller they will still met again if the universe is as suggested in my original post.

But if the universe is infinite the odds of a duplicate of your traveler existing is 1 , so you argument is not unique to a closed as the same result can be expected in an infinite universe.

I do not see how the "twin paradox" enters into this. Proper application of Special Relativity resolves the "twin paradox", so it is not a paradox.

 

[Perspicacious]

If the universe was closed ... wouldn't the twins paradox still be a paradox ... and this would prove that such a universe doesn't exist?

The paper, "On the Twin Paradox in a Universe with a Compact Dimension" presents a very clear answer to your question:

"We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of each twin to a preferred inertial reference frame which exists in such a universe because global Lorentz invariance is broken. The twins can perform 'global' experiments to determine their velocities with respect to the preferred reference frame (by sending light signals around the cylinder, for instance)."
http://arxiv.org/PS_cache/gr-qc/pdf/0503/0503070.pdf

See these references also:

http://physics.ucr.edu/Active/Abs/abstract-13-NOV-97.html
http://www.everythingimportant.org/viewtopic.php?t=79
http://cornell.mirror.aps.org/abstract/PRD/v8/i6/p1662_1
http://arxiv.org/PS_cache/gr-qc/pdf/0101/0101014.pdf
http://arxiv.org/PS_cache/physics/pdf/0006/0006039.pdf
http://www.everythingimportant.org/viewtopic.php?t=605
http://www.everythingimportant.org/relativity/simultaneity.htm

All this analysis has a pointed answer:

When the two twins meet again, the youngest, least-aged twin will be the one who is moving the fastest with respect to the absolute frame of reference.

Here's the main point:

Spatially compact spacetimes break global Lorentz invariance and define absolute inertial frames of reference.

 

[robphy]

Here was an earlier PF discussion
https://www.physicsforums.com/showthread.php?t=51197