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The Friedmann Equations describe three possibilities for the shape of our using General Relativity, I read in a book that the shape of our Universe is a 3-sphere such that in any direction if you travel far enough you will end up at the same place from which you started. This solves the problem of whether the Universe is infinite or has a boundary, since in this scenario it is both infinite and has a boundary. My question is that the Mobius strip is also a 3D curve with one side one boundary and one can travel an infinite distance on its surface. Is it possible for a non euclidean 4D spacetime to be a mobius strip?

Qmechanic
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Ajinkya Naik
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  • I would say if you travel in any direction in straight line and end up in the same place, then the place is finite and has no boundary. – Ján Lalinský May 12 '19 at 13:18
  • Possible duplicates: https://physics.stackexchange.com/q/3656/2451 , https://physics.stackexchange.com/q/1787/2451 and links therein. – Qmechanic May 12 '19 at 13:23
  • "Is it possible for a non euclidean 4D spacetime to be a mobius strip?" A mobius strip is 2 dimensional. – WillO May 12 '19 at 14:57
  • @JánLalinský : So the cylinder $S^1 × [0,1]$ has no boundary? – WillO May 12 '19 at 14:58
  • @WillO, on such cylinder if you travel along the long axis of the cylinder, you won't return to the initial position but will reach the boundary. – Ján Lalinský May 12 '19 at 16:52
  • @JánLalinský : Ah. I misread your quantifier. When you wrote "If you travel in any direction ... ", I thought this meant "If there exists a direction in which you can travel..." but you actually meant "If, for all directions ..". My bad. – WillO May 12 '19 at 17:17
  • @WillO yes I meant all directions. But I am not very knowledgeable about these things, just stating common sense. – Ján Lalinský May 12 '19 at 22:48
  • "This solves the problem of whether the Universe is infinite or has a boundary, since in this scenario it is both infinite and has a boundary." You've got that backwards. If the universe has positive global curvature (which it probably does not have), then it could be a 3-sphere, so it would be finite and have no boundary. – PM 2Ring May 13 '19 at 03:04

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