I Could Space-Time Curvature Enable Time Loops?

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The discussion explores the theoretical possibility of time loops in curved space-time, particularly referencing the Klein bottle as a model. While the Klein bottle suggests looping in every dimension, the conversation highlights that time loops could exist with just one time dimension. Examples of spacetimes with closed timelike curves, such as Godel spacetime and the interior of Kerr spacetime, are mentioned as evidence that complex topologies may not be necessary for time loops. Participants express interest in further investigating these examples. The conversation emphasizes the need for empirical evidence before drawing conclusions about time loops.
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If space-time is curved like a klein bottle, is it theoretically possible that events could loop back in time ? :wink:
 
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That is a big "if". Assuming it is like a Klein bottle, then it will loop back in every dimension. I wouldn't think too hard about it till there is some evidence.
 
Well in principle there could be a time loop just by having more time dimensions than one.
No need for anything as complicated as a Klein bottle topology.
However in reality we only observe one dimension of time and there is no reason to suspect more.
 
rootone said:
in principle there could be a time loop just by having more time dimensions than one.

This is not necessary; there are spacetimes with the usual metric signature (one timelike and three spacelike dimensions) which have closed timelike curves. The Godel spacetime is one; the deep interior (inside the inner horizon) of Kerr spacetime is another.
 
PeterDonis said:
This is not necessary; there are spacetimes with the usual metric signature (one timelike and three spacelike dimensions) which have closed timelike curves. The Godel spacetime is one; the deep interior (inside the inner horizon) of Kerr spacetime is another.
Thanks, I suspected this could be the case, I'll look into the examples you mentioned.
 

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