Is the Universe Shaped Like a Three-Torus?

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The theory suggests that the Universe may be shaped like a three-torus, allowing for a finite structure without edges. This configuration implies that light could travel around the Universe and return to its origin, potentially showing distant galaxies as earlier versions of our own. The discussion highlights that the conclusions of finite volume and light's complete circuit are not exclusive to the three-torus model. Additionally, the relationship between time and space is emphasized, indicating that a comprehensive understanding of the Universe must consider both dimensions. The concept was initially proposed by mathematician Kurt Gödel.
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There is a developing theory that the Universe may be shaped like a three-torus, the mathematical equivalent of a rubber cube that's bent so that all opposing sides are connected. This would mean that the Universe is finite, but does not have the problematic edge that's included in most theories. It also means that light traveling from one point, having effectively circumnavigated the Universe could eventually end up back where it started, meaning that one of the galaxies we can see through telescopes might be a baby picture of our own galaxy. Does anyone have any thoughts on this theory?
 
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Neither of the two conclusions:

1) Volume is finite, without bound
2) Light can make a complete circuit around the universe

are unique to a model of space being a 3-torus.

Relativists will also complain when you neglect time as being related to space.

- Warren
 
This idea was first introduced

by the mathematician Kurt G¨odel.
 
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