Re:John C. Mather: “There is no first moment of time” (2017)
by sounds on Monday September 12, 2022 @12:56PM
(#32813093)
Just hypothetical 3D curved spaces here, not saying this has any physical reality -
If the X axis curves into Y (i.e. wraps around the Z axis) and also has a slight negative Z component (i.e. to move in a helical fashioin) each of those curvatures would mean a line segment eventually intersected itself.
It's the nature of the curvature: the space is not sheared (like a rhombus), it is curved (like latitude and longitude), which is why the line segment eventually intersects itself.
Ah, indeed, quite a brain fart moment from me there, since you explained the structure right in the previous comment. Pondering cosmology while sleep-deprived is suboptimal, I guess.
Though now I'm curious about this:
> If it has even the tiniest curvature, then it curves back onto itself and is non-Euclidean
Would it be possible in theory that the three dimensions are curved like a helix—so they have constant curvature but don't intersect themselves? This way the universe would still stretch infinitely in most directions, but would be non-Euclidean, and you'd need to know where the ‘axis’ is to be able to see in a direction that shortcuts to another one.