If You Traveled Far Enough Through Space, Would You Return To Your Starting Point?
“Finally, could it be the case, just as the Earth has two dimensions we can move in on it (north-south and east-west, but not up-and-down), that the Universe might be a higher-dimensional structure like a hypersphere or a hypertorus where the various dimensions are closed and finite, curving back on themselves?
If that were the case, if you could travel in a straight line for long enough, you would wind up right back where you started. If you didn’t age, perhaps you could even wind up seeing the back of your own head just by looking for long enough, as your eyes would eventually encounter the light emitted from your own origin. If the Universe were like this, how would we figure it out?”
One of the things people curious about the Universe wonder, if they stare up at the sky for long enough and start pondering the possibilities, is whether it repeats itself on large enough scales. The Universe might loop back on itself, meaning that if you traveled in a straight line for far enough, you might eventually return to your starting point. If the Universe were like this, is there any way we could know? Would there be any unambiguous, observable signature? And if we didn’t see it, could we rule the possibility out, or would it linger as being plausible, but just out of reach of our cosmic horizons?