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[RedWarrior0]

So, as the title implies, I'm sort of interested in how a (four-dimensional, thus real) Klein Bottle World would work. Sure, there's Ring worlds, and their neighbors the Torus Worlds. However, a Giant in the Playground thread about a Möbius World made me wonder if Bay12 can take it up a notch.

And no, not using miracles.

[Grek]

It's functionally identical to living in a cylinder, as the world's rotation will send you flying off into the void of space if you go past the rim leading to the "outside" of the bottle. Just like on a mobius strip.

[alway]

You could construct and visualize one very easily IRL if you used time as the fourth dimension. It just wouldn't be at all interesting. It would consist of a pair of rings, starting at the same place and moving along the 'surface' in opposite directions at speeds such as to avoid having their areas intersect. When they meet up on the other end of the bottle, it is complete. If you were to visualize it with the time dimension removed, it would look like this:

Spoiler (click to show/hide)

The two rings are necessary rather than just the one to give it a proper connection in the time dimension, so if you were to trace a path along the surface the position in time would go on a gradient up before going on a gradient back down again. With one ring, it would be disconnected at the end due to the ring not ending at the same time position it started. Two rings maintain the connected-ness of the 4 dimensional klein bottle.


Well, 2 rings in the conventional sense; it could also be thought of as 1 ring which becomes time-reversed partway through as it continues on the path. And on that note, it may be more accurate if the rings stop/start existing at the moments they come into contact with one another. Thus for a true klein bottle, the ideal candidates would be turning photons into mater-antimatter pairs and somehow manipulating those along their separate paths until they meet up again, annihilating back into photons. Though doing so with the prescribed ring shape would be exceedingly difficult.