Non-orientable Wormhole - Alice Universe

In theoretical physics, an Alice universe is a hypothetical universe with no global definition of charge. What a Klein bottle is to a closed two-dimensional surface, an Alice universe is to a closed three-dimensional volume. The name is a reference to the character in Lewis Carroll's children's book, Alice Through the Looking-Glass.

An Alice universe can be considered to allow at least two topologically-distinct routes between any two points, and if one connection (or "handle") is declared to be a "conventional" spatial connection, at least one other must be deemed to be a non-orientable wormhole connection.

Once these two connections are made, we can no longer define whether a given particle is matter or antimatter. A particle might appear as an electron when viewed along one route, and as a positron when viewed along the other. If we define a reference charge as nominally positive and bring it alongside our "undefined charge" particle, the two particles may attract if brought together along one route, and repel if brought together along another - the Alice universe loses the ability to distinguish between positive and negative charges, except locally.

As with a Möbius strip, once the two distinct connections have been made, we can no longer identify which connection is "normal" and which is "reversed" — the lack of a global definition for charge becomes a feature of the global geometry. This behaviour is analogous to the way that a small piece of a Möbius strip allows a local distinction between two sides of a piece of paper, but the distinction disappears when the strip is considered globally.