Non-orientable wormhole

In wormhole theory, a non-orientable wormhole is a wormhole connection that appears to reverse the chirality of anything passed through it. It is related to the "twisted" connections normally used to construct a Möbius strip or Klein bottle.

In topology, this sort of connection is referred to as an Alice handle.

Theory

"Normal" wormhole connection

Matt Visser has described a way of visualising wormhole geometry:

Although this set of instructions seems straightforward, there are two topologically distinct ways in which the two surfaces can be mapped to one another. If we draw a map of the Earth's surface onto one wormhole mouth, how does this map appear at the second mouth?

For a "conventional" wormhole, the network of points will be seen at the second surface to be inverted, as if one surface was the mirror image of the other—countries will appear back-to-front, as will any text written on the map. This is as it should be, because in a sense, the second mouth is showing us the view of the same map seen "from the other side".