system
Given the following post, respond as if you're commenting on Reddit:
human
Can space-time warp in such a way as to allow me to start a journey and then return as my mirror image?
gpt
Nice question. You're asking whether spacetime can be non-orientable.

In general relativity itself, it can. No obstruction to it.

However the standard model is not parity-symmetric; in particular the weak force identifies a preferential choice of orientation on spacetime. In a non-orientable spacetime this choice cannot be made consistently and continuously: following the same path that turned you into your mirror image and taking track of how the preferential orientation identified by the weak force is along the path we would reach a contradiction as we'd find the orientation at our starting point is equal to its opposite.

However this can be salvaged if we assume the standard model is just an effective field theory (= an approximate description) of a more fundamental theory manifesting itself at very high energy which is actually non-chiral (left-right symmetric) - examples would be M-theory or type IIA superstring theory. The asymmetry would actually be created by a spontaneous symmetry breaking out of which the standard model arises.

In this case, what would happen is that the preferential orientation of the weak force would be allowed to reverse abruptly at a very energetic boundary in space called a domain wall, a 2-dimensional surface in space. Such an object would be composed by a thin layer of extremely energetic field configuration interpolating between the two different orientations of the standard model.

Following the path you did before the reversal of orientation due to the non-orientability of space would be cancelled by the fact you need to cross the domain wall, and you'd end up with the original orientation for the weak force when getting back home. You itself wouldn't really be able to become your mirror image because, being your body essentially a structure built in the context of a given "version" of the standard model, it has no hope of surviving crossing the domain wall towards another version.