I suppose my TL;DR was misleading. The purported issue arises only for classical spatial rotations, since classical orientation is a vector. The examples given by @Delta Kilo and @strangerep are spinor rotations, which apply only to quantum states. The example given by @A.T. restates the issue...
Hi, Andrew! Thanks for for insightful answer.
As far as I understand, the belt trick is a pedagogic device for developing intuition. The belt trick would represent classical rotations if and only if classical objects had unobservable strings thetering them to their surroundings. In this case, a...
I will ask a mathematical and a physical-cum-philosophical question pertaining to the fact that SO(3) is not simply connected.
Context
Classical rotations in three spatial dimensions are represented by the group SO(3), whose elements represent 3D rotations. Having said that, note that classical...