If there was a region of space-time shaped like a Mobius Strip

[Edward Solomo]

Would the spin of a particle be measured the same by any set of observers upon that strip?

Would an observer experience a reversal of spin if the particle traveled far enough along the strip?

 

[haael]

Would the spin of a particle be measured the same by any set of observers upon that strip?

Yes, if you correctly defined "the same". Spin is an axial vector. It will change coordinates when you roll upside down.

Would an observer experience a reversal of spin if the particle traveled far enough along the strip?

Yes, spin as an axial vector will change direction when you change the space orientation, which happens on the 3d equivalent of the Moebius strip.

If we lived on a Moebius strip, it would also mean that left-chiral particles can change into right-chiral. If we also assume that the Universe is homogenous, then there should be no assymetry between left-handed and right-handed particles, which is not the case. Thus, we don't live on a Moebius strip under most common assumptions.