# Non-Orientable Quantum Surface

1. Aug 11, 2012

### JPBenowitz

I've heard that the universe could not possibly be non-orientable because of P-Violation such that a left-handed neutrino would transform into a right-handed neutrino which do not exist do to the left-right asymmetry of the universe. However this problem is resolvable because charge would also be flipped in a non-orientable universe thus we would be left with a right-handed anti-neutrino. The actual problem arises with the arrow of time. A non-orientable spacetime would be akin to a closed timelike curve and causality loses its meaning.

On the other hand, there is a difference between a spinor and a vector when defining left and right handedness. Spinors require a 720 degree rotation to return to their original state not a 360 degree rotation required by a vector. So in the sense of preserving an arrow of time when an observer traverses back to the start they did not arrive back at the same physical system. So why is it that a non-orientable universe is impossible?

2. Aug 12, 2012

### Bill_K

Common misconception. Spinors change sign under a 360-degree rotation. But spinors are double-valued. So under the rotation all spinors simply change their sign, and the physical state is unchanged.

3. Aug 12, 2012

### JPBenowitz

Right, but we can treat a mirror-image as a 180 degree rotation such that the mirror image of a vector and a spinor are not the same. If spin was a vector then on a non-orientable surface both the direction of spin and momentum would be flipped and a particle would retain its handedness. The problem is really with no global definition of handedness or charge on a non-orientable surface. At one point in time as the system evolves you can distinguish charge and handedness, there is information present but then after a sufficient enough time you no longer would be able to distinguish them. Where did the information go? We know information is conserved at all times just like energy is conserved at all times.

Analogously, a point on this non-orientable surface cannot possibly be a single point in time they must be separated by something that behaves like a delayed choice quantum eraser where in this sense "which-handedness" information is erased and we are left with a probability distribution of possible states. Information is conserved but the entropy of the system increases and thus would preserve an arrow of time.