Greg Egan on Nostr: When we’re dealing with quantum spin, everything can be complex-valued, and it ...
When we’re dealing with quantum spin, everything can be complex-valued, and it turns out to be helpful to form two new subspaces, spanned by vectors:
A_j=(L_j + i K_j)/2
B_j=(L_j – i K_j)/2
where L_j is a rotation around the j-axis, K_j is a boost in the j-direction, and i=√-1. Mathematically, these A and B parts of the transform behave like two independent ordinary rotations.
If a fermion’s spin changes in a manner that depends *solely* on the A part or the B part, then the particle has a left- or right-handed chirality.
This “handedness” doesn’t depend on the state of motion of the observer!
And this is why statements like “all neutrinos are left-handed” can actually make sense.
A_j=(L_j + i K_j)/2
B_j=(L_j – i K_j)/2
where L_j is a rotation around the j-axis, K_j is a boost in the j-direction, and i=√-1. Mathematically, these A and B parts of the transform behave like two independent ordinary rotations.
If a fermion’s spin changes in a manner that depends *solely* on the A part or the B part, then the particle has a left- or right-handed chirality.
This “handedness” doesn’t depend on the state of motion of the observer!
And this is why statements like “all neutrinos are left-handed” can actually make sense.