Hans Bethe on spin implied by angular momentum commutator Here's a cool thing about spin and the Dirac equation I hadn't seen until I read Hans Bethe's book "Intermediate Quantum Mechanics". Commuting the Hamiltonian of the Dirac equation with the orbital angular momentum of a particle indicates that total angular momentum isn't conserved[2]. If you're new to, or not in quantum mechanics, the commutator determines how two quantities behave in a multiplication when the order of the multiply is reversed. In multiplication with real numbers, A times B is the same as B times A, (the commutative property). Quantum mechanics uses matrices and in matrix multiplication, A times B is not always the same as B times A. The commutator, [A,B] just subtracts B times A from A times B. If the two quantities commute the result will be zero. One last note for the non-QM inclined. In quantum mechanics, if you take the commutator of an operator matrix with somet...