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## Main Question or Discussion Point

Here I am considering the one particle free Dirac equation. As is known the spin operator does not commute with the Hamiltonian. However, the solutions to the Dirac equation have a constant spinor term and only an overall phase factor which depends on time. So as the solution evolves in time, surely the spin operator will act on the spinor part the same way at any moment.

How to reconcile this with the fact that the spin operator doesn't commute with the Hamiltonian and it is often said that spin is not conserved for the Dirac particle? I mean the solutions are even named spin up and spin down. I know if p is not zero the solutions aren't eigenvectors of the spin operator, but still the spinor is constant, so why isn't spin constant? In the basis of the spin operator the solution has constant components, except for overall phase.

How to reconcile this with the fact that the spin operator doesn't commute with the Hamiltonian and it is often said that spin is not conserved for the Dirac particle? I mean the solutions are even named spin up and spin down. I know if p is not zero the solutions aren't eigenvectors of the spin operator, but still the spinor is constant, so why isn't spin constant? In the basis of the spin operator the solution has constant components, except for overall phase.