Does a Lorentz boost change the "direction" of an electron's spin orientation? For example, if an electron is in a state "spin-up" along x, and this electron is subjected to a large boost along another direction, say z, will the electron's spin remain "spin-up" along x? What if the electron is instead boosted along the direction of its spin? I know that Dirac 4-spinors transform under Lorentz boosts and rotations, for example as shown in Peskin/schroeder, however it is not clear to me how the transformation affects (if at all) the orientation of the electron's spin. Please refer to my recent post a few hours ago: "Spin Direction and 4-spinor Components" for a more detailed and specific version of this question, including some calculations I did on boosting the spinors. Thank you very much for any help on this subject!