So the total angular momentum operator J commutes with any scalar operator S. The argument for this is that J is the generator of 'turntable rotations' (by this I mean we rotate the whole object about an axis, along with its orientation) and the expectation value of any scalar operator has to be invariant under such a rotation. This tells us that S commutes with the rotation operator and thus its generator J. My question is why doesn't a similar argument hold for the orbital angular momentum operator L? The difference is that L generates rotations that rotate only the object but not its orientation around an axis. However surely the expectation value of a scalar operator should still be invariant under this type of rotation, meaning L and S commute. However this is not the case, because I know that any component of L does not commute with J2.