« on: Yesterday at 19:29:57 »
The particle is measured by applying a magnetic field. The measurement will detect if the spin is up, aligned with the direction of the field or if it is down, aligned opposite of the field direction. Therefore the orientation of the lab frame is not important.It is the orientation of the field that is important. That defines the axis of measurement. It has nothing to do with choice of abstract coordinate system (lab frame).
This is not correct. The particles are no longer entangled. When 2 particles are entangled they have the same wave equation.Good point. The wave functions (at least that concerning their spin) are different now. Other parts (wave function of position say) were never the same, even though they were spin-entangled. You can't say that two entangled particles millions of miles apart are equally likely to be found at a given location.
When one of the particles is measured the wave function collapses and now the particles are no longer described by a single wave equation, now both of the particles are described by different wave equations.