On Stern‐Gerlach coincidence measurements and their application to Bell's theorem

We analyze a coincidence Stern‐Gerlach measurement often discussed in connection with the derivation and illustration of Bell's theorem. The treatment is based on our recent analysis of the original Stern‐Gerlach experiment [H. Wennerström and P.-O. Westlund, Phys. Chem. Chem. Phys. 14, 1677 (2012)], where it is concluded that it is necessary to include a spin relaxation process to account for the experimental observations. We consider two limiting cases of a coincidence measurement using both an analytical and a numerical description. In one limit, relaxation effects are neglected. In this case, the correlation between the two spins present in the initial state is conserved during the passage through the magnets. However, at exit the z-coordinate along the magnetic field gradient is randomly distributed between the two extreme values. In the other limit, T 2 relaxation is assumed to be fast relative to the time of flight through the magnet. In this case, the z-coordinate takes one of two possible values as observed in the original Stern‐Gerlach experiment. Due to the presence of a relaxation process involving transfer of angular momentum between particle and magnet, the initially entangled spin state changes character leading to a loss of correlation between the two spins. In the original derivations of Bell's theorem based on a coincidence Stern‐Gerlach setup, one assumes both a perfect correlation between the spins and only two possible values for the z-coordinate on exit. According to the present calculations, one can satisfy either of these conditions but not both simultaneously.