Abstract
We analyze the spin coincidence experiment considered by Bell in the derivation of Bells theorem. We solve the equation of motion for the spin system with a spin Hamiltonian, Hz, where the magnetic field is only in the z-direction. For the specific case of the coincidence experiment where the two magnets have the same orientation the Hamiltonian Hz commutes with the total spin Iz, which thus emerges as a constant of the motion. Bells argument is then that an observation of spin up at one magnet A necessarily implies spin down at the other B. For an isolated spin system A-B with classical translational degrees of freedom and an initial spin singlet state there is no force on the spin particles A and B. The spins are fully entangled but none of the spin particles A or B are deflected by the Stern-Gerlach magnets. This result is not compatible with Bells assumption that spin 1/2 particles are deected in a Stern-Gerlach device. Assuming a more realistic Hamiltonian Hz + Hx including a gradient in x direction the total Iz is not conserved and fully entanglement is not expected in this case. The conclusion is that Bells theorem is not applicable to spin coincidence measurement originally discussed by Bell.
Highlights
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We have analyzed the arguments leading to the formulation of Bells theorem for spin coincidence measurements
Summary
Maxwells laws that there is a matching gradient in some other direction; in the SG case the x-direction Using such a setup Stern and Gerlach observed [4] that silver atoms, later realized to have spin. Wennerstrom particles once they had left the source This observation, later coined Bells theorem, has given rise to a large discussion concerning nonlocality effects in quantum systems. Following Bohms reasoning Bell concluded that by necessity IzB = −1/2 for this particle and it should be observed at −∆z in the second magnet. It follows that the total spin in the z-direction Iz = IzA + IzB commutes with the Hamiltonian and Iz is a constant of the motion. We note that the two basic arguments have different origins; one empirical and one theoretical
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