Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device

Per-Olof Westlund¹, Håkan Wennerstrôm²

¹Department of Chemistry, Theoretical Chemistry, Umeå University, Umeå, Sweden.
²Department of Physical Chemistry, Lund University, Lund, Sweden.

DOI: 10.4236/jmp.2019.1010083                

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, H_z, 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 H_z commutes with the total spin I_z, 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 H_z + H_x including a gradient in x direction the total I_z 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.

Keywords

Bells Theorem, Disentanglement, Stern-Gerlach Coincident Measurement, Singlet Spin State

Conflicts of Interest

The authors declare no con ict of interest.

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