JMP  Vol.10 No.10 , September 2019
Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device
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.

Cite this paper
Westlund, P. and Wennerstrôm, H. (2019) Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device. Journal of Modern Physics, 10, 1247-1254. doi: 10.4236/jmp.2019.1010083.
References
[1]   Bell, J.S. (1966) Reviews of Modern Physics, 38, 447-452.

[2]   Bohm, D. and Aharonov, Y. (1957) Physical Review, 108, 1070.
https://doi.org/10.1103/PhysRev.108.1070

[3]   Wennerstrom, H. and Westlund, P.-O. (2017) Entropy, 19, 186.
https://doi.org/10.3390/e19050186

[4]   Gerlach, W. and Stern, O. (1922) Zeitschrift fr Physik, 9, 349-352.
https://doi.org/10.1007/BF01326983

[5]   Einstein, A. and Ehrenfest, P. (1922) Zeitschrift fr Physik, 11, 31-34.
https://doi.org/10.1007/BF01328398

[6]   Schlosshauer, M., Ed. (2011) Elegance and Enigma. Springer Heidelberg, Dordrecht, London, New York.

[7]   Bohm, D. (1952) Physical Review, 85, 180.
https://doi.org/10.1103/PhysRev.85.180

[8]   Bohm, D. (1951) Quantum Theory. Dover Publications, New York, 326.

[9]   Scully, M.O., Shea, R. and McCullen, J. (1978) Physics Reports, 43, 485-498.
https://doi.org/10.1016/0370-1573(78)90210-7

[10]   Scully, M.O., Lamb Jr., W.E. and Barut, A. (1987) Foundations of Physics, 17, 575-583.
https://doi.org/10.1007/BF01882788

[11]   Wennerstrom, H. and Westlund, P.-O. (2012) Physical Chemistry Chemical Physics, 14, 1677-1684.
https://doi.org/10.1039/C2CP22173J

[12]   Wennerstromm H. and Westlund, P.-O. (2013) Physics Essays, 26, 174-180.
https://doi.org/10.4006/0836-1398-26.2.174

[13]   Utz, M., Levitt, M.H., Cooper, N. and Ulbricht, H. (2015) Physical Chemistry Chemical Physics, 17, 3867-3872.
https://doi.org/10.1039/C4CP05606J

[14]   Gomis, P. and Perez, A. (2016) Physical Review A, 94, Article ID: 012103.
https://doi.org/10.1103/PhysRevA.94.012103

 
 
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