Abstract
When Humpty-Dumpty had his great fall nobody could put him together again. A vastly more moderate challenge is to reunite the two partial beams of a Stern-Gerlach apparatus with such precision that the original spin state is recovered. Nevertheless, as we demonstrate, a substantial loss of spin coherence always occurs, unless the experimenter is able to control the magnetic field's inhomogeneity with an accuracy of at least one part in 105.
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References
D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, 1951).
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Other models of SGAs have been considered by M. O. Scully, R. Shea, and J. M. McCullen,Phys. Rep. 43, 487 (1978), as well as by M. O. Scully, W. E. Lamb, and A. Barut,Found. Phys. 17, 575 (1987).
The uncertainty δΦ of the accumulated Larmor precession angle must also be kept very small. This is more easily achieved for magnetic field configurations different from the one in Fig. 1. For details consult J. Schwinger, M. O. Scully, and B.-G. Englert, “Is Spin Coherence like Humpty-Dumpty? II. General Theory,” to appear in the Otto Stern Centennial Issue ofZ. Phys. D (1988).
Incidentally, in the original experiment by W. Gerlach and O. Stern,Z. Phys. 8, 110 (1922), and9, 349 (1922), the deflection of the two partial beams showed a strong asymmetry.
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Englert, BG., Schwinger, J. & Scully, M.O. Is spin coherence like Humpty-Dumpty? I. Simplified treatment. Found Phys 18, 1045–1056 (1988). https://doi.org/10.1007/BF01909939
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DOI: https://doi.org/10.1007/BF01909939