In 1975, two experimental groups have independently observed the \(4\pi \)-symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical \(4\pi \)-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron’s phase change, when passing through the magnetic field, is due to a longitudinal Stern–Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is \(2\pi \) rotated, but strongly indicate that the latter, like any other elementary “particle,” would be a genuinely non-spatial entity.
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I would like to thank Gérard Wanders, professor emeritus of the University of Lausanne, for having suggested me, when I was a student, to explore the physics of neutron interferometry experiments. Many of the calculations presented in the first part of this article, describing the passage of a neutron through a LLL crystal, are drawn from some of his handwritten notes. No need to say, possible errors are solely my responsibility.
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Sassoli de Bianchi, M. Theoretical and Conceptual Analysis of the Celebrated 4π-Symmetry Neutron Interferometry Experiments. Found Sci 22, 627–653 (2017). https://doi.org/10.1007/s10699-016-9491-x
- Neutron interferometry
- Larmor precession
- Spin rotation
- Stern-Gerlach effect