The Aharonov-Casher phase is the electromagnetic dual of the Aharonov-Bohm phase. It arises when a neutral particle with a magnetic moment encircles, for example, a line charge, or moves on a closed circle around a point charge. The simple plausibility argument for the effect to occur uses the relativistic transformation of the electric field generated by the line charge (or point charge) into the rest frame of the moving particle, in which the neutral particle 'sees' a magnetic field $$ {\mathbf B} = \frac{1}{c^2}{\mathbf v}\times{\mathbf E}. $$ This magnetic field couples to the magnetic moment of the moving particle and leads to the Aharonov-Casher phase. Details are nicely worked out in an answer to the SE-question here. The existence of the phase has been experimentally measured with neutron interferometry in this reference.
A similar plausibility argument is used, when a charged particle with a magnetic moment moves, in atomic physics, through the electric field of the atomic nucleus, or, in solid state physics, through that of the crystal lattice. This is the well-known spin-orbit coupling, which can, in suitable solid-state interferometers, also lead to a phase-difference in interference experiments.
My question is: are there fundamental arguments for or against the notion that spin-orbit interaction effects are essentially a manifestation of the Aharonov-Casher effect? Or are they completely different things?
From my perspective, an essential difference is the absence of the charge of the moving particle in Aharonov-Casher physics, and its presence in spin-orbit physics. I have seen this question and its answer on SE about the Aharonov-Casher effect for charged particles. However, there is no mention of spin-orbit interaction, and the answer was very technical. There are also numerous questions and answers about spin-orbit coupling, which did not clarify the question. The topic may be controversial, but all the different opinions would be highly appreciated.
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