These three paradoxes (Vaidman's paradox, Mansuripur's paradox, the Aharonov-Casher effect) and be resolved without assuming hidden momentum exists in charge-magnet systems or an induced electric dipole resides on a moving magnet.

Redfern, F. Canadian Journal of Physics, 2019, 97(2): 125-132

There is no charge separation on a moving magnetic dipole. The apparent presence of charge is due to the relativity of simultaneity. An electric dipole does not appear on a moving magnetic dipole and a magnetic dipole does not appear on a moving electric dipole. I argue that the magnetization-polarization tensor is not a genuine four-tensor and is not a valid way to find transformed fields. Only the Lorentz transformation of fields directly can give the correct transformed fields.

Correction: The magnetization-polarization tensor is a relativistic four-tensor if you transform the space and time coordinates the elements of the tensor depend upon at the same time you transform the tensor.

Redfern, F. Eur. Phys. J. D (2017) 71: 325.

Magnetic coils in electric fields contain no hidden momentum.

Redfern, F. Eur. Phys. J. D (2017) 71: 163.

In 1967 Shockley and James addressed the situation of a magnet in an electric field. The magnet is at rest and contains electromagnetic momentum, but there was no obvious mechanical momentum to balance this for momentum conservation. They concluded that some sort of mechanical momentum, which they called “hidden momentum”, was contained in the magnet and ascribed this momentum to relativistic effects, a contention that was apparently confirmed by Coleman and an Vleck. Since then, a magnetic dipole in an electric field has been considered to have this new form of momentum, but this view ignores the electromagnetic forces that arise when an electric field is applied to a magnet or a magnet is formed in an electric field. The electromagnetic forces result in the magnet gaining electro- magnetic momentum and an equal and opposite amount of mechanical momentum so that it is moving in its original rest frame. This moving reference frame is erroneously taken to be the rest frame in studies that purport to show hidden momentum. Here I examine the analysis of Shockley and James and of Coleman and Van Vleck and consider a model of a magnetic dipole formed in a uniform electric field. These calculations show no hidden momentum.

Redfern, F. Phys.Scr, (2016) 91: 045501.

Updated discussion of hidden momentum, the Mansuripur paradox, moving dipoles, and electromagnetic momentum in a charge-dipole system. Also, analysis of the paradox involving a magnetic dipole moving in an electric field and the Aharonov-Casher effect.

A discussion of this paradox and momentum flow

I show that the usual harmonic plane-wave equation can be derived from kinematic principles only; that is, requiring the wave to propagate without changing shape in a non-dissipative medium. Not only can the usual second order wave equation be acquired this way, but also an equation that is quadratic and of first order. These equations have a common set of solutions. The second-order equation corresponds to the restoring forces of a physical medium whereas the first-order quadratic equation corresponds to energy in a conservative medium. Properties of electromagnetic waves, including energy conservation (Poynting's theorem) and radiation pressure can be obtained from this kinematic approach.