We argue that the Lorentz law must be abandoned in favor of a more general expression of the electromagnetic force density, such as the one discovered by A. Einstein and J. Laub in 1908.Wenerever relativity is invoked I know they are adding another axis of symmetry. Going straight to the chase. Phase imbalance changing in a circular axis induce a standing wave with two axis, down the radius and perpendicular to the center of rotation. I am sure these authors discovered the spiral action of small and large bubbles, making a third axis of symmetry, the spiral; otherwise known as the spin effect in the standard model. The spiral will have an independent axis, composed of the rate of spiral and the tilt of the spiral. Both the these determined by the mixing angle, (the quark thing), I am sure.
Go to the ice cream shop, by the swirly cone, vanilla is my favorite. The ice cream is circular, gets steeper up from the center, and swirls. That is three axii. Being filled toward the center is what we call charge, going up perpendicular from the center is what we call magnetism, and the swirl is what small and large bubbles do when packing. We do not generally bother with the swirl in classical approximations, but it will be in the equations of wave motion whenever the wave is circular about an axis.
There, in one paragraph, the complete course in electro magnetism.
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