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CellBioGuy comments on Rebutting radical scientific skepticism - Less Wrong
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To a point, classical electromagnetism. You can treat the B field as the difference due to special relativity between the E field of a stationary arrangement of particles and the E field of that arrangement in motion. Also when you change the reference frame you view an arrangement of moving charges in, you see the force they feel as having come from different combinations of electric and magnetic fields but always adding up to the same thing.
http://en.wikipedia.org/wiki/Relativistic_electromagnetism
http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity
That was Einstein's argument: Maxwell's equations are not compatible with Galilean relativity. But we observe Maxwell's laws to be true in all seasons, so some relativity must apply.