OK FINE, magnetism is explained away by relativity

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Afaik there are configurations of the electric and magnetic field (dependent on the sign of E^2 - B^2, which cannot be transformed into purely electric configurations by a Lorentz transformation.
 
E \cdot B and E^2 - B^2 are both Lorentz-invariants. If B=0 and E \neq 0 in one frame, then E \cdot B = 0 and E^2 - B^2 > 0 in that frame, and hence in all frames.

Also, if E \cdot B \neq 0 or if E \cdot B = 0 and E^2 - B^2 < 0 in one frame, then there does not exist a frame in which B = 0.
 
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No comprende, but thanks for the effort.
 
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