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Joel Rauber stated:
One interesting limitation that doesn't resort to special relativity or
questions of propagation times of forces is the electro-magnetic force. In
particular the magnetic force of one moving on another moving charge doesn't
obey Newton's 3rd law.
Actually this example IS relativistic. The classical nonrelativistic limit of
electromagnetism is electrostatics with no magnetic field or forces. The
"the magnetic force of one moving charge on another moving charge" is a
(directional non-central) force of the order of v_1 * v_2 / c^2 of the
electrostatic force between them. In the nonrelativistic limit this
contribution is dropped as c --> infinity. (Of course, I'm ignoring the
quantum effects here which allow charged elementary particles to possess
intrinsic magnetic dipole moments whose magnetic fields persist when the
particles are at rest. But in this case these static magnetic dipole field
interactions DO obey N3 in the nonrelativistic limit--just like the electro-
static forces obey N3 in this limit.) :)

David Bowman
Georgetown College