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Consider 2 points (A and B) separated by some large distance and not moving with respect to one another. Suppose one places a charged particle at A, and leaves it there for a sufficient length of time for observers at B to see the field. Once observers at point B are able to measure the field at B from A, they place a charged particle at B. This particle will, of course, accelerate under the influence of the field. Observers at point A have not yet received any information about the charge which was placed at point B, and remove the charge from point A before the field from point B can reach them.

Now, what has happened appears to be in violation of either form (strong or weak) of Newton's third law, and by extension, conservation of momentum. If the charge at A accelerated, then information would be carried from B to A faster than light (which we know is impossible). If the charge at A does not accelerate, momentum in our nonaccelerating reference frame has not been conserved (which we also know is impossible). Even if we speculate that the field from the charge at B carried some momentum away as B accelerated, we run afoul of energy conservation. I am sure there is an explanation, but over the last couple of days of thinking about it, I have yet to come up with one.

Oh, and as for the 'placing' and 'removing' of charges being nonphysical, they could just as easily be dipoles or a particle-antiparticle which we allow to annihilate at the appropriate times. I just kept them as single point charges for simplicity.