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There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges.

Can the same be done in an analagous way to ensure Newton's third law is also true?

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Well, Newton's third law is just conservation of momentum...

$$F_1 = -F_2 \Rightarrow \frac{dp_1}{dt} + \frac{dp_2}{dt} = 0$$

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    $\begingroup$ The point is that Newton's third law fails for point charges in motion with a magnetic interaction. $\endgroup$ – Ron Maimon Oct 25 '11 at 23:21
  • $\begingroup$ But conservation of momentum doesn't in general (I can't think about an example of failure now) isn't it? $\endgroup$ – stringparser Oct 25 '11 at 23:32
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    $\begingroup$ Conservation of momentum works, Newton's third law fails, because there is field momentum. This can lead to paradoxical forces even when the field is not radiating. $\endgroup$ – Ron Maimon Oct 25 '11 at 23:38

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