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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.

see Tipler 3rd edition page 813.

I won't say more as I have no more time, but there is a fairly good
explanation and diagrams on this point in the above text

Joel Rauber