Classical Electromagnetism
In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that the forces between two particles are equal and opposite. Electromagnetic forces violate this law. Under some circumstances one moving charged particle can exert a force on another without any return force. Moreover, Maxwell's equations, the foundation of classical electrodynamics, are Lorentz-invariant. However, momentum is still conserved.
Read more about this topic: Kinetic Momentum
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“Several classical sayings that one likes to repeat had quite a different meaning from the ones later times attributed to them.”
—Johann Wolfgang Von Goethe (1749–1832)