You are assuming, then, that the field of your point source is very nearly zero very far away, at very early times. But this is obviously a non-local condition. Whether it is satisfied cannot be determined by inspecting only the immediate (spacetime) vicinity of your source.
So no theory of electromagnetic radiation can ever be purely local. In a purely local theory, no constraints are possible on the radiative content of the theory; the radiation field can be whatever you want it to be -- like the gradient of the Newtonian gravitational potential.
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Ok, I start wondering if we are talking different languages. What do you mean EXACTLY by non-local? Because to me it means essentially "spooky action at distance", i.e. the ability to influence the system from far away without having to wait for the wave to propagate 'till there.
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I certainly do NOT mean non-local in the quantum-mechanical sense, nor even in the relativistic sense, but rather in the classical mathematical sense -- "local" means "completely determined by information discernible by inspecting the immediate vicinity of the point in question."
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