#Physicsfactlet (88)
A charge emits radiation when accelerated, so we can apparently tell if the charge is in free fall or not, violating the equivalence principle.
Solution: the charge will still be at thermal equilibrium with the vacuum, which will look hotter (Unruh effect).
My point is that you are tacitly augmenting the laws of Nature here. Local physics gives differential equations. By privileging a particular solution to those differential equations, you are going beyond local physics. And you must, too, to speak about radiation intelligibly.
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Yes, I am assuming a "retarded Green's function" solution. But the "zero at infinity" boundary is only relevant after an infinite amount of time, i.e. is not physically relevant.
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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.
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