#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).
No other consideration can privilege this particular Green function (and the inhomogeneous solutions to which it leads.) Boundary conditions alone can distinguish it. One may argue that certain boundary conditions are physically appropriate. But they're inevitably non-local.
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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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