#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).
But there is no "the" inhomogeneous solution, and indeed there cannot be. That is the whole point. One can only distinguish between inhomogeneous solutions by the imposition of boundary conditions. This is a fundamental mathematical inevitability.
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There is privileged inhomogeneous solution: the one that describes the sources that are actually there. And those sources are perfectly local.
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What physical law are you invoking here? Certainly not the laws of electricity and magnetism, for these are fully expressed by Maxwell's equations -- which, as a matter of mathematical fact, cannot prefer any inhomogeneous solution without the imposition of boundary conditions.
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