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2

Jinawee and dmckee have already given answers describing the bounds from the spherical capacitor technique. A different, and more model-dependent, approach is to build and test empirically a theory in which the photon has nonzero mass. There are some theoretical difficulties involved, e.g., local gauge invariance is broken, and it's not trivial to show that ...

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Quoting from my copy of the 2nd edition of Jackson's book on Classical Electrodynamics, section 1.2: Assume that the force varies as $1/r^{2+\epsilon}$ and quote a value or limit for $\epsilon$. [...] The original experiment with concentric spheres by Cavendish in 1772 gave an upper limit on $\epsilon$ of $\left| \epsilon \right| \le 0.02$. followed a ...

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I know that the inverse square law has been verified at least 1 part in $10^{16}$. Feynman Lectures said something about that.

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On the upper end, Coulomb's law has not been observed to break for any large collection of charge that can be put together. In principle, if you tried to put more and more charge together then there would be a lot of energy stored in the field, and if the mass equivalent of this energy density got too high, there would be general relativistic effects to ...

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Regarding your first question. When you are asking it, you should understand that it has an answer only in some model -- there is no universal relation that holds in every imaginable model of electromagnetic interactions. I personally do not know a model that would break the inverse square law in the way you want. However, if you accept that electromagnetic ...

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