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What Griffiths meant by "the potential is not unique"?
The potential is not unique—any constant can be added to $V$ with impunity, since this will not affect its gradient.
The vector potential is not unique—the gradient of any scalar function can be ...
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Should the potential of a point charge be taken from the Hubble boundary instead?
The expansion of space yields a limit to our observable universe, somewhere roughly 13.8 billion light years away. Past this point, galaxies and any other particles are expanding away from us faster ...