sci.physics.research

I tried this on , but I'm hoping for a clearer answer
here.

Numerous textbooks (including Feynman's Lectures and the Berkeley
Physics series) make statements along the lines of "Maxwell's
equations suffice to determine the electric and magnetic fields,
given the charge and current distributions". (The Berkeley Physics
series adds the qualification "up to the addition of a constant
vector field").

This is patently false. If E and B satisfy Maxwell's equations,
(for given charge and current distributions) then so do E+grad(f)
and B+grad(g), where f and g are arbitrary harmonic functions.

In other words, given the charge and current distributions, the
solutions to Maxwell's equations are not unique, and therefore the
equations alone do not determine the fields. Which leads to my
question: What *does* determine the fields? Does it all come
down to a completely arbitrary initial condition? Or is there
additional property that pins the fields down uniquely? Or....?

--

Steven E. Landsburg
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