Is it possible for the phase of electric charge to change over large general relativistic distances? Jackson provides examples of how magnetic charge and electric charge form together to create complex charge,
\begin{align}
\rho = \rho_e+i\rho_m
\end{align}
which gives rise to the complex faraday field
\begin{align}
\boldsymbol{F}=\boldsymbol{E}+i\boldsymbol{B}
\end{align}
I assume magnetic charge has not been observed on a local scale, however is it possible to bend space such that two charges are observed to have different phases over vast cosmic distances. For example
\begin{align}
\rho = \rho_e e^{i r/\lambda}
\end{align}
 A: If every electromagnetic charge has the same ratio of magnetic and electric charge then you can rotate that complex charge $\rho=\rho_e+i\rho_m$ (and a duality rotation for the fields) to get a purely real (electric) charge with the normal maxwell equations.
In quantum mechanics as a gauge theory, you set up a gauge field to change a global phase change (of the complex quantum phase) to a local gauge.  It's never been clear to me why if all quantum systems have a global invariance under global complex quantum phase rotations that only the electrically charged ones get to turn that into a local symmetry.
But, as a pure research speculation, if the phase in question is the electric-versus-magnetic duality only electromagnetically charged objects have that, so maybe that can be what we gauge into a local symmetry.
If that's the case, then we can now have any phase we want anywhere, with a different choice of gauge, so it's not observable.  But at least it could explain why it is only charged things that have this electromagnetic gauge field.
To summarize the speculative part.  Maybe the existence of complex charge, but the inability to see a phase difference between different points is exactly why there is an electromagnetic interaction.
