  It is shown that every regular electromagnetic field in vacuum identically
satisfy Maxwell equations in a new manifold where the roles of space and time
have been exchanged. The new metric is Lorentzian, depends on the particular
solution and forces the flow of time to tilt somehow in the direction of the
field lines. We give a detailed description of the transformation and discuss
several of its properties, both in the algebraic and differential settings.
Examples are given where the new metrics are explicitly computed and carefully
analyzed. We conclude with possible applications of the transformation as well
as future perspectives.
