  We describe the interplay between electric-magnetic duality and higher
symmetry in Maxwell theory. When the fine-structure constant is rational, the
theory admits non-invertible symmetries which can be realized as composites of
electric-magnetic duality and gauging a discrete subgroup of the one-form
global symmetry. These non-invertible symmetries are approximate quantum
invariances of the natural world which emerge in the infrared below the mass
scale of charged particles. We construct these symmetries explicitly as
topological defects and illustrate their action on local and extended
operators. We also describe their action on boundary conditions and illustrate
some consequences of the symmetry for Hilbert spaces of the theory defined in
finite volume.
