Twistors and electromagnetic knots

Since its discovery in 1931, the Hopf fibration has played an important role in physics in seemingly unrelated situations ranging from qubits to Taub-NUT spaces in general relativity [1]. Recently the structure of this fibration has been considered in relation to solutions of the source-free Maxwell equations and led to linked and knotted forms of electromagnetic fields [2, 3]. In twistor theory, it was the structure of the Hopf fibration that gave a twistor its name [4]. Here we present a deeper correspondence between a (non-null) twistor and the knotted electromagnetic fields, in which the Poynting vector plays a central role.