Knotted spacetime electromagnetic vortex unlinking and unknotting with vector and scalar reconnections and field twist compensation

Abstract

Optical vortex knots have been realized in monochromatic laser beams, but monochromatic fields are stationary and their topology is frozen. Here we show that knotted spatiotemporal vortices, whose phase singularities form closed loops in spacetime, undergo topology changing reconnections with free space propagation. When null lines of different vector components unlink, the electric spin, magnetic spin, linear momentum, and electromagnetic helicity densities, each built from a specific pair of field components, twist to exactly compensate the change in linking number. This compensation is enforced by the argument principle where the total for each component pair, combining mutual phase twist, geometric linking, and open-line threading, vanishes identically and remains exactly zero through all reconnection events.