Static Schwinger-level threshold electric field nonlinearities and their significance to photons and chaos.

In this work we postulate that Schwinger's threshold for a dynamic electric field intensity to induce spatial nonlinearity is a special case and, more generally, it is the threshold field for both static and dynamic electric fields. Fields of this magnitude induce negative energy charges to adapt positive energy attributes; within an atom they also support inter-state energy transfers and intra-state chaotic mixing of time-varying fields. Nonlinearity-induced chaos forms the basis for the probabilistic nature of photon creation. Answers to physical problems at atomic and lower scales continuously evolve because chaotic-like electron movements change their configurations on a time scale of 10 zs. Within atoms, frequency mixing that creates an optical frequency field occurs in the nonlinear region surrounding the nucleus. On a probabilistic basis a ring of vacuum charge can be induced that forms into an equivalent waveguide that confines the energy as it travels permanently away from the atom. The propagating relativistically augmented fields losslessly induce charges that bind and protect the energy carrying fields. The photon charge-field ensemble, which we show is localizable, is thermodynamically closed and possesses all first-order photon properties including zero rest mass and permanent stability. For near neighbor photons traveling at a speed approaching c we find a small, constant, attractive force between photons with circularly antiparallel polarization.