Wave particle duality: Merging de Broglie's ''double solution'' waves into (3+0)D electromagnetic solitons

Abstract

The well known light filaments, are obtained in various media whose index of refraction increases before a saturation with the electric field; adding a small perturbation which increases the index with the magnetic field, and neglecting the absorption, a filament curves and closes into a torus. This transformation of a (2+1)D soliton into a (3+0)D soliton shows the existence of those solitons, while a complete study, with a larger magnetic effect, would require numerical computations, the starting point being, possibly, the perturbed, curved filament. The flux of energy in the regular filaments is nearly a ''critical flux'', depending slightly on the external fields, so that the energy of the (3+0)D soliton is quantified, but may be slightly changed by external interactions. The creation of electron positron pairs in the vacuum by purely electromagnetic fields shows a nonlinearity of vacuum at high energies; supposing this nonlinearity convenient, elementary particles may be (3+0)D solitons. Set that the nearly linear part of the soliton is the $\Psi$ wave while the remainder, (the torus) is the $u$ wave; if the torus is not absorbed by Young slits, it is guided by the transmitted, interfering remainder of the $\Psi$ wave.