Particles as Maxwellian Solitons

[Anton Vrba]

This talk shows that EM-field waves can travel on closed and curved 3-dimensional paths and proposes EM-potential and EM-flux waves. The new insight developed here could provide a tool box to envision Maxwellian solitons, a possible aid to further the understanding of particles. The talk presents the proof that the simultaneous vector cross product equations { E = u × B; u = (B×E)/∥B∥^2; B= ( E×u)/∥u∥^2} — (1) are a powerful reformulation of the Maxwell equations in vacuum, if u , B and E are functions of time only. The velocity vector u can now describes EM-waves in 1D (radio waves and photons), 2D and 3-dimensions (particles). The fundamental nature of (1) is demonstrated by a purely mathematical derivation for ϵ _0 and μ_0, in terms of e and h. Leveraging (1) to describe flux-waves requires the equivalent expressions for ϵ_f and μ_f,  and after deriving these the Planck energy equivalence E=hf emerges from (1). The solutions to (1) set in flux are easily quantifiable; for the 3D-wave the following are identifiable: up/down, spin on two axes, charge polarity, and path closure 2nπ, with n an integer and OAM for photons.  The proposed description for particles is congruent to the Bohm ˗de Broglie interpretation of quantum mechanics and a nonlocal hidden variable; this is discussed too.

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