Double-slit and electromagnetic models to complete quantum mechanics

We analyze a realistic microscopic model for electronic scattering with the neutral differential delay equations of motion of point charges of the Wheeler-Feynman electrodynamics. We propose a microscopic model according to the electrodynamics of point charges, complex enough to describe the essential physics. Our microscopic model reaches a simple qualitative agreement with the experimental results as regards interference in double-slit scattering and in electronic scattering by crystals. We discuss our model in the light of existing experimental results, including a qualitative disagreement found for the double-slit experiment. We discuss an approximation for the complex neutral differential delay equations of our model using piecewise-defined (discontinuous) velocities for all charges and piecewise-constant-velocities for the scattered charge. Our approximation predicts the De Broglie wavelength as an inverse function of the incoming velocity and in the correct order of magnitude. We explain the scattering by crystals in the light of the same simplified modeling with Einstein-local interactions. We include a discussion of the qualitative properties of the neutral-delay-equations of electrodynamics to stimulate future experimental tests on the possibility to complete quantum mechanics with electromagnetic models.Comment: 4 figures, the same post-publication typos over the published version of Journal of Computational and Theoretical Nanoscience, only that these correction are not marked in red as in V7, this one is for a recollectio

Variational electrodynamics of Atoms

We generalize Wheeler-Feynman electrodynamics by the minimization of a finite action functional defined for variational trajectories that are required to merge continuously into given past and future boundary segments. We prove that the boundary-value problem is well-posed for two classes of boundary data and show that the well-posed solution in general has velocity discontinuities, henceforth broken extrema. Along regular segments, broken extrema satisfy the Euler-Lagrange neutral differential delay equations with state-dependent deviating arguments. At points where velocities are discontinuous, broken extrema satisfy the Weierstrass-Erdmann conditions that energies and momenta are continuous. The electromagnetic fields of the variational trajectories are derived quantities that can be extended only to a bounded region B of space-time. For extrema with a finite number of velocity discontinuities, extended fields are defined for all point in B with the exception of sets of zero measure. The extended fields satisfy the integral laws of classical electrodynamics for most surfaces and curves inside B. As an application, we study globally bounded trajectories with vanishing far-fields for the hydrogenoid atomic models of hydrogen, muonium and positronium. Our model uses solutions of the neutral differential delay equations along regular segments and a variational approximation for the collisional segments. Each hydrogenoid model predicts a discrete set of finitely measured neighbourhoods of orbits with vanishing far-fields at the correct atomic magnitude and in quantitative and qualitative agreement with experiment and quantum mechanics, i.e., the spacings between consecutive discrete angular momenta agree with Planck's constant within thirty-percent, while orbital frequencies agree with a corresponding spectroscopic line within a few percent.Comment: Full re-write using same equations and back to original title (version 18 compiled with the wrong figure 5). A few commas introduced and all paragraphs broken into smaller ones whenever possibl