Two-vortex structure of electron, nonlocality and Dirac equation

Abstract

The dimensionless electromagnetic coupling constant $\alpha =e^2/\hslash c$ may have three interpretations: as the well known ratio between the electron charge radius $e^2/m{c}^2$ and the Compton wavelength of electron ${\lambda }_c=\hslash /mc$, as a ratio of two angular momenta since Planck constant has the dimension of angular momentum, and two flux quanta $e$ and $hc/e$. The anomalous part of the electron magnetic moment together with the unified picture of the three interpretations of $\alpha$ is suggested to have deep physical significance. The electric charge is proposed to be a new quantum of flux such that a two-vortex structure of electron is envisaged. In analogy with quantum conditions we postulate sub-quantum conditions applicable in a region of the order of ${\lambda }_c$ replacing $\hslash$ by a universal constant $f=e^2/2\pi c$ and apply it to Dirac equation in internal space that gives rise to the anomalous magnetic moment of electron. Dirac spinor and 2-spinor representation for vortex structure of electron in the single particle Dirac framework are discussed. The role of sub-quantum rules and the internal variables for developing the present ideas is also debated. A critical discussion on the past attempts to give fundamental importance to magnetism and flux quantum is given to delineate the new ideas in the present work.

12 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1104.3506

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