  The dimensionless electromagnetic coupling constant $\alpha=e^2 /\hbar c$ may
have three interpretations: as the well known ratio between the electron charge
radius $e^2/mc^2$ and the Compton wavelength of electron $\lambda_c= \hbar
/mc$, 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 $\hbar$ 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.
