  In this work, the action of the relativistic electron is derived from the
hydrodynamic formulation of the Dirac equation. In particular, in the
hydrodynamic scenario, the four-velocity of the electron is regarded as an
Eulerian field and the electron spin interacts with the corresponding vorticity
field. In the second part of the work, it is shown how the second order Dirac
equation can be derived from a principle of Minimum Fisher Information.
