Relativistic Mechanics Theory for Electrons that Exhibits Spin, Zitterbewegung, Superposition and Produces Diracs Wave Equation

A neo-classical relativistic mechanics model is presented where the spin of an electron is a natural part of its space-time path. The fourth-order equation of motion corresponds to the same Lagrangian function in proper time as in special relativity except for an additional spin energy term. The total motion can be decomposed into a sum of a local circular motion giving the spin and a global motion of the spin center, each being governed by a second-order differential equation. The local spin motion corresponds to Schrodingers zitterbewegung and is a perpetual motion; it produces magnetic and electric dipoles through the Lorentz force on the electrons point charge. The global motion is sub-luminal and described by Newtons second law in proper time, the time for a clock fixed at the spin center, where the inertia to acceleration resides. The total motion occurs at the speed of light c, consistent with the eigenvalues of Diracs velocity operators having magnitude c. A spin tensor is introduced that is the angular momentum of the electrons total motion about its spin center. The fundamental equations of motion expressed using this tensor are identical to those of the Barut-Zanghi theory; they can be expressed in an equivalent form using the same operators as in Diracs theory for the electron but applied to a state function of proper time satisfying a Dirac-Schrodinger spinor equation. This state function produces a neo-classical wave function that satisfies Diracs relativistic wave equation for the free electron when the Lorentz transformation is used to express proper time in terms of an observers space-time coordinates. In summary, the theory provides a hidden-variable model for spin that leads to Diracs relativistic wave equation and explains the electrons moment coupling to an electro-magnetic field, albeit with a magnetic moment that is one half of that in Diracs theory.