O the Identification and Interpretation of Variables in the Dirac Theory of Spin - 1/2 Particles.

Chen, Xiaodong

Using 2 more time variables as the quantum hidden variables, we derive the equation of Dirac field under the principle of classical physics, then we extend our method into the quantum fields with arbitrary spin number. The spin of particle is shown naturally as the topological property of 3-dimensional time + 3-dimensional space . One will find that the quantum physics of single particle can be interpreted as the behavior of the single particle in 3+3 time-space .

Erik Plahte

Richard Warren Gurtler, David Hestenes

Properties of observables in the Pauli and Schrödinger theories and first order relativistic approximations to them are derived from the Dirac theory. They are found to be inconsistent with customary interpretations in many respects. For example, failure to identify the ’’Darwin term’’ as the s−state spin−orbit energy in conventional treatments of the hydrogen atom is traced to a failure to distinguish between charge and momentum flow in the theory. Consistency with the Dirac theory is shown to imply that the Schrödinger equation describes not a spinless particle as universally assumed, but a particle in a spin eigenstate. The bearing of spin on the interpretation of the Schrödinger theory is discussed. Conservation laws of the Dirac theory are formulated in terms of relative variables, and used to derive virial theorems and the corresponding conservation laws in the Pauli−Schrödinger theory.

David Hestenes

The Dirac equation is presented as a complete theory of the electron as a gyromagnetic particle clock with precise physical interpretation for all degrees of freedom. The electron is modeled as a point charge with toroidal zitter and variable zilch. That is to say, the charge oscillates at the speed of light on a torus centered on a circular orbit around its center of mass$\mathbf {z}=\mathbf {z}(t)$, with an axis at a variable angle$\beta =\beta (\mathbf {z}(t))$with respect to its spin vector$\mathbf {s}=\mathbf {s}(t)$. The Dirac wave function$\Psi =\Psi (ct+\mathbf {x})$has a unique factorization$\Psi =(\rho e^{i\beta })^{\scriptstyle \frac {1}{2}}U$, where$U=U(ct+\mathbf {x})$is a spatial rotor with magnetic degrees of freedom, and the quantity$\Psi \widetilde {\Psi }=\rho e^{i\beta }$specifies an embedding of electron paths in the vacuum, where the zilch function$\beta =\beta (ct+\mathbf {x}-\mathbf {z}(t))$is a measure of electron energy density. It culminates in a new synthesis of Dirac electron theory with Maxwell’s electrodynamics by identifying zilch as a common factor that binds them together.