The Classical and Quantum Roots of Pauli’s Spin-statistics Relation

Ian Duck, E. C. G. Sudarshan

Ian Duck, E. C. G. Sudarshan, Arthur S. Wightman

W. E. Baylis, Renán Cabrera, D. Keselica

Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to the quantum/classical interface is based on a formulation of relativistic classical mechanics that uses spinors. Spinors and projectors arise naturally in the Clifford's geometric algebra of physical space and not only provide powerful tools for solving problems in classical electrodynamics, but also reproduce a number of quantum results. In particular, many properites of elementary fermions, as spin-1/2 particles, are obtained classically and relate spin, the associated g-factor, its coupling to an external magnetic field, and its magnetic moment to Zitterbewegung and de Broglie waves. The relationship is further strengthened by the fact that physical space and its geometric algebra can be derived from fermion annihilation and creation operators. The approach resolves Pauli's argument against treating time as an operator by recognizing phase factors as projected rotation operators.

C. Salazar-Lazaro

We proposed a Quaternionic mechanical system motivated by the Foucault pendulum as a classical model for the dynamics of the spin 1/2 system. We showed that this mechanical system contains the dynamics of the spin state of the electron under a uniform magnetic field as it is given by the Schrodinger-Pauli-Equation (SPE). We closed with a characterization of the dynamics of this generalized classical system by showing that it is equivalent with the dynamics of the Schrodinger Pauli Equation as long as the solutions to the generalized classical system are roots of the Lagrangian, that is the condition L = 0 holds.