Advances in Applied Clifford Algebras

, Volume 20, Issue 3–4, pp 517–545 | Cite as

Quantum/Classical Interface: Classical Geometric Origin of Fermion Spin

  • W. E. Baylis
  • R. Cabrera
  • J. D. Keselica


Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence 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 in classical electrodynamics, but also reproduce a number of quantum results. We show in particular that many properties 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, Zitter-bewegung, and de Broglie waves. Spinors are also amplitudes that can undergo quantum-like interference. The relationship of spin and geometry is further strengthened by the fact that physical space and its geometric algebra can be derived from fermion annihilation and creation operators. The approach is important because of the insights it provides about spin and quantum phenomena more generally.

Mathematics Subject Classification (2000).

15A66 81P15 81R25 83A05 


Fermion spin quantum/classical interface intrinsic angular momentum algebra of physical space Bell’s inequalities entangled systems 


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Copyright information

© Springer Basel AG, Switzerland 2010

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WindsorWindsorCanada

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