Foundations of Physics

, Volume 36, Issue 3, pp 369-384

First online:

Hidden Variables as Computational Tools: The Construction of a Relativistic Spinor Field

  • Peter HollandAffiliated withGreen College, University of Oxford Email author 

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Hidden variables are usually presented as potential completions of the quantum description. We describe an alternative role for these entities, as aids to calculation in quantum mechanics. This is illustrated by the computation of the time-dependence of a massless relativistic spinor field obeying Weyl’s equation from a single-valued continuum of deterministic trajectories (the “hidden variables”). This is achieved by generalizing the exact method of state construction proposed previously for spin 0 systems to a general Riemannian manifold from which the spinor construction is extracted as a special case. The trajectories form a non-covariant structure and the Lorentz covariance of the spinor field theory emerges as a kind of collective effect. The method makes manifest the spin 1/2 analogue of the quantum potential that is tacit in Weyl’s equation. This implies a novel definition of the “classical limit” of Weyl’s equation.


hidden variables spinor quantum hydrodynamic trajectories Weyl’s equation Riemannian geometry classical limit Lorentz covariance