Particles, Fields, and the Measurement of Electron Spin

TL;DR

This paper analyzes electron spin measurement across various theories, showing how classical and quantum models explain the observed uniqueness and discreteness in detector outcomes, with a focus on Dirac field theory.

Contribution

It provides a novel analysis of electron spin measurement within classical Dirac field theory, highlighting limitations and explanations of measurement features across different physical frameworks.

Findings

Classical Dirac field theory explains electron detection location but not discreteness.

Quantum mechanics explains both uniqueness and discreteness.

Classical Dirac theory can account for some spin features but not all.

Abstract

This article compares treatments of the Stern-Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector (uniqueness) but we cannot explain why there are only two locations where the electron is ever found (discreteness). Using non-relativistic or relativistic quantum mechanics, we can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum (discreteness) but we cannot explain another feature that could be explained within any of the other theories (uniqueness).