Particles, fields, and the measurement of electron spin
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Particles, fields, and the measurement of electron spin Charles T. Sebens1 Received: 12 March 2020 / Accepted: 20 August 2020 © Springer Nature B.V. 2020
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). Keywords Electron spin · Dirac equation · Dirac field · Stern–Gerlach experiment
Contents 1 Introduction . . . . . . . . . . . . 2 Classical rigid body mechanics . . 3 Classical point particle mechanics . 4 Non-relativistic quantum mechanics 5 Relativistic quantum mechanics . . 6 Classical field theory . . . . . . . . 7 Quantum field theory . . . . . . . . 8 Conclusion . . . . . . . . . . . . . References . . . . . . . . . . . . . . .
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Charles T. Sebens [email protected] Division of the Humanities and Social Sciences, California Institute of Technology, 1200 E California Blvd, Pasadena, CA, USA
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1 Introduction The measurement of electron spin through the Stern–Gerlach experiment serves as one of the primary touchstone experiments used to introduce and understand quantum physics, vying with the double-slit experiment for placement at the beginning of introductions to the subject. In philosophical discussions of the foundations of quantum physics, this experiment is ubiquitous.1 The experiment is ordinarily used to illustrate the ways in which quantum particles differ from classical particles. Here I w
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