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Foundations of Physics

, Volume 45, Issue 6, pp 611–643 | Cite as

On the Gyromagnetic and Gyrogravito-Magnetic Ratios of the Electron

  • M. D. PollockEmail author
Article
  • 191 Downloads

Abstract

The magnetic dipole moment of the Kerr–Newman metric, defined by mass \(M\), electrical charge \(Q\) and angular momentum \(J\), is \(\mu =QJ/M\), corresponding, for all values of \(J/M\), to a gyromagnetic ratio \(g_1=2\), which is also the value of the intrinsic gyromagnetic ratio of the electron, as first noted by Carter. Here, we argue that this result can be understood in terms of the particle-wave complementarity principle. For \(\mu \) can only be defined at asymptotic spatial infinity, where the metric appears to describe a spinning point particle, and therefore setting \(M=m\), \(Q=e\), we necessarily have a model of the electron. From the Dirac equation  we can construct a covariantly conserved four-current \(J_i\) that is the source of the electromagnetic  field generated by the charge \(e\). The result \(g_1=2\) then follows from the minimal gauge principle \(\partial _j\rightarrow \partial _j -\mathrm {i}e A_j\) which is implicit in the formulation of the spinorial wave equation, and which can also be justified from the line action for a spin-1/2 point particle interacting with an external electromagnetic  field, due to Berezin and Marinov. By contrast, analysis of the gyrogravito-magnetic effect, investigated classically by Wald and quantum mechanically by Adler et al., yields the result \(\tilde{g}=1\) in all non-relativistic cases, which can be explained from the principle of equivalence. The results are in accord with the correspondence principle.

Keywords

Dirac equation Kerr-Newman space-time Classical and quantum spin Gauge principle Gravito-magnetism 

Notes

Acknowledgments

This paper was written at the University of Cambridge, Cambridge, England.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.V. A. Steklov Mathematical Institute, Russian Academy of SciencesMoscowRussia

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