A novel quantum-mechanical interpretation of the Dirac equation

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Abstract

A novel interpretation is given of Diracs wave equation for the relativistic electron as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different topological spin states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such bi-particle structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN) spacetime in the zero-gravity limit (here, zero-gravity means the limit G → 0, where G is Newtons constant of universal gravitation). This novel interpretation resolves the dilemma that Diracs wave equation seems to be capable of describing both the electron and the positron in external fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two-as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called anomalous magnetic moment of the physical electron, not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electrons reduced Compton wavelength.

Original languageEnglish (US)
Article number135301
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number13
DOIs
StatePublished - Feb 19 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

Keywords

  • Dirac equation
  • electron and positron
  • quantum mechanics

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