Dirac’s Point Electron in the Zero-Gravity Kerr–Newman World

Kiessling, Michael K.‐H.; Tahvildar-Zadeh, A. Shadi

doi:10.1007/978-3-319-26902-3_19

Cited by 1 publication

(2 citation statements)

References 48 publications

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“…9 While 'switching off gravity' should not be viewed as a troublesome step, our statement that the zero-G limit is important to get our electron/anti-electron bi-particle interpretation of its ring singularity off the ground, in the sense that the KN 'ring singularity' cannot be given a bi-particle interpretation for > G 0, could seem to deal a fatal blow to our proposal. However, the > G 0 problems we have in mind are similar to those affecting the usual textbook formulation of Dirac hydrogen, viz 'Dirac's equation for a point (test) electron in the field of a point proton at rest in Minkowski spacetime'-as soon as one 'switches on G' to compute the general-relativistic corrections to the Sommerfeld spectrum from eigenstates for Dirac's equation of a point (test) electron in the Reissner-Nordström spacetime, 'all hell breaks lose' (see [54] for a review). The reason is once again the local non-integrability of the energy-momentum-stress tensor of the classical electromagnetic field, which in the usual textbook case is the field of a point charge.…”

Section: A Novel Proposalmentioning

confidence: 99%

“…However, the G > 0 problems we have in mind are similar to those affecting the usual textbook formulation of Dirac Hydrogen, viz. "Dirac's equation for a point (test) electron in the field of a point proton at rest in Minkowski spacetime" -as soon as one "switches on G" to compute the general-relativistic corrections to the Sommerfeld spectrum from eigenstates for Dirac's equation of a point (test) electron in the Reissner-Nordström spacetime, "all hell breaks lose" (see [54] for a review). The reason is once again the local non-integrability of the energy-momentum-stress tensor of the classical electromagnetic field, which in the usual textbook case is the field of a point charge.…”

Section: A Novel Proposalmentioning

confidence: 99%

See 1 more Smart Citation

A novel quantum-mechanical interpretation of the Dirac equation

Kiessling¹,

Tahvildar-Zadeh²

2016

J. Phys. A: Math. Theor.

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A novel interpretation is given of Dirac's "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 spacetime in the zero-gravity limit (here, "zerogravity" means the limit G → 0, where G is Newton's constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac's 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 Kerr-Newman 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 electron's reduced Compton wavelength.

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Section: A Novel Proposalmentioning

confidence: 99%

Section: A Novel Proposalmentioning

confidence: 99%