Completing Dirac’s work. The Dirac electron is a 2D hologram

Abstract

The QED-physical (QED-P) theory [J. H. Wilson, Phys. Essays 35, 5 (2022)] is actually the theory Dirac sought in 1962 in his attempt to predict the muon as an “extensible model of the electron.” Recently, Lerche attempted to produce a classical solution to Dirac’s equation for the radial motion of an extensible, basically classical, model of the electron. Both Dirac and Lerche proceeded in the wrong, classical direction in this effort. The QED-P center of charge (CoC) position operator is derived directly from the Dirac equation (DE) CoC velocity operator, cα with no ad hoc assumptions. QED-P was integrated with QED into a single theory, and that integration is proved by the highly accurate estimates of QED that are dependent on the DE velocity operator cα. Both QED and QED-P are based directly on the same Dirac Equation (DE) four current c(α,I) that QED couples with an external electromagnetic field. QED uses covariant perturbation theory to produce highly accurate results, except for the electron selfenergy, which is infinite. The DE velocity operator, cα, is the spatial part of the free electron four current, and has highly unusual properties compared to classical velocity vectors. QED could not produce highly accurate answers without the 4 × 4 complex matrix cα as the electron CoC “velocity” operator. QED-P simply integrates the same Dirac equation four current used so successfully in QED, and produces the discrete internal spatial and time coordinate operators (ISaTCOs) to give the electron field’s internal structure a very specific, but highly, nonclassical geometric description, with no ad hoc assumptions. QED and QED-P are complementary theories, and both are proven to be true by the accurate results of QED. The physical interpretation of QED-P is discussed in this paper as a two-dimensional, rapidly vibrating “point” charge, that is always located on a 2D CoC sphere in the electron rest frame, oscillating rapidly through eight eigenvalues with an ISaTCO period of ∼10−22 s. The fact that the CoC’s eight ISaTCO spatial eigenvectors are always are located on a 2D shell encompassing the electron’s 3D “space” inside the CoC’s 2D shell is a direct consequence of the DE, and nothing else. In this paper, it is shown that the “discrete” ISaTCOs produce a one dimensional, discrete quantum harmonic oscillator with its ISaTCOs always located on a 2D CoC shell. The CoC shell is an “2D hologram” emerging from a 3D volume inside the 2D CoC shell with a vibrational electronic clock” producing an internal phase that is propagated throughout space/time. The QED-P point electron charge rotates 720° to complete one internal electron discrete period. The electron’s spin and magnetic moment [J. H. Wilson, Phys. Essays 29, 402 (2016); ibid. 31(1), 59‐67 (2018); ibid. 34, 17 (2021)] are generated by the CoC ISaTCO in QED-P, and there is no need for “intrinsic” properties. The QED-P electron properties described above d are far different than the standard model’s very small point particle with intrinsic properties of spin and magnetic moment.