The Electron Center of Charge Internal Position and Time Coordinate Operators Derived Directly from QED’s Velocity Operator cα

The electron model developed by the author in 6 peer reviewed journal articles is unique, and is derived directly from the Dirac Equation velocity operator, cα,whose four current (cα,I) in QED is coupled with the external electromagnetic (EM) field to produce results that are very accurate computationally. In fact, cα is the "velocity zitter" part of zitterbewegung. with eigenvalues +/- c. Simply integrating the velocity operator, cα, produces the unique electron Center of Charge (CoC) Internal Position and Time Coordinate Operators (IPaTCO) that produces a physical description of the free electron missing in its companion QED theory. We will call this "position zitter" part of zitterbewegung" QED companion theory "QED-position (QED-p)" and the existing, very successful theory, QED- velocity (QED-v) to emphasize their direct connection. QED-v is a “Relativistic Quantum Field Theory” (RQFT) that has no information about the electron’s internal structure. QED-p currently applies to only a free electron embedded in the vacuum, but defines a very specific, unique, highly non classical, structure to a free electron. If one refutes QED-p then must refute QED-v, but QED-v is irrefutable. Although QED-v is a RQFT, its photon propagator has no natural high frequency cutoff, and predicts the electron self-energy to be infinite. Renormalization assumes that infinity ∞ - ∞ = 0. QED-v’s photon propagator lacks a natural high frequency cutoff, which QED-p provides. The electron self-energy is finite, making renormalization unnecessary. For a free electron at rest (p^com = 0), there are eight discrete internal “point” CoC position eigenvalues, all on a spherical shell of radius 3h/8πmc, which yields the EXACT Darwin Term in the non-relativistic limit. The electron’s internal time coordinate is also discrete, with a point CoC position eigenvalue appearing every ~1.4x10^-21 seconds. The CoC motion only “seems continuous” when measurements are made over a long time compared to 10^-22seconds. The QED-p electron CoC is only at one place at any one time, but the CoC oscillations create the electron spatial structure over time. Finally, one must ask what is the source of power in the vacuum to rapidly vibrate the electron’s CoC in perpetuity? The free electron is stable and will radiate its EM field in perpetuity.