Measuring Zitterbewegung predicted by the Dirac equation for a free electron
The fact that the Dirac equation predicts Zitterbewegung (ZBW) for a free electron is well known from Schrödinger [E. Schrödinger, Sitzungsber Preuss. Akad. Wiss. Berlin (Math. Phys.) 24, 418 (1930)] from the very early days of Dirac's relativistic quantum theory. Schrödinger
described ZBW qualitatively as a persistent interference between positive and negative energy states, and the objective of this and previous papers by this author [Phys. Essays 28, 1 (2015); Phys. Essays 29, 402 (2016)] is to describe ways to measure the presence or absence of
ZBW for a free (or nearly free) electron. If ZBW measurements show that it is not present for a free electron, then the Dirac Equation and Schrödinger's analysis [E. Schrödinger, Sitzungsber Preuss. Akad. Wiss. Berlin (Math. Phys.) 24, 418 (1930)] are inaccurate. If ZBW is
present as Schrödinger's analysis [E. Schrödinger, Sitzungsber Preuss. Akad. Wiss. Berlin (Math. Phys.) 24, 418 (1930)] of the Dirac Equation asserts, then a description of a free electron emerges that is significantly different than the present very small, static point electron
with “intrinsic” properties of spin and magnetic moment accepted by most physicists [Eides et al., Phys. Reports 342, 63 (2001).] today. This paper develops a quantitative theory of the free electron directly from the Dirac Equation and Schrödinger's analyses
[E. Schrödinger, Sitzungsber Preuss. Akad. Wiss. Berlin (Math. Phys.) 24, 418 (1930)] without any other assumptions. The fact that ZBW exists for the electron in the hydrogen atom is confirmed by the Darwin term [J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley,
Reading, MA, 1967)]. It seems unnatural to the author that ZBW would vanish when the electron is removed from the hydrogen atom, and becomes free. The unanswered question is whether ZBW can be confirmed or refuted by measurement for a free electron, and possible ways to measure its presence
or absence are described in this paper. The remainder of the paper describes the free electron, assuming ZBW exists. The Dirac Equation [J. H. Wilson, Phys. Essays 28, 1 (2015); Phys. Essays 29, 402 (2016)] produces a physical description of a free electron's ZBW as rapidly oscillating,
quantized Center of Charge (CoC) point rotating about a fictitious Center of Mass (CoM) at a radius of 3
/ 2 times the electron's Compton wavelength. The results in the remainder of this paper, as well as Schrödinger's analyses [E. Schrödinger, Sitzungsber Preuss. Akad. Wiss. Berlin (Math. Phys.)
24, 418 (1930).], are only true if ZBW can be confirmed by measurement. In case measurements show no ZBW exists for a free electron, the Dirac Equation is not a correct description of a single free electron, and more serious problems arise. The static point like electron deduced from
scattering experiments [Eides et al., Phys. Rep. 342, 63 (2001)] that give estimates of the free electron's internal structure based on far field measurements can be misleading in estimating the free electron's internal structure. In Classical Electrodynamics, when one observes
the electric field from a point electron and from a sphere with the same charge spread uniformly over its surface from the far field, Gauss' Law shows that the electric fields are identical. When one tries to “observe” or “measure” the free electron's internal structure
with the high-energy photons required, the single particle free electron is completely destroyed by the measurement process. In fact, any attempt to observe or measure a free electron's structure ensures that the electron is no longer a totally free single particle, and one must be careful
to use only elastic observation methods [J. H. Wilson, Phys. Essays 28, 1 (2015); Phys. Essays 29, 402 (2016)] for this very difficult measurement. Observing a free Quark, much less its internal structure, has proven very difficult, if not impossible.
Keywords: Electron's Center of Charge (Coc) Shell; Entangled Electron/Proton Radius Puzzle; Hydrogen Atom; Photon Propagator; QED; Static Point Electron; The Dirac Electron Model; The Electron as a Stable Fluctuation in the Vacuum; The Electron's Internal Harmonic Oscillator; Ultraviolet Divergences; Zitterbewegung
Document Type: Research Article
Publication date: 13 March 2018
- Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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