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The Zitterbewegung and the de Broglie Wavelength

Jean Louis Van Belle

Published Feb 1, 2019• 0 citations
OpenAlex

Abstract

This paper explores some more philosophical aspects of the Zitterbewegung model of an electron, including a geometric interpretation of the de Broglie wavelength.

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This paper explores how the Zitterbewegung interpretation and the Uncertainty Principle might mesh. It also further details our geometric interpretation of the de Broglie wavelength.

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Zitterbewegung and de Broglie matter waves are both phenomena associated with the quantum-mechanical properties of the electron, but they are usually discussed in different contexts. Zitterbewegung is understood as a rapid oscillatory motion appearing in the Dirac equation, whereas the de Broglie matter wave is understood as a wave corresponding to the linear momentum of a particle. Some previous studies have attempted to derive the de Broglie matter wave from an internal clock of the electron or from Zitterbewegung. In the present study, however, no causal relation in which the matter wave is generated by Zitterbewegung is assumed. Instead, the two are regarded as different geometrical representations of a common phase degree of freedom. Specifically, Zitterbewegung is interpreted as a phenomenon corresponding to an internal rotational degree of freedom, while the de Broglie matter wave is interpreted as spatial phase progression associated with linear momentum. and are interpreted, respectively, as the rates of phase progression in the temporal and spatial directions. Furthermore, using the relation introduced in previous work, and reinterpreting it as the ratio of the internal rotational velocity to the external propagation velocity, this study shows the possibility of describing internal rotation, translational motion, matter waves, and the fine-structure constant within a common phase geometry.

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The original wave theory proposed by de Broglie necessitates a stationary (localized) monochromatic plane wave of high frequency νo associated with particle. As particle moves the de Broglie wavelength appears as an observable (a relativistic effect). The nature and interpretation of high frequency oscillations remained unrevealed so far. This paper presents a self trapped circular Electromagnetic (EM) travelling wave model of Electron (specifically) and other charged particles generally. Curling EM wave is localized (stationary) and still a plane monochromatic travelling wave, against the customary wave packet approach, where number of frequencies are made to interfere to build a stationary localized wave-packet. The model reveals facts such as interpretation of wave function ψ (de Broglie wave) as a relativistic effect of a real wave function and removes the discrepancy of very high phase velocity (c 2 /v) associated with it. The model also incorporates zitterbewegung of electron and 4π rotation needed, for a complete round of wave cycle.

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A Point-Coincident N-Mass Swarm as a Deterministic Toy Model for Electron Detection: A Variant of Zitterbewegung -Type Models

Wael M. H. Ghanem

We present a fully formulated variant of Zitterbewegung-type composite models in which the electron is modeled as N distinct mass-entities qi sharing a common spatial point xi(t) = xe(t) and a common de Broglie clock f0 = me c^2 / h. Unlike de Broglie's original single-clock hypothesis with a single wavelength lambda = h/p, we retain fi = f0 for all i but allow distinct masses mi = mj with ∑︁ mi = me. Consequently each sub-entity carries a different momentum pi = mi * ve and wavelength lambda_i = h / pi. Detection randomness is reduced to which qi delivers its momentum to the detector, while constant scintillation energy follows from conservation of f0. We discuss binding, Lorentz invariance, cooling, and open problems. To our knowledge this point-coincident multi-wavelength clock has not been formulated in this exact form.

•Sep 19, 2026•0 citations
Zitterbewegung and de Broglie matter waves are both phenomena associated with the quantum-mechanical properties of the electron, but they are usually discussed in different contexts. Zitterbewegung is understood as a rapid oscillatory motion appearing in the Dirac equation, whereas the de Broglie matter wave is understood as a wave corresponding to the linear momentum of a particle. Some previous studies have attempted to derive the de Broglie matter wave from an internal clock of the electron or from Zitterbewegung. In the present study, however, no causal relation in which the matter wave is generated by Zitterbewegung is assumed. Instead, the two are regarded as different geometrical representations of a common phase degree of freedom. Specifically, Zitterbewegung is interpreted as a phenomenon corresponding to an internal rotational degree of freedom, while the de Broglie matter wave is interpreted as spatial phase progression associated with linear momentum. and are interpreted, respectively, as the rates of phase progression in the temporal and spatial directions. Furthermore, using the relation introduced in previous work, and reinterpreting it as the ratio of the internal rotational velocity to the external propagation velocity, this study shows the possibility of describing internal rotation, translational motion, matter waves, and the fine-structure constant within a common phase geometry.
The original wave theory proposed by de Broglie necessitates a stationary (localized) monochromatic plane wave of high frequency νo associated with particle. As particle moves the de Broglie wavelength appears as an observable (a relativistic effect). The nature and interpretation of high frequency oscillations remained unrevealed so far. This paper presents a self trapped circular Electromagnetic (EM) travelling wave model of Electron (specifically) and other charged particles generally. Curling EM wave is localized (stationary) and still a plane monochromatic travelling wave, against the customary wave packet approach, where number of frequencies are made to interfere to build a stationary localized wave-packet. The model reveals facts such as interpretation of wave function ψ (de Broglie wave) as a relativistic effect of a real wave function and removes the discrepancy of very high phase velocity (c 2 /v) associated with it. The model also incorporates zitterbewegung of electron and 4π rotation needed, for a complete round of wave cycle.
We present a fully formulated variant of Zitterbewegung-type composite models in which the electron is modeled as N distinct mass-entities qi sharing a common spatial point xi(t) = xe(t) and a common de Broglie clock f0 = me c^2 / h. Unlike de Broglie's original single-clock hypothesis with a single wavelength lambda = h/p, we retain fi = f0 for all i but allow distinct masses mi = mj with ∑︁ mi = me. Consequently each sub-entity carries a different momentum pi = mi * ve and wavelength lambda_i = h / pi. Detection randomness is reduced to which qi delivers its momentum to the detector, while constant scintillation energy follows from conservation of f0. We discuss binding, Lorentz invariance, cooling, and open problems. To our knowledge this point-coincident multi-wavelength clock has not been formulated in this exact form.