Predicted Electron Channeling Resonances from a Compton-Period Charge Winding: A Test That Separates the Compton Clock from Zitterbewegung

De Broglie proposed in 1924 that the electron carries an internal clock at the Compton frequency ν_C = mc²/h. In 2008 Catillon et al. reported an 8% dip in the transmission of electrons channeled along the ⟨110⟩ rows of a silicon crystal, within 0.5% of the momentum at which such a clock ticks once per atomic row (80.9 MeV/c). Hestenes showed that a clock at twice that frequency, the zitterbewegung of the Dirac electron, fits the same dip, and Bauer has argued that the feature is consistent with Dirac's free-particle dynamics, with a resonance ladder whose first member lies at twice the momentum. One dip cannot separate these readings. This note makes a prediction that does. (i) The resonance follows from the phase read along the electron's path, Et − px, the proper-time Compton clock; the laboratory phase Et alone gives no resonance at any momentum. The condition is d·λ_dB = k·λ_C², with k the harmonic index of the row potential and d the row spacing. (ii) The row potential has strong harmonics, so a real clock produces a ladder of resonances at p_k = mc·d/(kλ_C). (iii) In The Volumes: Geometry of Electromagnetism the particle's mass is a motion at c around a closed cycle, held there to be a real motion, and the candidate arrangement that gives g = 2 has the charge winding once per Compton period on a loop of radius ħ/mc while the energy circulates twice on half that radius. If that motion is real, the crystal, which acts on charge, couples at ν_C; the doubled frequency enters only at second order, suppressed by ∼10⁻⁴. The prediction for Si ⟨110⟩ is resonances at 80.9, 40.4, 27.0 and 20.2 MeV/c, and none at 161.8, 53.9, 32.4 and 23.1 MeV/c, where a doubled clock and Bauer's ladder place them. A scan near 161.8 MeV/c decides between the readings. The prediction tests the reading of the circulation as a motion in space and the candidate double loop, not the forced results of the framework, which hold under either reading.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23757267
Primary Topic
Crystallography and Radiation Phenomena
Type
preprint
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preprint

Predicted Electron Channeling Resonances from a Compton-Period Charge Winding: A Test That Separates the Compton Clock from Zitterbewegung

Alexander Fromnic
Zenodo (CERN European Organization for Nuclear Research)
Crystallography and Radiation Phenomena
preprint

Predicted Electron Channeling Resonances from a Compton-Period Charge Winding: A Test That Separates the Compton Clock from Zitterbewegung

Alexander Fromnic
preprint en

Abstract

De Broglie proposed in 1924 that the electron carries an internal clock at the Compton frequency ν_C = mc²/h. In 2008 Catillon et al. reported an 8% dip in the transmission of electrons channeled along the ⟨110⟩ rows of a silicon crystal, within 0.5% of the momentum at which such a clock ticks once per atomic row (80.9 MeV/c). Hestenes showed that a clock at twice that frequency, the zitterbewegung of the Dirac electron, fits the same dip, and Bauer has argued that the feature is consistent with Dirac's free-particle dynamics, with a resonance ladder whose first member lies at twice the momentum. One dip cannot separate these readings. This note makes a prediction that does. (i) The resonance follows from the phase read along the electron's path, Et − px, the proper-time Compton clock; the laboratory phase Et alone gives no resonance at any momentum. The condition is d·λ_dB = k·λ_C², with k the harmonic index of the row potential and d the row spacing. (ii) The row potential has strong harmonics, so a real clock produces a ladder of resonances at p_k = mc·d/(kλ_C). (iii) In The Volumes: Geometry of Electromagnetism the particle's mass is a motion at c around a closed cycle, held there to be a real motion, and the candidate arrangement that gives g = 2 has the charge winding once per Compton period on a loop of radius ħ/mc while the energy circulates twice on half that radius. If that motion is real, the crystal, which acts on charge, couples at ν_C; the doubled frequency enters only at second order, suppressed by ∼10⁻⁴. The prediction for Si ⟨110⟩ is resonances at 80.9, 40.4, 27.0 and 20.2 MeV/c, and none at 161.8, 53.9, 32.4 and 23.1 MeV/c, where a doubled clock and Bauer's ladder place them. A scan near 161.8 MeV/c decides between the readings. The prediction tests the reading of the circulation as a motion in space and the candidate double loop, not the forced results of the framework, which hold under either reading.

Zenodo (CERN European Organization for Nuclear Research)
Crystallography and Radiation Phenomena
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Predicted Electron Channeling Resonances from a Compton-Period Charge Winding: A Test That Separates the Compton Clock from Zitterbewegung — Alexander Fromnic · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS