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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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Alexander Fromnic (2026) studied this question.
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