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Annales de la fondation Louis de Broglie/Annales de la Fondation Louis de Broglie

Experimental observation compatible with the particle internal clock

M. Gouanère, M. Spighel, Nelson Cue, M. J. Gaillard, R. Genre, R. Kirsch, Jean-Claude Poizat, J. Rémillieux, Ph. Catillon, L. Roussel

Published Jan 1, 2006• 6 citations
OpenAlex

Abstract

The particle internal clock conjectured by L. de Broglie in 1924 was looked for in a channeling experiment with -80 MeV electrons traversing a 1-μm thick silicon crystal aligned along the 〈110〉 direction. Part of them undergo what is called the rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows an 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the internal clock frequency. Our observation is compatible with the de Broglie hypothesis.

Related papers

Electron channeling, de Broglie's clock and the relativistic time operator

M. Bauer

Electron channeling in silicon crystals has brought forward the possibility of having detected a particle's "internal clock", as an intrinsic oscillation with de Broglie's frequency. The transmission probability along a major axial direction is reduced with respect to neighboring angles, except for a sharp peak at the atomic row direction. The pattern observed is a "W" instead of a "U". This central peak is attributed to a process known as "rosette motion", in which the crossing of successive atoms would be related to the de Broglie frequency. A classical multiple scattering calculation found that, to represent the experimental results, the interaction frequency had to be about twice the de Broglie's clock frequency; that is, the "Zitterbewegung" frequency. In the present paper, the observed characteristics of this process are shown to be consistent with a free particle quantum mechanical motion described by Dirac's Hamiltonian, albeit with an effective mass resulting from the interaction with the crystal atoms. The introduction of a self-adjoint dynamic time operator provides the connection with an internal "system time", the de Broglie clock.

arXiv:1403.4580•Mar 18, 2014•2 citations

On electron channeling and the de Broglie internal clock

M. Bauer

Electron channeling in silicon crystals has brought forward the possibility of having detected the particle's "de Broglie internal clock", as giving rise to the observed resonance peak at the center of the expected transmission probability dip. A classical multiple scattering calculation fails to represent the experimental results unless, surprisingly, the interaction frequency is twice the de Broglie's clock frequency, that is, the "Zitterbewegung" frequency. In the present paper, the observed characteristics of this process are shown to be consistent with a free particle quantum mechanical motion described by Dirac's Hamiltonian.

arXiv:1409.0888•Sep 2, 2014•0 citations

Measuring the internal clock of the electron

M. Rivas

The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge around the centre of mass of the particle. This internal motion has a frequency twice de Broglie's frequency, which corresponds to the frequency found by Dirac when analysing the electron structure. To get evidence of this internal electron clock a kind of experiment as the one performed by Gouanére et al. \cite{Gouanere} will show a discrete set of momenta at which a resonant scattering effect, appears. The resonant momenta of the electron beam are given by $p_k=161.748/k$ MeV$/c$, $k=1,2,3,...$, where only, the corresponding to $k=2$, was within the range of Gouanére et al. experiment. The extension of the experiment to other values of $p_k$, would show the existence of this phenomenon.

arXiv:0809.3635•Sep 22, 2008•4 citations

de Broglie clock, electron channeling, and time in quantum mechanics

M. Bauer

De Broglie’s association of a wave to particles is a fundamental concept in the quantum mechanical description of nature. The wave oscillation is referred to alternatively as the “de Broglie clock”, the “Compton clock”, or the “de Broglie periodic phenomenon”. In the present paper it is shown that Dirac’s relativistic quantum mechanics, complemented with the dynamical time operator recently introduced, provides a consistent theoretical description of: (i) the generation of the de Broglie wave through Lorentz boosts; and (ii) the characteristics of the resonance observed in electron channeling through thin crystals as responding to both the periodicity derived from the adjustment of the de Broglie period to the crystal interatomic distance (resonance energy) and the periodicity of the predicted trembling motion (Zitterbewegung). One can conclude that the channeling experiments provide the first direct evidence of the electron Zitterbewegung, and that the de Broglie period is an intrinsic property of matter arising from a self-adjoint dynamical time operator.

Canadian Journal of Physics•May 17, 2018•4 citations

An experiment on the particle–wave nature of electrons

Gioṙgio Matteucci, A. Migliori, Francisco F. Medina +1 more

A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.

European Journal of Physics•Dec 22, 2008•9 citations

A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling

Philippe Catillon, Nelson Cue, M. J. Gaillard +7 more

Foundations of Physics•Jul 1, 2008•68 citations
The particle internal clock conjectured by L. de Broglie in 1924 was looked for in a channeling experiment with -80 MeV electrons traversing a 1-μm thick silicon crystal aligned along the 〈110〉 direction. Part of them undergo what is called the rosette motion, in which they interact with a single atomic row. When the electron energy is finely varied, the rate of electron transmission at 0° shows an 8% dip within 0.5% of the resonance energy, 80.874 MeV, for which the frequency of atomic collisions matches the internal clock frequency. Our observation is compatible with the de Broglie hypothesis.
Electron channeling in silicon crystals has brought forward the possibility of having detected a particle's "internal clock", as an intrinsic oscillation with de Broglie's frequency. The transmission probability along a major axial direction is reduced with respect to neighboring angles, except for a sharp peak at the atomic row direction. The pattern observed is a "W" instead of a "U". This central peak is attributed to a process known as "rosette motion", in which the crossing of successive atoms would be related to the de Broglie frequency. A classical multiple scattering calculation found that, to represent the experimental results, the interaction frequency had to be about twice the de Broglie's clock frequency; that is, the "Zitterbewegung" frequency. In the present paper, the observed characteristics of this process are shown to be consistent with a free particle quantum mechanical motion described by Dirac's Hamiltonian, albeit with an effective mass resulting from the interaction with the crystal atoms. The introduction of a self-adjoint dynamic time operator provides the connection with an internal "system time", the de Broglie clock.
Electron channeling in silicon crystals has brought forward the possibility of having detected the particle's "de Broglie internal clock", as giving rise to the observed resonance peak at the center of the expected transmission probability dip. A classical multiple scattering calculation fails to represent the experimental results unless, surprisingly, the interaction frequency is twice the de Broglie's clock frequency, that is, the "Zitterbewegung" frequency. In the present paper, the observed characteristics of this process are shown to be consistent with a free particle quantum mechanical motion described by Dirac's Hamiltonian.
The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge around the centre of mass of the particle. This internal motion has a frequency twice de Broglie's frequency, which corresponds to the frequency found by Dirac when analysing the electron structure. To get evidence of this internal electron clock a kind of experiment as the one performed by Gouanére et al. \cite{Gouanere} will show a discrete set of momenta at which a resonant scattering effect, appears. The resonant momenta of the electron beam are given by pk=161.748/kp_k=161.748/kpk​=161.748/k MeV/c/c/c, k=1,2,3,...k=1,2,3,...k=1,2,3,..., where only, the corresponding to k=2k=2k=2, was within the range of Gouanére et al. experiment. The extension of the experiment to other values of pkp_kpk​, would show the existence of this phenomenon.
De Broglie’s association of a wave to particles is a fundamental concept in the quantum mechanical description of nature. The wave oscillation is referred to alternatively as the “de Broglie clock”, the “Compton clock”, or the “de Broglie periodic phenomenon”. In the present paper it is shown that Dirac’s relativistic quantum mechanics, complemented with the dynamical time operator recently introduced, provides a consistent theoretical description of: (i) the generation of the de Broglie wave through Lorentz boosts; and (ii) the characteristics of the resonance observed in electron channeling through thin crystals as responding to both the periodicity derived from the adjustment of the de Broglie period to the crystal interatomic distance (resonance energy) and the periodicity of the predicted trembling motion (Zitterbewegung). One can conclude that the channeling experiments provide the first direct evidence of the electron Zitterbewegung, and that the de Broglie period is an intrinsic property of matter arising from a self-adjoint dynamical time operator.
A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.