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1 Transluminal Energy Quantum (TEQ) Model of the Electron Richard Gauthier Santa Rosa Junior College Santa Rosa, CA American Physical Society Annual Meeting, Denver CO Session T14: New Directions in Particle Theory May 4, 2009

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2 A Transluminal Energy Quantum Generates a Photon or an Electron A transluminal energy quantum (TEQ) is a helically moving point-like quantum object having a frequency and a wavelength, and carrying energy and momentum. can easily pass through the speed of light (being massless). can generate a photon or an electron depending on whether the energy quantum’s helical trajectory is open or closed.

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3 TEQ Model of the Electron A charged TEQ moves in a closed double-looped helical trajectory with its wavelength (helical pitch) equal to one Compton wavelength. The TEQ moves along the surface of a closed self-intersecting torus.

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4 Electron Quantum’s Trajectory: Speed, Distance and Time The maximum speed is c The minimum speed is c Superluminal time: 57% Subluminal time: 43% Superluminal distance: 76% Subluminal distance: 24% Along the TEQ’s trajectory for an electron “at rest”:

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5 Speed of the Electron’s TEQ along its Double-looped Helical Trajectory

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6 TEQ Trajectory in the Electron Model Parametric equations of the TEQ trajectory - a closed, double-looped helical trajectory along the surface of a self-intersecting spindle torus

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7 Parameters of the TEQ Electron Model Compared to the Dirac Electron Dirac Equation TEQ Model Electron Parameter Parameter 1.Mass/energy Compton wavelength 2.Point-like charge Point-like charge 3.Spin Radius of helical axis 4.Magnetic moment Radius of helical ring 5.Electron or positron Chirality of helix L,R

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8 Heisenberg Uncertainty Relations and the TEQ Electron Model TEQ electron model’s x and y coordinates: Heisenberg uncertainty relations: The TEQ electron model is ‘under the radar’ of the Heisenberg uncertainty relations.

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9 Experimental Support for the TEQ Electron Model Electron Channeling experiment (Saclay, France) P. Catillon et al, A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling, Foundations of Physics (2008) 38: 659–664 Found experimental evidence (resonance effect in electron channeling through a thin silicon crystal) at twice the de Broglie frequency as an “internal clock” in an electron. The de Broglie frequency is the frequency of a photon of light having the electon’s mass: De Broglie frequency: from The de Broglie frequency, as well as twice this frequency -- the zitterbewegung (jitter) frequency -- are contained in the TEQ model of the electron.

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10 Electron Channeling through Silicon Crystal – Experimental Results From: Catillon et al, Foundations of Physics (2008) 38: 659–664 The dip in counts at electron momentum 81.1 MeV/c corresponds to an electron clock frequency of two times the de Broglie frequency (i.e. the zitterbewegung frequency)

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11 Conclusions The TEQ electron model is a spatially-extended quantum model containing several Dirac equation-related quantitative properties of the electron. The TEQ electron model can be tested and compared with other zitterbewegung-type electron models through further electron channeling experiments in silicon or other crystals.

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12 References Gauthier, R., “FTL Quantum Models of the Photon and Electron,” in proceedings of Space Technology and Applications International Forum (STAIF-07), edited by M. El-Genk, AIP Conference Proceedings 880, Melville, NY, (2007), pp Available at Gauthier, R., Transluminal Energy Quantum (TEQ) Model of the Electron, paper presented at the Annual Meeting of the American Physical Society, Denver, CO, May 4, Available at

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