Transluminal Energy Quantum (TEQ) Model of the Electron

1. 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 www.superluminalquantum.org Transluminal Energy Quantum (TEQ) Model of the Electron

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.

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.

4. Electron Quantum’s Trajectory: Speed, Distance and Time Along the TEQ’s trajectory for an electron “at rest”: • The maximum speed is 2.515 c • The minimum speed is 0.707 c • Superluminal time: 57% • Subluminal time: 43% • Superluminal distance: 76% • Subluminal distance: 24%

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

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

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

8. Heisenberg Uncertainty Relationsand 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.

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.

10. Electron Channeling through Silicon Crystal – Experimental Results 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) From: Catillon et al, Foundations of Physics (2008) 38: 659–664

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.

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. 1099-1108. Available at http://superluminalquantum.org/STAIF-2007article.pdf • 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, 2009. Available at http://www.superluminalquantum.org/DenverAPSarticle.pdf