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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 www.superluminalquantum.org 1 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. 2 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. 3 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% 4 Speed of the Electron’s TEQ along its Double-looped Helical Trajectory 5 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 x(t ) R0 (1 2 cos(0t )) cos(20t ) y (t ) R0 (1 2 cos(0t ))sin(20t ) z (t ) R0 2 sin(0t ) 1 R0 =1.9 10-13m 2 mc 0 mc 2 7.9 1020 / sec 6 Parameters of the TEQ Electron Model Compared to the Dirac Electron Dirac Equation Electron Parameter mc TEQ Model Parameter 2 Compton wavelength e Point-like charge 1. Mass/energy 2. Point-like charge 3. Spin 4. e Magnetic moment 2m Radius of helical ring 5. Electron or positron Chirality of helix L,R 1 2 h / mc e Radius of helical axis 1 2 2 2 / mc / mc 7 Heisenberg Uncertainty Relations and the TEQ Electron Model root mean square (rms) value • TEQ electron model’s x and y coordinates: 1 xpx ( / mc)( 2 1 y p y ( / mc)( 2 1 h mc) .707 4 2 1 h mc) .707 4 2 • Heisenberg uncertainty relations: h xpx 4 h and yp y 4 The TEQ electron model is ‘under the radar’ of the Heisenberg uncertainty relations. 8 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: 2 20 hf mc f B 1.24 10 cycles / sec from • The de Broglie frequency, as well as twice this frequency - the zitterbewegung (jitter) frequency -- are contained in 9 the TEQ model of the electron. 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 10 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. 11 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 12