Download (TEQ) Model of the Electron - Superluminal quantum models of the

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
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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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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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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%
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Speed of the Electron’s TEQ along
its Double-looped Helical Trajectory
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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(20t )
y (t )  R0 (1  2 cos(0t ))sin(20t )
z (t )  R0 2 sin(0t )
1
R0 
=1.9 10-13m
2 mc
0 
mc 2
 7.9 1020 / sec
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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
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Heisenberg Uncertainty Relations
and the TEQ Electron Model
  root mean square (rms) value
• TEQ electron model’s x and y coordinates:
1
xpx  (
/ mc)(
2
1
y p y  (
/ mc)(
2
1
h
 mc)  .707
4
2
1
h
 mc)  .707
4
2
• Heisenberg uncertainty relations:
h
xpx 
4
h
and yp y 
4
The TEQ electron model is ‘under the radar’
of the Heisenberg uncertainty relations.
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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
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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
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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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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
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