Download Superluminal Quantum Models of the Photon and Electron

Superluminal Quantum Models
of the Electron and the Photon
Richard Gauthier
www.superluminalquantum.org
American Physical Society Annual Meeting
Dallas, April 23, 2006
Session H12: New Directions in Particle Theory
Introduction
• 1. Superluminal quantum model of the photon—
Uncharged superluminal quantum moves in an
open helical trajectory of radius R   / 2 .
• 2. Superluminal quantum model of the electron—
Charged superluminal quantum moves in a
closed double-looped helical trajectory with 
equal to one Compton wavelength h / mc.
• 3. Zitterbewegung (Dirac equation electron’s
“jittery motion”) and the superluminal quantum
model of the electron
Parameters of superluminal
quantum model of the photon
Photon
Parameter
1.
Detected particle
Superluminal Quantum
Model Parameter
Uncharged superluminal
point-like quantum

2.
Energy
Angular frequency along helix
3.
Momentum
Pitch of helix
4.
Spin
Radius of helical axis
5.
Polarization
Helicity of helix
6.
Speed
Longitudinal velocity component

 / 2
 or 
c
Trajectory equations for superluminal
quantum model of a photon
photon spin sz 
photon momentum pz  h / 
Position and momentum components
for a right-handed photon:
h
px (t )   sin(t )

x(t ) 
cos(t )

2
h
p y (t )  cos(t )

y (t ) 
sin(t )

2
h
pz (t ) 
z (t )  ct

Superluminal Quantum Model
of the Photon
Superluminal quantum’s speed along helical trajectory is 1.414c.
Superluminal quantum model of the photon
and the Heisenberg uncertainty relation
  root mean square (rms) value
• In photon model: superluminal quantum’s
transverse coordinates:
1 
1 h
h
xpx  (
)(
)
4
2 2
2
• Heisenberg uncertainty relation:
h
x  p x 
4
Parameters of superluminal
quantum model of the electron
Electron
Parameter
Superluminal Quantum
Model Parameter
1.
Mass/energy
Compton wavelength
2.
Charge
Point-like charge
3.
Spin
Radius of helical axis 1
4.
Magnetic moment
Radius of helix
5.
Electron or positron
Helicity of helix
h / mc
e
/ mc
2
/ mc
2
 or 
2
Superluminal quantum model
of the electron
Equations of the superluminal quantum’s trajectory
—a closed, double-looped helix
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 )
R0 
2mc
=1.9 10-13m
0 
mc 2
 7.9 1020 / sec
Two views of the superluminal
quantum model of the electron
The small circle is the axis of the double-looped helical trajectory. The
maximum speed of superluminal quantum along its trajectory is
2.515c .
Dirac equation’s Zitterbewegung
(“jittery motion”) properties of the
superluminal quantum model of the electron
1. Superluminal quantum circulates with a longitudinal component of velocity equal
to the speed of light c (The eigenvalue of the Dirac Zitterbewegung solution).
2. Superluminal quantum model of the electron has internal Zitterbewegung angular
frequency:
zitt  20  2mc /  1.6 10 / sec
2
21
3. Superluminal model of the electron has Zitterbewegung amplitude:
R0 
13
/ mc  1.9 10 m
Superluminal quantum model of electron: x
rms  yrms  zrms  R0
1
2
Other Dirac equation properties
of the superluminal quantum model
of the electron
4. Spin of superluminal quantum model of electron
sz 
1
2
5. Magnetic moment of superluminal quantum model of electron
M z  e / 2m
6. Gyromagnetic ratio of superluminal quantum model of electron
g2
7. Superluminal quantum positron predicted -- 2 possible helicities of
superluminal quantum model of electron: electron and positron
Conclusions
• The superluminal quantum models of the
electron and the photon are visualizable
quantum models containing many quantitative
properties of the electron and the photon.
• The superluminal quantum model of the electron
can be tested by projecting left and right-handed
gamma photons on electrons and comparing
scattering rates. (Different scattering rates –
model supported).