Download Superluminal Quantum Models of the Photon and Electron

Is Matter Made of Light?
Superluminal Quantum Models of the
Photon and the Electron
Richard Gauthier
Santa Rosa Junior College
Santa Rosa, CA
Best, The Netherlands
March 29-April 2, 2009
www.superluminalquantum.org
1
What exactly is a quantum (or a
photon or an electron)?
A Brief History
of the Quantum
2
Stoney: Electric charge is quantized
George Johnstone Stoney
• introduced the term “electron” as a
fundamental quantity of electric charge in
1891 and first calculated a value of this
charge. But he didn’t introduce the term
“quantum”.
• contributed to the development of electron
theory
• helped lay the foundations for the eventual
discovery of the electron particle.
3
Thompson’s electron
carried a fixed (quantized)
amount of electric charge
and mass
J.J. Thompson discovered the electron as a sub-atomic particle in 1897. He
measured the charge to mass ratio of the electron. Later he measured the
charge of the electron and calculated its mass.
He concluded that electrons come from within atoms and so atoms are
divisible.
He didn’t introduce the term “quantum”.
But… Thompson had no model of the electron.
4
Planck’s “energy quantum”
Max Planck proposed in 1900 that radiation (blackbody
radiation) is emitted from or absorbed by matter in discrete
amounts he called quanta (plural for quantum) (Quantum =
“how much?” in Latin.) h is now called Planck’s constant.
E  hf
E = radiation energy
emitted or absorbed by a
material oscillator
f = the frequency of
vibration of the oscillator
h is Planck’s constant
Blackbody spectrum of light at
different temperatures
5
Einstein’s “light quantum”
Albert Einstein proposed in 1905 that a corpuscle of light
(‘light quantum”, later named a photon) has an energy given by
E  hf
E = energy of light quantum
f = frequency of light quantum
h = Planck’s constant
He also proposed that a particle of matter like the electron
contains an amount of energy given by
E  mc
2
E = energy contained in a a
mass
m = the quantity of mass
.
c = the speed of light
But… Einstein had no model of the photon or the electron .
6
Rutherford’s model of the
atom
Ernest Rutherford, based on experiments scattering alpha
particles (helium nuclei) from thin gold foil, proposed in 1909
that an atom has a positively charged nucleus that is very
small compared to the size of an atom and contains most of
the mass of an atom. In his model, negative electrons orbited
the nucleus.
.
But… Rutherford had no model of the electron.
7
Bohr’s planetary model of the
atom
Neils Bohr proposed in 1913 an atom has stable orbits, and
photons are emitted or absorbed when an electron jumps from one
orbit to another
hf  E2  E1
.
But… Bohr had no model of the photon or the electron .
8
Parson’s Magneton or Toroidal Ring
Model of the Atom and the Electron
Alfred Lauck Parson proposed in 1915 that an electron
is formed of a helical vortex or circular ring of charged
filiments circulating at high speed along a common
continuous path in an atom. Also known as the
"magnetic electron", "plasmoid ring", "vortex ring", or
"helicon ring". Parson’s magneton model for chemical
bonding and electron sharing influenced chemist Gilbert
N. Lewis (who coined the name “photon” in 1926) to
propose chemical bonding rules for atoms.
In the model, charge fibers are twisted an integer
number of times, to account for the quantum number of
angular momentum of an electron in an atom. The
helicity or handedness of the twist was later thought to
distinguish an electron from a proton.
Helical and toroidal models of the electron have taken several forms up to the
present day, though none has been scientifically accepted.
9
De Broglie’s electron
Louis de Broglie proposed in 1923 that the electron has a
frequency given by
hf  mc
2
This frequency gives rise to a wavelength for a moving
electron..
  h / mv
The wave nature of electrons was experimentally confirmed in 1927
by Davisson and Germer.
.
De Broglie proposed that electron orbits in
Bohr’s model of the atom are composed of a
whole number of wavelengths.
But… De Broglie had no model of the electron.
10
Uhlenbeck and Goudsmit
Uhlenbeck and
Goudsmit’s
Quantized Spinning
Electron Model
In 1925, George Uhlenbeck and Samuel Goudsmit proposed that the electron is an
electrically charged particle spinning on its own axis, and whose spin value or
and its magnetic moment by
angular momentum is given by
h
s

4 2
e
B 
2m
1 Bohr magneton
But… this spinning electron model was later replaced by a point-like
model of the electron carrying an “intrinsic spin”.
11
Heisenberg and Schrodinger
Found Quantum Mechanics
Werner Heisenberg
Matrix Mechanics
Erwin Schrodinger
Wave Mechanics
In 1925, Werner Heisenberg introduced matrix mechanics to describe
what is observable about radiation from atoms – light frequencies and intensities.
In 1926, Erwin Schrodinger in introduced wave mechanics to predict
the observed energy levels of atoms based on electron wave properties.
The two theories seemed very different, but were shown by Schrodinger to be
mathematically equivalent, and both theories came to be called quantum mechanics.
But Heisenberg and Schrodinger each intensely disliked the other’s theory.
Heisenberg rejected all visual models, while Schrodinger’s model of the electron
based on his wave theory failed because the model didn’t hold together in space.12
Dirac’s Point-like Electron
Paul Dirac (1928) derived his relativistic equation for the electron
based on the relativistic particle energy formula E 2  p 2c 2  m2c 4 .
i     mc  0

1)Dirac assumed that the electron is point-like.
The Dirac Equation
2) Gives the correct electron spin 1
2
3) Gives the nearly correct electron magnetic moment e / 2m (pre-QED)
Predicts the electron’s theoretical Jittery Motion (zitterbewegung):
4) Frequency 2mc 2 / h
5) Amplitude 12 / mc
6) Speed c
7) Predicts the electron’s antiparticle (positron)
8) Predicts an electron with a quantum rotational periodicity of 720 degrees or
4.
13
But… Dirac had no model of the electron to go with his equation.
The proposed transluminal quantum model of the electron has all 8 of these properties.
Solvay conference 1927 –
“Electrons and Photons”
14
The Transluminal Energy Quantum (TEQ):
a new unifying concept for a photon
and an electron
A transluminal energy quantum
* is a helically moving point-like object having a
frequency and a wavelength, and carrying energy
and momentum.
* can pass through the speed of light.
* can generate a photon or an electron depending
on whether the energy quantum’s helical trajectory
is open or closed.
15
TEQ Model of the Photon
For a photon, the quantum
travels a 45-degree helical
path.
The quantum produces an
angular momentum (spin)
of 1unit and is uncharged.
The quantum’s speed
along the helical trajectory
is 1.414c.
The quantum is point-like and
has energy and momentum but
not mass.
16
Parameters of the Photon model
Photon Parameter
Photon Model Parameter
Detected particle
Uncharged point-like quantum

Energy
Momentum
h/
Angular frequency along helix
Pitch of helix

 / 2
Spin
Radius of helical axis
Polarization left or right
Helicity of helix left or right
Speed
c

Longitudinal velocity component
c
17
Trajectory Equations for 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

18
Heisenberg Uncertainty Relations
and the Superluminal Photon Model
 means root mean square (rms) value
The superluminal quantum’s position-momentum relations:
1
xpx  (
2
1
yp y  (
2

)(
2

)(
2
1
2
1
2
h
h
)

4
h
h
)

4
TheHeisenberg position-momentum uncertainty relations:
h
h
and y p y 
x  p x 
4
4
The photon model’s transverse coordinates are at the
19
exact limit of the Heisenberg uncertainty relation.
TEQ Model of the Electron
A charged transluminal quantum moves in a closed
double-looped helical trajectory with its wavelength
equal to one Compton wavelength
.
C  h / mc  2.43 10 m
12
The Compton wavelength is the wavelength of a photon whose energy is
the same as the energy contained in the mass of an electron at rest.
20
Transluminal Quantum Model
of the Electron
21
Red trajectory: quantum is superluminal. Blue trajectory: quantum is subluminal.
Transluminal Quantum
Model of the Electron
22
Transluminal Quantum Model
of the Electron
Equations of the transluminal 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 )
1
R0 
=1.9 10-13m
2 mc
0 
mc 2
 7.9 1020 / sec
23
Transluminal Quantum Model
of the Electron
Superluminal (red) and
subluminal (blue)
portions of electron
quantum’s trajectory
24
Electron Quantum’s Trajectory:
Distance and Time Ratios
• Superluminal distance: 76%
• Subluminal distance: 24%
• Superluminal time: 57%
• Subluminal time: 43%
25
Transluminal Quantum Model
of the Electron
Along the quantum’s trajectory:
o The maximum speed is 2.515c .
o The minimum speed is 0.707c .
The small circle is the axis of the double-looped helical trajectory.
26
Speed of electron's quantum
versus distance from z-axis
27
28
29
30
Heisenberg Uncertainty Relations
and the Electron Model
  root mean square (rms) value
• 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 electron model is under the ‘radar’
of the Heisenberg uncertainty relation.
31
Parameters of the Transluminal
Quantum Model of the Electron
Electron
Parameter
Electron Model
Parameter
mc
2
1.
Mass/energy
2.
Charge
3.
Spin
4.
e
Magnetic moment
2m
Radius of helix
5.
Electron or positron
Helicity of helix L,R
e
1
2
Compton wavelength
Point-like charge
h / mc
e
Radius of helical axis 1
2
2
2
/ mc
/ mc
32
Dirac Equation Properties of the
Transluminal Quantum Model
of the Electron
1. Spin
sz  12
2. Magnetic moment
z  e / 2m
3. Anti-particle predicted -- Positron model is mirror image of electron model
33
Dirac Equation’s“Jittery Motion” Properties of
the Transluminal Quantum Model of the Electron
1. Zitterbewegung speed of electron (eigenvalue of Dirac equation for free
electron):
vzitt  c
Longitudinal component of speed of electron’s quantum along circular axis.
vlongitudinal  c
2. Zitterbewegung angular frequency:
2
zitt
Electron model angular frequency in x-y plane

 2mc /
 20  1.6  1021 / s
 xy  20
3. Zitterbewegung amplitude:

/ mc  R  1.9  10
1
zitt
0
2
Root mean square size of electron quantum’s trajectory:
R
xrms  yrms  zrms  R0
13
m
34
Inertia and the Electron Model
The electron’s inertia may be related to the electron model’s internally
circulating momentum
• The electron model’s internal circulating momentum in the x-y
plane is
p  mc
.
2
2 2
• The relativistic equation for mass-energy is
E  p c m c
• This can be rewritten as
2 4
E2
2
2

p

(
mc
)
c2
mc
• Which means that
may cause the electron’s
inertia or ‘momentum at rest’ within the electron, corresponding to the
electron’s external momentum
p
35
Is the transluminal quantum a
virtual particle?
A virtual particle (introduced in quantum electrodynamics or
QED) is not directly detectable because it is beneath the
‘radar range’ of the Heisenberg Uncertainty relations.
• Virtual photons exchanged between electric charges cause the
charges to attract or repel and produce Coulomb’s force law.
• Virtual electron-positron pairs surround a “bare” electric point charge
and partly screen its electric field to yield the measured value of the
electron’s charge. This is called vacuum polarization.
• Virtual photons and virtual electron-positron pairs contribute to
calculating the electron’s magnetic moment. The theoretical result
matches the experimental value extremely precisely (1part in 10^10)
The transluminal quantum is at or below the “radar range”
of the Heisenberg Uncertainty relations
• While possibly not directly detectable, it may be the cause of
observable particle properties such as the electron’s mass, charge,
spin and magnetic moment.
36
Experimental support for the TEQ
model of the electron
• Electron Channeling experiment:
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 for twice the 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 in37
the TEQ model of the electron.
Electron channeling experiment
From: Gouanere et al, Annales de la Fondation Louis de Broglie, Volume
33, no 1-2, 2008
38
Electron channeling through silicon
– 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
From: Catillon et al, Foundations of Physics (2008) 38: 659–664
DOI 10.1007/s10701-008-9225-1
39
Conclusions
• The superluminal quantum models of the electron
and the photon contain quantitative experimental
and theoretical properties of the electron and the
photon based on superluminal and transluminal
quantum trajectories.
• While superluminal and transluminal quanta are
point-like, the continuous internal structure of
photon and electron models generated by the
quantum can be modeled and visualized in 3D.
40