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Is Matter Made of Light?Superluminal Quantum Models of the

Photon and the Electron

Richard Gauthier

Santa Rosa Junior CollegeSanta Rosa, CA

Sonoma County Astronomical Society November 12, 2008

www.superluminalquantum.org

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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.

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Thompson’s electronJ.J. Thompson discovered the electron as a sub-atomic particle in 1897. He measured the charge to mass ratio of the electron and later he measured the charge of the electron.

He concluded that electrons come from within atoms and so atoms are divisible.

But… Thompson had no model of the electron .

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Planck’s quantum of radiationMax Planck proposed in 1900 that radiation (blackbody radiation) is emitted from or absorbed by matter in discrete amounts he called quanta. h is now called Planck’s constant. E hf

Data from COBE (Cosmic Background Explorer) showed a perfect fit between the blackbody curve predicted by the big bang theory and that observed in the microwave background.

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Einstein’s “light quantum”

. But… Einstein had no model of the photon or the electron .

Albert Einstein proposed in 1905 that a corpuscle of light (‘light quantum”, later named a photon) has an energy given by E hf

He also proposed that a particle of matter like the electron contains an amount of energy given by

2E mc

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Rutherford’s model of the atom

. But… Rutherford had no model of the electron.

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.

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Bohr’s planetary model of the atom

. But… Bohr had no model of the photon or the electron .

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

2 1hf E E

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Parson’s Magneton Model of the Atom and the Electron

Helical and toroidal models of the electron have taken several forms up to thepresent day, though none has been scientifically accepted.

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 "toroidal ring model","magnetic electron", "plasmoid ring", "vortex ring", or "helicon ring". Parson’s magneton model for chemical bonding and electron sharing influenced chemist Gilbert N. Lewis 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.

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De Broglie’s electron

. But… De Broglie had no model of the electron.

Louis de Broglie proposed in 1923 that the electron has a frequency given by 2hf mc

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.

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Uhlenbeck and Goudsmit’s

Quantized Spinning Electron Model

4 2

hs

But… this spinning electron model was later replaced by a point-like model of the electron carrying an “intrinsic spin”.

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 angular momentum is given by

Uhlenbeck and Goudsmit

2B

e

m

and its magnetic moment by

1 Bohr magneton

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Dirac’s Point-like Electron2 2 2 2 4E p c m c

12

12 /mc

1)Dirac assumed that the electron is point-like. The Dirac Equation2) Gives the correct electron spin 3) Gives the nearly correct electron magnetic moment (pre-QED) Predicts the electron’s theoretical Jittery Motion (zitterbewegung): 4) Frequency 5) Amplitude 6) Speed c

7) Predicts the electron’s antiparticle (positron)8) Predicts an electron with a quantum rotational periodicity of 720 degrees or . 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.

Paul Dirac (1928) derived his relativistic equation for the electronbased on the relativistic particle energy formula .

22 /mc h

/ 2e m

0i mc

4

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Quantum Model of the Photon

The quantum’s speed along the helical trajectory is 1.414c.

For a photon, the quantum travels a 45-degree helical path.

The quantum is point-like and has energy and momentum but not mass.

The quantum produces an angular momentum (spin) of 1unit and is uncharged.

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Parameters of the Photon model

c

Photon Parameter Photon Model Parameter

Detected particle Uncharged point-like quantum

Energy Angular frequency along helix

Momentum Pitch of helix

Spin Radius of helical axis

Polarization left or right Helicity of helix left or right

Speed Longitudinal velocity component

/ 2

c

/h

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Trajectory Equations for Quantum Model of a Photon

photon spin photon momentum /

Position and momentum components

for a right-handed photon:

( ) cos( )2

( ) sin( )2

( )

z zs p h

x t t

y t t

z t ct

( ) sin( )

( ) cos( )

( )

x

y

z

hp t t

hp t t

hp t

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Heisenberg Uncertainty Relations and the Superluminal Photon Model

The Heisenberg position-momentum uncertainty relations:

means root mean square (rms) value

1 1( )( )

2 42 21 1

( )( )2 42 2

x

y

h hx p

h hy p

The photon model’s transverse coordinates are at the exact limit of the Heisenberg uncertainty relation.

4x

hx p

4y

hy p

and

The superluminal quantum’s position-momentum relations:

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Transluminal Quantum Model of the Electron

A charged transluminal quantum moves in a closed double-looped helical trajectory with its wavelength equal to one Compton wavelength .

12/ 2.4 10 me h mc

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Transluminal Quantum Model of the Electron

Red trajectory: quantum is superluminal. Blue trajectory: quantum is subluminal.

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Transluminal Quantum Model of the Electron

Superluminal (red) and subluminal (blue) portions of electron quantum’s trajectory

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Electron Quantum’s Trajectory: Distance and Time Ratios

• Superluminal distance: 76%• Subluminal distance: 24%

• Superluminal time: 57%• Subluminal time: 43%

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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.

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Speed of electron's quantum versus distance from z-axis

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Transluminal Quantum Model of the Electron

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Transluminal Quantum Model of the Electron

Equations of the transluminal quantum’s trajectory - a closed, double-looped helix

0 0 0

0 0 0

0 0

2-13 20

0 0

( ) (1 2 cos( )) cos(2 )

( ) (1 2 cos( ))sin(2 )

( ) 2 sin( )

1=1.9 10 m 7.9 10 / sec

2

x t R t t

y t R t t

z t R t

mcR

mc

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Heisenberg Uncertainty Relationsand the Electron Model

• Electron model’s x and y coordinates:

• Heisenberg uncertainty relations:

and 4 4x y

h hx p y p

1 1( / )( ) .7072 421 1

( / )( ) .7072 42

x

y

hx p mc mc

hy p mc mc

root mean square (rms) value

->The electron model is under the ‘radar’ of the Heisenberg uncertainty relation.

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Parameters of the Transluminal Quantum Model of the Electron

Electron Electron Model Parameter Parameter

1. Mass/energy Compton wavelength

2. Charge Point-like charge

3. Spin Radius of helical axis

4. Magnetic moment Radius of helix

5. Electron or positron Helicity of helix L,R

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2

e

m

/h mc

e12 /mc

22 /mc

e

2mc

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Dirac Equation Properties of the Transluminal Quantum Model

of the Electron

1. Spin

2. Magnetic moment

3. Anti-particle predicted -- Positron model is mirror image of electron model

12zs

/ 2z e m

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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):

Longitudinal component of speed of electron’s quantum along circular axis.

2. Zitterbewegung angular frequency:

Electron model angular frequency in x-y plane

3. Zitterbewegung amplitude:

Root mean square size of electron quantum’s trajectory:

zittv c

2 2102 / 2 1.6 10 / szitt mc

13102 / 1.9 10 mzittR mc R

0rms rms rmsx y z R

longitudinalv c

02xy

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Inertia and the Electron ModelThe 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

.• The relativistic equation for mass-energy is

• This can be rewritten as

• Which means that may cause the electron’s inertia or ‘momentum at rest’ within the electron, corresponding to the

electron’s external momentum

2 2 2 2 4 E p c m c 2

2 22

( ) E

p mcc

mc

p mc

p

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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 causes 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.

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Testing the Transluminal Electron Model

• Special Ratios: The electron model’s predicted superluminal/subluminal ratios may be compared with unexplained particle data.– For distance along trajectory, FTL/STL = 76%/24% – For time along the trajectory, FTL/STL = 57%/43%

• Predicting the electron’s charge? Another (luminal) electron model with toroidal topology predicts the electron’s charge to be about .91e *

*Williamson and van der Mark, “Is the electron a photon with toroidal topology?”, p.9, Annales de la Fondation Louis de Broglie, Volume 22, no.2, 133 (1997).

Available at http://members.chello.nl/~n.benschop/electron.pdf

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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.

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Vision Value of the Models The transluminal quantum models of the photon and electron

are anchored in the physics and mathematics of Dirac and Schroedinger. These models may be of practical value in suggesting new qualitative and quantitative approaches to: – Explaining Elementary (Standard Model) particles– Exploring Sub-elementary structures– Energy – Quantum Entanglement– FTL Communication – FTL Transport– FTL Travel