An Orbiting Charge model of Particles with Spin
By PhD. Martin Rivas
The Classic Model of the Electron
We usually think of an electron as a little sphere with negative charge turning around itself…
Some of its known characteristics are:
- It is a fundamental particle, not known to have substructure, that is, it is not known to be made up of smaller particles
- Charge: -e −1,6 × 10−19 Coulombs
- Spin: ½ (in units of Planck’s constant, h)
- Mass: 0,511 MeV/c2 = 9,1 × 10−31 kg
- Size: <10−19 m
- Gyromagnetic ratio g=2
And usually assumed:
- The Center of Mass (CM) and the Center of Charge (CC) are both at the center of this “sphere”.
But this model raises some questions:
- How is the negative charge distributed? If the charge is spread…Why doesn’t it “repel” itself and “explode”?
- The Spin is an angular momentum, and if the size is so small, it has to rotate faster than light to produce such spin. (calculation)
- Why the measured gyromagnetic ratio g=2 if in a sphere g=1?
- How electrons can be paired and form Boson Condensates with integer spin like in Superconductors?
- If we are not able to determine its mass and charge distribution, why are we assuming that CC and CM are the same point?
The Spinning Particle Model of the Electron
We would like to propose a different model:
- The electron is described as a Point Charge spinning around its Center of Mass.
- The Center of Mass (CM) and the Center of Charge (CC) are separated, and with the CM at rest, the CC turns around at a constant velocity (=c as shown later).
Some predictions of this model are:
- This model of particle can be extended to any Dirac particle (lepton or quark with g=2)
- Chirality: Matter is left-handed and antimatter right-handed.
- Particles and antiparticles have the same relative orientation between the spin and magnetic moment.
- A repulsive force between equal charges does not forbid the formation of bound states, provided the spins are parallel.
- Bose condensates and Superconductivity phenomena can occur at normal temperatures.
- Tunneling can also be described classically.
- Spin polarized tunneling and Giant Magnetoresistence can be explained.
- Radiation has to be produced whenever the CM is accelerated.
Explaining the Questions raised by the Classical Model:
- With our model the electron is described as a Point Charge spinning around its Center of Mass
- In this model the charge is located at one Point with no size and thus there is no way for the electron charge to “repel” itself and “explode”.
- Now we have a Radius from the spinning charge CC to the CM, related to the Spin (angular momentum) by: R=S/mc and because S=h/2, R is half Compton’s wavelength, ≈10−13m
- In this model g=2. See slide: “Gyromagnetic Ratio”
- Boson Condensates as in Superconductors. See slide: “Negative Charges attracting each other”
- In this model the CM & CC are NOT the same point
- Spin = Angular Momentum = S = V * M * R (Velocity * Mass * Radius)
- Spin = S = h/2 = 5,27 10−35 Js
- Mass = 9,1 × 10−31 kg
- Radius = 10−19 m
Velocity = V = S / (M*R) = 5,27 10−35 Js/ (9,1 × 10−31 kg * 10−19 m)= 5,79*1014 m/s >> 3,00×108 m/s = C, the speed of light
=> This model is not possible, because the velocity to explain the spin should be much bigger than the speed of light.
In the Spinning Particle Model of the Electron:
- V=c
… and then:
Radius = R = S / (M*c) = 5,27 10−35 Js/ (9,1 × 10−31 kg * 3 × 108 m)= 1,93 × 10−13 m
Chirality
Once the spin direction is fixed, and when looking in that direction, the motion of the CC is counterclockwise for the particle while it is clockwise for the antiparticle. Matter is left-handed while antimatter is right-handed.
The antiparticle motion is the time reversed motion of the particle, and because the charge is opposite both objects have the same relative orientation between spin and magnetic moment. The ground state of the positronium (electron + positron) and neutral pion (quark + antiquark), corroborates this prediction.
Particle AntiParticle
Negative charges attracting each other
In the classic sphere-like model of the electron, the repulsive force between equal charges will always take them apart, making it impossible for them to form bound states. This is not true with the Spinning Particle Model.
If the charge is distributed around the sphere, as soon as the particles get close enough to interact, they will change their trajectories and repel each other.
Particle & Wave Behavior
Certain models tell us that particles are waves because they show some wave-like behavior…
When two sources of particles are “overlaid” they create interference patterns as any other wave…
Tunnel Effect
A potential barrier: It represents the potential energy of the particle. It produces a force to the left on the left hand side and to the right on the right hand side of the barrier
For a point particle the sum of kinetic and potential energy is conserved so that when it reaches the potential barrier the kinetic energy vanishes and the point stops. The force to the left rejects the particle.
Spin Polarized Tunneling (Giant Magneto-resistive materials)
It is the effect produced by an external magnetic field in the behavior of an electric current with a potential barrier.
The resistivity is highly decreased by polarizing the electrons.
These materials are named Giant Magnetoresistive materials. The resistivity is changed by an external magnetic field.
Theory of Radiation
The classical theory of radiation tells us that a particle emits radiation whenever it is accelerated. But in our model the CC is constantly moving in a circular motion and thus it is always accelerated. This means that it is the acceleration of the CM the one that matters regarding radiation.
The theory of radiation has to be rewritten.
Our free particle conserves its kinetic energy but its CC is accelerated, so that no radiation has to be associated to an accelerated CC moving at the speed of light whenever the CM is moving at constant velocity.
The electron cannot decrease its CM velocity spontaneously. Just consider the analysis by the CM observer. A free electron cannot emit radiation.
Radiation has to arise whenever the CM is accelerated and its velocity decreases, so that we need both, an external accelerating force or impulse and a decrease of the CM velocity.
Gyromagnetic Ratio g=2
The gyromagnetic ratio of a particle or system is the ratio of its magnetic dipole moment to its angular momentum.
Suppose we divide the classical spherical charged electron in rings. Each ring has radius r, area A = πr2, mass m, charge q, and angular momentum L=mvr. Then the magnitude of the magnetic dipole moment is:
But the measured experimental data is :
With Gyromagnetic Ratio g=2
- This means once more that our electron cannot have a classical sphere like structure.
- This gyromagnetic ratio comes from the two-fold spin structure.
- The spin is expressed in terms of the orbital motion of the CC around the CM and also of the rotation of the body frame.
- The orbital motion quantizes with value 1.
- The rotational motion quantizes with value ½ in the opposite direction, so that the total spin is ½ in the direction of the orbital angular momentum.
But the magnetic moment of the electron is related to the orbital part of its angular momentum with a normal g=1 relation but with g=2 when expressed in terms of the total spin S.
Measuring the Size of the Electron
Experiments to measure the size of the electron consists on colliding two beams of electrons against each other and counting how many are scattered and altered their trajectories.
By counting the collisions, and knowing how many particles we have thrown, we can estimate the average size of each particle in the beam.
Up to the highest energy of the electrons reached in the LEP experiment at CERN, the estimated size of the electron is below 10−19 m.
This is consistent with our point-like structure for the CC, because the radius R is six orders of magnitude larger than this value.
The Hydrogen Atom Model
The Bohr model of the orbit of a spinless electron is not sustainable because the ground state of the atom corresponds to a zero Angular Momentum, or L = 0 state.
This means, literally, that the orbit of the CM of the electron goes through the center of the proton. The linear momentum of the electron is always pointing to the center of the proton.
RB = 5.3 x 10−11m
R0 = λC / 2 ≈10−13m
Rp ≈10−15m
Ree <10−19m
As shown in the picture, this can easily be understood with the Spinning Particle Model: the CM of the electron can go directly through the center of the proton, while its charge is spinning far away.
We can compare the size of the proton Rp with the radius R0.
The CM of the electron oscillates up to a distance RB, the Bohr radius.
Relativity: Time and Speed
The Theory of Relativity tells us that Time runs slower for a moving particle the faster it moves.
For a static particle, Time can only be measured as “tics” each time it completes a turn around its center of mass at the speed of light C.
If the CM of our particle begins moving with velocity v, necessarily its transversal speed vT will be smaller than c and thus takes more time to complete its turn.
Time goes “slower” for our moving particle.
A brief summary of the ideas exposed:
- The electron is a fundamental particle with spin.
- The electron can be described as a Point Charge spinning around its Center of Mass, at the speed of light.
- The mass is just a reflection of the Energy of the spinning charge.
- This model allows negative charges to “attract” each other at short distances
- Electrons can form stable “bound” states with spin=1, allowing boson condensates, like in superconductivity.
- Electrons have an internal frequency, associated to the spinning motion of the CC and which depends on the velocity of its CM. Therefore, a beam of electrons of the same velocity can show a wave behavior when interacting with a slit or a hole, thus producing a diffraction pattern.
- Matter are particles with some internal frequency and therefore an internal clock whose frequency depends on its CM velocity.
- Spinning electrons can tunnel through potential barriers.