You can see the following examples preconfigured as Bookmarks by clicking the "+" sign in the upper-right corner:

1. Electron Scattering: electrons colliding at slow speeds repel each other and their trajectories deviate.

2. Sharp Angle Scattering: electrons colliding at higher speeds make their center of mass turn in sharp angles.

3. Forward Scattering: electrons colliding at high speeds seem to go through each other. The higher their energy or speed the smaller size they seem to have.

4. Paired Electrons: the repulsive force between charges turns into an attractive force between the centers of mass forming bound states, provided their spins are parallel and their distance is below Compton's wavelength.

5. Paired Electrons in Electric Field: an electric field moves the "bound" (spin 1) particles without destroying their pairing.

6. Paired Electrons in Magnetic Field: a magnetic field destroys the pairing immediately.

This same solver and equations work perfectly in 3D. You can try by simply adding the z coordinate in the Plot functions of the Initialization Code.

The initial conditions for the two-particle system analyzed in the center of mass frame are

•

separation:

•

separation:

• Initial angle for the phase of the first particle:

• Initial angle for the phase of the second particle:

• Speed components between both particles:

,

,

(

, speed of light)

• Spin orientation of particle 2 relative to particle 1:

,

• Electric field components:

,

,

• Magnetic field components:

,

,

Some predictions of this model are

• Spin-polarized tunneling and giant magnetoresistance can be explained with this classical model.

• Tunneling can also be described classically.

• 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 stable bound states, provided the spins are parallel.

• Bose condensates and superconductivity phenomena can occur at normal temperatures.

• Radiation has to be produced whenever the CM is accelerated.

• Chirality: matter is left-handed and antimatter is right-handed.

• This model of particles can be extended to any Dirac particle (lepton or quark).

The thumbnail shows electron scattering.

Screenshot 1: sharp angle scattering

Screenshot 2: paired electrons: two negative charges "attracting" each other in a stable configuration

Screenshot 3: paired electrons in electric field

[Disclaimer: the reader should be informed that this Demonstration is based upon a classical formalism that suggests a Zitterbewegung interpretation of quantum mechanics, which is not in the mainstream of current theories on relativistic quantum mechanics, as accepted by most physicists. Nonetheless it is a very intriguing model. For a review see, for example, D. Hestenes,

*Foundations of Physics*,

**20**(10), 1990 pp. 1213–1232.]

[1] M. Rivas,

*Kinematical Theory of Spinning Particles, Classical and Quantum Mechanical Formalism of Elementary Particles*, Dordrecht: Kluwer Academic Publishers, 2001.