Aireal's Blog

Spin and Charge in Particles
As Related to The
Semi-Classical Model Presented in my Book
For Undergraduate Education

In my book I struggled with a way to explain spin and charge in particles where the average reader could grasp it using a semi-classical model. I came up with a way to do so that I would like to expand on. As the scalar wave of the electron can also be modeled as a string in string theory and it can be used in QED if one wanted, it can be used in more than just a semi-classical manner.

In the scalar wave of the 3-D semi-classical electron I used, when the wave collapses to form the point particle aspect, the scalar wave must complete a 180-degree spin, ½ a revolution, before it starts to expand again p 129 [1]. Thus the scalar wave is “facing” the same direction as its direction of travel.

In string theory, strings were first defined as a number of 0-dimensional harmonic oscillators. So from that perspective, the string collapses to a single 0-dimensional harmonic oscillator that completes a 180-degree spin before expanding again in the 3-dimensional world.

Hopefully this allowed the reader to separate the quantum spin of the point particle component, as distinct from any rotational spin of the electron in its extended form of a standing wave.

The point particle aspect of the electron is where the vacuum and source field combine. The quantum ½ spin of the point particle can now be used in a visual way to explain how charge is created at this point.

Draw a circle and divide it in half top to bottom. At the top we have no charge, 180 degrees around it at the bottom we have a charge of 1 electron volt. Think of half of this circle as being a generator. As you travel around the circle, the electron generates a charge during its ½ spin. An arrow at the top on the circumference can be used to show the direction of rotation.

Semi-classically I modeled this “Generator/Motor” as a homopolar motor with the scalar wave as the armature and its interaction with the vacuum and the electromagnetic field p 129 [1]

This was as far as I went in my book, but it can also represent more than this. It is easy to see how a 0-spin particle does not generate any charge, as it does not travel around the circle. If the other half of the circle were modeled as a motor that uses this charge, a 1-spin particle would have 0 net charge after completing a full revolution.

Anti-particles can be represented with a mirror image of this circle where the generator and motor sides are reversed. A 0-spin anti-particle still develops no charge and a 1-spin anti-particle still has a 0 net charge. For positive ½ spin lets assign a clockwise or positive direction for our arrow which generates a positive charge. The negative ½ spin would then spin counter clockwise, in a negative direction, to generate a negative charge.

If you overlay the circles of a particle and it’s anti-particle, the two spins cancel out, and the two sides, generator and motor, cancel each other out. So both circles cancel each other out just like they are supposed too.

This circle model could also be used with Feynman Diagrams in QED if one wanted. The point for a particle or anti-particle would just be enlarged to a small circle with a vector to denote which it is. Pair production or annihilation would be a small circle with two vector arrows in opposite directions. One could use as little or as much detail as needed. A 1-spin particle would be as we just described. A 0-spin particle would be a circle with no vector arrow, and a ½ spin particle would have a line dividing it in half with a vector arrow.

This works well, but particles with a fractional charge must be included as well. Dividing the circle into six segments. Starting at the top and going in the direction of the vector arrow will be the starting point.

When you have traveled 1/6 of a circle, which is 1/3 of the way around the generator side, you have 1/3 of an electron volt. The divided circle representing ½ spin particles would have a line for this point to the center to denote a 1/3-spin particle with 1/3 charge. We would then denote a line at 2/3 around the generator side for a particle with 2/3 charge.

Particle and anti-particles circles will still cancel each other out. This model worked well for particles in the semi-classical model where the Up quark was the electron waveform at reduced amplitude, this predicted a mass of 1.533 MeV and a charge of 2/3 p. 149 [1]. By modeling the Down quark as the Up quark at reduced amplitude it gave a mass 4.599 MeV and a 1/3 charge.

This suggests that all ½ spin particles were the same basic waveform that was stable with the energy level of its surrounding. So we should expect to find more ½ spin particles as we reach higher energy levels, which is consistent with current observations p 149 [1].

So this gives us a semi-classical model of spin and charge that can be used at the undergraduate level that can also be related to other fields of physics and serve as a good introduction to other fields of physics.



References:

[1] Little Feather 2011 Simple Logic and Reason Virtualbookworm.com Publishing College Station, Texas ISBN 978-1-60264-782-4 and 978-1-60264-783-1 (Ebook)