The Actual Electron Spin
by Tom Gilmore
All graphics by Tom Gilmore
The Electromagnetic Helix Spiral
The Electro-magnetic wave is defined as a sine-wave with a "spin". The sine-wave spin is a lateral rotation of the wave. The result is a helix spiral.
In trigonometry, the sine and cosine are the 2 lines of a right triangle that are opposite the hypotenuse (see shaded triangle in the graphic below). The sine-wave is a plot of the points on the circumference of a circle with a radius of 1, as measured on the Y-axis. (The cosine-wave is a plot of the points as measured on the X-axis.)
The “points” are a continuum of values in the imaginary transit around the circumference of the circle, beginning on the positive side of the X-axis. Another way this is expressed is with the angle (labeled “t”) of a radian going from 0 to 360 degrees, and intersecting with the circumference (called “sin(t)”).
The graph of the sine-wave is shown below. The circles above the sine-wave illustrate the movement of the radian in each quadrant of the sine-wave.
The radian begins the circuit from coinciding with the positive side of the X-axis (to the right). The position on the Y-axis is at zero. As the radian transits the circle counterclockwise, (1): the sin(t) value increases from 0 to 1 (when coinciding with the Y-axis), then (2): the value decreases back down to zero (lying on the negative X-axis). In the graph below of sin(t), this is the left half of the sine-wave. As the radian continues the transit, (3): the value continues decreasing down to –1 (at the Y-axis), and then (4): increases back up to zero (at the X-axis). In the graph, this is the right half of the sine wave. Since the circumference of a circle is (Pi x 2R), and R=1, the length of the sine-wave is 2Pi.
The mathematical sine-wave describes 2 dimensions of the wave. The spin is actually a measure of the wave along the Z-axis (3rd dimension), which is equal to the oscillation on the X-axis. The wave completes one sine-wave and one full spin in the distance of 2Pi. The spin is actually 1. It is commonly expressed as ½ spin in the distance of Pi.
In the series of diagrams above, the cylinder below the sine-wave graph shows the 3-dimensional helix that the spin produces, and this wave is shown by itself below that.
Helix to Positron/Negatron Spin
The sine-wave helix is bi-directional. There is no cosine-wave, the “cosine-wave” is merely a section of the sine-wave offset from the continued sine-wave by the distance of Pi.
In the series of diagrams below, two Spheres are substituted for the cylinder, one under the up stroke of the wave, and one on the down stroke. Below that, the wave breaks in two, and forms a "baseball seam" on the Spheres, one going up, and one going down (positron and negatron).
The spin immediately reduces to its ground state (tighter loops), sending off 2 gamma rays containing the energy differential. (This reduction occurs because of the square power ratio detailed below).
The Geometry of Wave Conversion
There is a square power ratio of
surface area between a cylinder the length of 2Pi (the length of a sine wave),
and 2 Spheres of equal diameter to the cylinder.
(For this proof, the cylinder length is 2Pi and the cylinder and Sphere diameters are 1)
The surface area of a sphere is (4Pi x R2) so for a unit sphere with a radius of ½, (4Pi x 1/22) = Pi
The surface area of a
cylinder is (circumference x length).
Circumference = (Pi x D). Length is 2Pi. Diameter is 1.
Thus the surface area is ((Pi x D) x 2Pi) = ((Pi x 1) x 2Pi) = (Pi x 2Pi) = 2Pi2
Since half the cylinder surface is Pi2 and a single sphere
surface is Pi (the square-root)
the total surface area of the 2 spheres equals the square-root of the surface area of the cylinder.
This square-root relationship of surface area is why after conversion of the photon’s wave to the electrons’ spins, the spins reduce to the ground state.
When the initial (called energized) electron spin reduces to a tighter loop it releases energy in the form of gamma rays. In order for the electromagnetic wave to be restored, two electron spins must become energized (by absorbing the correct wave-length of paired positron/negatron gamma rays). The Photon and Electron are the same particle, called a Photon when traveling on an electromagnetic wave, and called an Electron when spinning on a Sphere surface.
The Role of the Neutrino
The Sphere is a compressed Neutrino (a spherical force field with a single Proton inside). The Electron is attracted to the Proton and this draws it to the outside surface of the Neutrino (Sphere), which it cannot penetrate. The electromagnetic wave is bent to the surface, and forms loops that alternate in direction (due to the alternation of the electromagnetic wave). This looping motion is the Electron spin, as illustrated below right. The path of the Electron crosses under the centers of all 12 edges of a cube with the Sphere’s unit diameter, as illustrated below left.
This spin model also explains the parallel and anti-parallel spin property, and the experimental determination that there are 8 different spin orientations. In the ground state there are 8 possible spins in relation to the containing cube (see diagram below). These 8 insure that any contained Sphere can have a different spin from all of it neighbors.
In the diagram above the front loop is shown in the 8 different directions corresponding to the 8 corners of the cube. This explains the known complexity of the anti-parallel spins. In effect all 8 are somewhat anti-parallel to each other, but there are symmetry groups. Each front loop is diagonal to the cube, and thus leans in 2 directions. The arrows in the diagram indicate these 2 directions for each spin. The spins are organized by anti-parallel pairs.
In the diagram above the 4 spins on the top row are each anti-parallel to the 4 spins on the bottom row (this is indicated by the vertical arrows that point in the direction of the front loop). The spins are broken into 2 groups of 4, those with front loops emerging from the right and left side of the cube, and those with front loops emerging from the top and bottom sides of the cube. These 2 groups of 4 are organized into anti-parallel pairs indicated by the horizontal arrows at the top.
In the Geocubic Model, for each Proton/Electron pair in an atom there is a compressed contained Sphere (the Neutrino), with a Proton inside the Sphere and an Electron spinning on the outside surface, held to the surface by the Coulomb attraction to the Proton inside. The Helium atom has 2 proton/electron pairs (2 compressed Spheres). This is diagrammed below showing the anti-parallel spins, which can be identified by having loops facing opposite directions.
The Electrons are shown as red dots on the spins.
There are major quantum issues that are explained by this model. It is known that each Element has different sets of electromagnetic absorption and emission quanta wave-lengths. This is explained by the fact that the Neutrinos are compressed to different sizes in different Elements because they have different numbers of Neutrinos compressed into the same sized unit cube. In addition, the internal arrangements result in varying Sphere sizes within a given Element. The different sizes of the compressed Neutrinos result in different size Electron Spins, absorbing and emitting different quantum-sized electromagnetic waves. The packing of the Neutrinos also explains the so-called "orbital shells" exhibited by the Electrons, in that Neutrinos pack into the cubic containment such that only the outer Spheres can be detected.
Another phenomenon explained is electric conductivity of the Elements. Since multiple Neutrinos are compressed into the unit cube, some Neutrinos touch others and this point of contact allows Electrons to pass between them. Certain internal arrangements of the Neutrinos facilitate passing an Electron through the atom and on to the next atom in the molecular lattice of an Element. Other internal arrangements and/or crystal lattices inhibit the passage, and are insulators.
Read the color-cube article for detail on how the electron spin was discovered in the myth of Gilgamesh.
The Orbital Model
In the “orbital” atomic model, the term “quantum” refers to atomic emission spectra.
Scientists were trying to account for the discontinuous atomic spectra (absorption and emission of light by atoms only at discrete wavelengths). Planck had developed a mathematical constant that he postulated was the elemental measure of angular momentum, for which he claimed all atomic wavelengths were multiples (6.6 x 10 erg sec). Of course, since there are a finite number of atomic spectral wavelengths, it is meaningless to find the lowest common factor and call it a constant (but it does mean that all the absorption spectra can be specified by integer numbers of the Planck constant).
Academia arbitrarily adopted the orbital model of the atom put forward by Rutherford, consisting of a central clump of Protons and Neutrons (called the Nucleus, a bogus term) being orbited by the Electrons. The orbital model should never have been adopted because it was known from the start that an electron could not be kept in orbit by angular velocity counteracting the Coulomb force, but this critical issue was relegated to a mysterious undetectable “electroweak” particle that purported to keep the Proton and Electron apart (their imaginary friend).
Bohr built his “dynamical” theory of “quantum” atomic structure on Rutherford’s model, even as the inconsistencies accumulated. Sommerfeld postulated non-competing elliptical orbits for the Electrons, but this had no actual specifics, and also did not match with the non-elliptical wave-forms of emissions.
In an orbiting model the orbital radius must correspond with the spectra emissions, and since there exist multiple spectral emission wavelengths from some Elements, Bohr postulated “orbital shells”. This boiled down to much ado about nothing meaningful, The approximate success of the Bohr model in predicting the observed energies of atomic spectra began to unravel as advancements were made in the field, and the model totally failed when applied to molecules and the bonds between atoms.
In an attempt to refine the orbital shell concept, the vague yet complicated notion of “wave mechanics” was put forward by de-Broglie. They like to compare this concept with the property of sound being the same from a guitar string regardless of where the string is struck, and only dictated by the length of the string. This also was an excursion into complications about nothing.
Sommerfeld developed a sequence-series (now called quantum mechanics) that roughly emulated the results of spectroscopic analysis for the first 18 Elements. The use of integers in the sequence-series was labeled “quantum numbering”, and involved adding the “quantum” numbers “l” and “m” to the integer “n” representing the orbital shell. Sommerfeld defined "l" as the azimuthal number determining the pretended angular momentum, and "m" as the orientation of the “orbit” relative to a pretended magnetic field. The problem with this model is the azimuthal number "l" which, in the Bohr model could not take a value of 0 (as required) because the ellipse would collapse to a line which would have to pass through the nucleus assumed to be at the center. Never mind, ignore the man fumbling behind the curtain, concentrate on the abject abstruse complexity in the formulation.
To salvage the quantum mechanical formula, Schrodinger postulated that the quantum numbers "n", "l", and "m" merely represent the 3 degrees of freedom of movement in space, divorcing the quantum mechanical formula from Sommerfeld's abysmal azimuthal number "l".
Quantum “Mechanical” Numerology
The quantum mechanical formula is a sequence-series based on the number "n" as an integer (1, 2, 3, 4, 5). For each integer a sequence series is applied with triad numbers. Firstly the number "l" is allowed every value from 0 to "n"-1. Secondly, for every ("n": "l") in the series the number "m" is allowed every value from +"l" to -"l". Finally, each series member can take one of 2 spins.
The “shell” is “n”.
For “n”=1, the series is simply (1,0,0) x [2 spins]
For “n”=2, the series is (2.0,0), and (2,1,1), (2,1,0), (2,1,-1) x [2 spins]
For “n”=3. (3,0,0), and (3,1,1), (3,1,0), (3,1,-1), and (3,2,2), (3,2,1), (3,2,0), (3,2,-1), (3,2,-2) x [2 spins]
The series triad numbers are wholly irrelevant to the scheme.
Instead, the groups in the shells defined by “l” are called electronic “states”.
The states are labeled with jumbled small-case letters.
If "l" =0 the state is s
If "l" =1 the state is p
If "l" =2 the state is d
If "l" =3 the state is f
The complete series is:
1: 2s (=2, running 2)
2: 2s,6p (=8, running 10)
3: 2s,6p,10d (=18, running 28)
4: 2s,6p,10d,14f (=32, running 60)
5: 2s,6p,10d,14f,18? (=50, running 110)
In true hubris they cut off shell 5 at 14f to achieve running 92.
The shells and states are meaningless numeric artifices.