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SPIN

 
The definitions that follow in this section are from engineering physics, mechanics, etc. - things engineers have known and used for many years. If one still thinks that the electron is not a vortex, and that it is a gyroscope-like particle, the following may cause him to pause.

Electron spin is more formally called electron angular momentum. Angular momentum is a stepchild of linear momentum. Linear momentum is the product of mass and velocity, "mv". Linear momentum is handy in tracking some kinds of motion without having to use the energy equations. However, momentum is based upon velocity and velocity is always a relative quantity. So momentum changes according to that to which velocity is relative. Energy is never really noticed until something accelerates something else and really has nothing to do with velocity except as a shortcut in math.

Angular momentum is based upon linear momentum with a radius of curvature added so that it becomes a means of measuring through the use of angular velocity. Its use is necessary when rotation is involved.

Electron spin is, in reality, the means by which the vortex can exist. To those who think of the electron as a particle, spin is angular momentum. By definition, the angular momentum, p, of a rotating body such as a gyroscope is

p = Iw = mr_g²w

where I = moment of inertia, w = angular velocity, r_g = radius of gyration, and m = mass of the rotating body.
 

Center of Gyration

The center of gyration of a body is defined as a point that, if all the mass of the body were concentrated at that point, its moment of inertia would be the same as that of the body. In other words, this is the center about which the body can rotate without moving linearly or vibrating.
 

Torque (Moment)

When working with rotation, "torque" or "moment" is the product of force and the distance between the force and the center of rotation. The distance is called the "moment arm", and the force is simply the product of mass and acceleration [F = ma]. So the product of force and the radius or moment arm is the torque "T" or moment [T = Fr = mar].
 

Moment of Inertia

The moment of inertia "I of a body is defined as the sum of all moments of inertia of its parts. The moment of inertia of a part is defined as the product of its mass and the square of its distance from the center of gyration. The distance from the center of gyration is "r_g" known as the radius of gyration. The equation is

I = mr_g²

The need for a moment of inertia comes from angular velocity, and the energy and momentum of rotation or gyration. The sum of the moments of inertia of various parts of a body is difficult to calculate with linear motion. The distance that one part is from the center of gyration is not the same as the distances of the other parts. Therefore, when calculating kinetic energy in a linear fashion, the velocity squared part of
"(1/2)mv²"
is not easy to average. Or when calculating the momentum in a linear fashion,
"mv"
the velocity part is not easy to average. However, if it were possible to have all of the parts move the same velocity, the calculation would be simple.

By going to a circular measure, the angle of rotation per length of time is the same for all of the parts. When translating to circular measure, in place of "v" we have (2pi)(n/t). The expression (2pi) is one circumference measured in radians. A radian is the same length as a radius but is a circular linear measure. There are 2pi radians in one circle. The "n/t" is the number of circumferences of rotation per second. The expression "(2pi){n/t)" is usually known as "w", and is the circular velocity. It applies to all parts of the rotating body equally, making it very convenient for use.
 

Radius of Gyration

The radius of gyration of a body is defined as the square root of the quantity that is the moment divided by the mass of the body.

r_g = (I/m)^1/2

This is just another version of the equation above for the moment of inertia.

I = mr_g²
 

Angular Velocity

Angular velocity of a body is its circular movement per unit of time. The circular movement is usually calculated in radians, with 2pi radians for every 360 degrees. An angle in radians is the arc distance divided by the radius. Such an angle divided by time is angular velocity. The usual equation is

w = (2pi)(n/t)

This comes from a linear velocity of (2pi)r(n/t) in which "(2pi)r" is one circumference of a circle, and "n/t" is the number circles traversed in one second. For angular measure, it is divided by "r" which converts it to radians per second rather than a straight linear distance per second.
 

Linear Momentum

Linear momentum equals the product of mass and velocity.

Linear momentum = mv

Linear momentum of a body rotating about an axis is "mv" in which "v" is (2pi)r_g(n/t).

Linear momentum of a body rotating about an axis = m[(2pi)r_g(n/t)]
 

Angular Momentum

Angular momentum is the linear momentum about an axis multiplied by its moment arm.

The linear momentum about an axis is m[(2pi)r_g(n/t)].

The moment arm is r_g.

Angular velocity is: w = (2pi)(n/t)

So the angular momentum "p" is

p = m[(2pi)r_g(n/t)]r_g
p = mr_g²[(2pi)(n/t)]
p = mr_g²w

Using mr_g² as the moment of inertia "I" makes calculating easier.

p = Iw = mr_g²w

As was shown above.
 

Finding r_g

Let us assume that we have a cylinder like a length of pipe. The wall thickness of the pipe is infinitely small and it is rotating about an axis at its center where fluid would flow if the pipe were in use. This means that all the parts of the pipe's mass are the same distance, "r", from the axis of rotation. Then the torque or rotational momentum can be computed in a linear fashion is "mrv" where "m" is the sum of all the masses in the pipe, "r" is the distance of all of the masses from the axis of rotation, and "v" is the linear velocity at the pipe wall.

"v" may be in radians per second or "(2pi)r(n/t)" where "n" is revolutions and "n/t" is revolutions per second. Then

mrv = mr[(2pi)r(n/t)] = (2pi)mr²(n/t).

p = mr²[(2pi)(n/t)} = mr²w.

The reasoning above is especially true in the case of electron momentum which has the same Mass moving inward at any radius and therefore has the same mass at any radius. So for the electron,

If we can solve the equation "p = mr_g²w" for "r_g", we may have the radius of gyration.

However, the electron vortex extends to infinity and has a disc-like shape that is distorted by other forces at distances very far from its center. So it has a radius of gyration that ranges from about 10^-57 meter (which is the Schwarzschild radius) to infinity. It has no particular radius of gyration because "m" (the total inward nether flow rate) is the same at all radii and the product of velocity and circumference is always the same at all radii.

To elaborate, the transverse velocity of the of the incoming nether is the same as the incoming velocity at all radii, and is proportional to 1/r (same as the radius to the minus one power) - while the circumference at all radii is proportional to the radius. This makes the product of the velocity and the circumference the same at all radii, meaning that the product of the mass, velocity, and circumference are the same at all radii.

The result of the above is that the angular acceleration for the electron, according to the definition in the book, can be found at any radius where the mass and velocity are known. And there is a gyroscopic action which depends upon gyration.

The electron produces an acceleration that we call planck's constant and moves outward in the form of a light wave. It takes about 10^-22 second for the electron to rotate to produce half of this wave. The relatively slow rotation indicates that the electron has a tendency to remain oriented in space until acted upon by a force (one of the properties of a gyroscope). This proves that the electron does have something like angular momentum. But this acceleration is merely a change in velocity caused by the 180 degree rotation of the electron during the production of a half-wave of light.
 

Rigid Body vs a Vortex

The foregoing has been used to prove that the electron has angular momentum when treating it as a rigid body. But the vortex is fluid and very "flexible" as compared to a rigid body. This is not so true of the vortex center where the forces keep the nether in a strong grip. The incoming nether takes a shape similar to a modified cylinder or a hemisphere. Although the electron Mass increases in density as it approaches the electron center, the fact that the electron acts like a small gravity funnel except for a difference in shape causes its mass to remain the same at any distance from its center.

[The electron's incoming nether (that produces micro-gravity) takes almost a disc-like shape as compared to the spherical shape of gravity funnel for a planet.]

What is usually considered the vortex in nether theory and has been treated as a rigid body, is actually the part close to the electron center. This is the part of the electron where the radius is such that the exiting accelerating half-waves have not achieved lightspeed yet due to a very fast nether inflow. Outside of this distance from the electron center, there is more flexibility and the speed of the incoming nether is quickly overcome by the light half-wave. This outside part is a reality, but difficult to use in working with angular acceleration because the electron nether flow becomes masked or distorted by other nether flows. This is not a problem because we can use the part that we know best to establish angular momentum (since any radius will do for this purpose).
 

Electron Angular Momentum

The electron has an innate tendency to maintain something which seems to be angular momentum even though a specific radius of gyration does not exist. At any radius from the electron center, a theoretical mass moves perpendicular to the theoretical radius at a theoretical angular velocity. The electron radius of gyration is any radius we can use from about 10^-57 (the Schwarzschild radius) to infinity. But the easiest radius to use is the Schwarzschild radius itself because here we know that the velocity of both the incoming nether and the tangential nether is the speed of light "c".

Actually, the hole that is the electron center creates a vortex that is the electron. The vortex extends to infinity even though the electron center is constantly re-orienting itself. Because it is a lightweight entity re-orienting itself frequently, most of the vortex becomes eclipsed by other forces as the radius increases. So it does not act like a body extending to infinity. Also, the geometrical law for nether inflow into the electron means that the higher speeds of inflowing Mass at shorter distances from the electron center dominate the vortex that extends outward. This domination is so great that the electron mimics a solid body - even though the electron vortex is actually a flexible disc or hemisphere. Yet it is true that the use of the equation for a solid body - in the strictest sense - is improper for electron angular momentum.
 

Quantum Spin

Angular momentum is said to be already known as "-h/2", and the equation which describes it is of theoretical value for use in discovering the nature of a photon. But this is not angular momentum.

In quantum theory, spin is considered a quality that can be accepted but is not really angular momentum as we understand it. The Bohm interpretation of quantum theory is not far from nether theory in many ways, but is largely designed to express "large-scale" results without knowing the details of how these are achieved. In quantum theory, the Planck unit of action, "h" equals "h/(2pi)", and is the unit used for spin.

The value h/(2pi) is used for the Planck unit of action. It comes from "hf" as the energy of a photon - "hf" is the same as the energy in one lightwave multiplied by the number of of waves in a photon. And "f" is merely the number of waves per second. If one assumes that a wave is a cyclic thing produced with a circumference, then "2pi" is the circumference of that wave in radian form. So h/(2pi" is a logical means of having a unit of action for the electron.

"S" is spin and "S = M_sh".

"M_s" is the quantum number which can be "-1/2" for electron spin "up" or "1/2" for spin "down". Most of the time "M_s" and "h" are combined so that "h" is a spin of one and "h/2" is a spin of "1/2". This value of electron spin has been determined by math and experiment when dealing with photons.

So for the electron, the unit of quantum spin is considered "h/2" or "h/(4pi)" - and h is called the "Planck unit of action".
 

Calculating Electron Angular Momentum

Angular momentum, "p", is usually defined as the product of the moment of inertia, "I", and the angular velocity, "w". With "v" for velocity, "n" for number of revolutions, "t" for time, and the subscript "g" for "gyration", the correct equations follow.

p = Iw = m_gr_g²w           n_g = n/t = v_g/[(2pi)r_g]

w = (2pi)(n/t)
w = (2pi)n_g
w = (2pi){v_g/[(2pi)r_g]}
w = v_g/r_g

p = m_gr_g²w
p = m_gr_g²(v_g/r_g)
p = m_gr_gv_g

The value of "r(mv)" for the electron does not change as one moves from its center outward. So we may use the mass for the electron "m_e", the Schwarzschild radius "r_s" and the velocity at the Schwarzschild radius "c" (the speed of light) in the equation.

p = m_er_sc
p = (9.10956x10^-31 kilogram)(1.3530x10^-57 meter) (2.9979x10⁸ meters/second)
p = 3.6949819x10^-79 kilogram meter²/second

The above value is incredibly small, but that appears to be the answer.
 

New Known

Electron Angular Momentum = p = 3.6949819x10^-79 kilogram meter²/second
 

Confusion with Compton

When I first began to look seriously at the equations for the energy and momentum in a light wave, I was concerned that Compton had inadvertently divided by the wrong term to discover the momentum and that energy had an extra divisor that was "time". Much of my concern had to do with the fact that his energy term did not follow the equation for kinetic energy correctly - it did not have a "1/2" in front of it when translated into nether theory. I now realize that, in one sense, it is there and that the extra time divisor is not there. So his interpretations were correct for what was known in his day.

Others had found that the energy in a photon is "hf " where "h" is Planck's constant and "f" is frequency. Frequency is "n/t" where "n" is number of events and "t" is time (one second). Compton found that the momentum of the photon is hf/c. This implies that
energy = hf = kmc²,     where "k" is a constant, or at least has a term with "c² " in it. So very likely, the correct equation would follow the format of:

hf = (1/2)mc².

But if this were divided by "c" the result would be half of momentum:

hf/c = (1/2)mc²/c = (1/2)mc.

This discrepancy bothered me, so I proposed that perhaps actually

hf = (1/2)mc²/t

where "t" is one second of time.

"(1/2)mv²" is a mathematical shortcut for "mad" so that

hf = mad, which in nether theory is

hf = m(c/t)d   where "d" is the distance the mass is moved by acceleration "c/t" and is equal to "ct". This gives us an equation with units similar to the one below.

hf = m(c/t)ct

If Compton were to divide this by "c/t" it would be

hf/(c/t) = mct.

But another "1/t" is needed for the right side of the equation to be true momentum.

If hf = m(c/t)(ct/t), there is no "1/2" to worry about. The numerical value is still the same as

hf = m(c/t)ct   because "t" is one second. Dividing

hf = m(c/t)(ct/t) by "c/t", we have

hf/c = mc   which is true momentum.

Later, I discovered that the correct equation for the half-wave is

h/(2t) = [m(t_s/t)](2c/t_s)(ct_s/2)   where "t_s"is a tiny fraction of the usual "t" of one second.

The equation can be simplified and becomes:

h/(2t) = [m(t_s/t)]c²

The above equation is exactly the same dimensionally as

h/(2t)= kmc²   in which k = t_s. Except that for the complete wave it would be

k = 2t_s.

Dividing by "c" changes the equation to

h/(2t)= kmc

The elusive difficulty with the "1/2" might lie within "k". So the "1/2" problem could remain with Compton's work. I thought that probably the difficulty lay in the fact that the true energy and momentum is with the light half-wave and that the half-wave and the wave can be confused by the experimenter. In any case, Compton found a value for his divisor that was twice what would have been normal for dividing energy to obtain momentum. I was wrong when I thought "c/t" was the answer. Yes, I make lots of stupid mistakes. Most of the time I find them with a good cross-check.

The Answer

In early 2014, I began working on a part of light theory that explained the apparent paradox. When producing a light half-wave, the electron reverses direction and sends out the half-wave acceleration. The acceleration creates a tangential momentum as it travels outward. The tangential momentum is from the circumferential mass and velocity of the ripple that is the half-wave. Once the half-wave passes a point, the velocity of the momentum is in a particular direction relative to that point. It is not until the electron reverses and sends out the subsequent half-wave that the new half-wave ripple can cause the circumferential changes that include the reversal of the velocity in the momentum. It was not possible for Compton to measure two opposite half-wave momentums that were separated by a time interval. What he measured was the momentum of the half-wave.
 

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