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Introduction to Light
The product of Planck's constant, "h", and frequency, "f ", equals the energy in a photon. Planck's constant is the kinetic energy, EK, in the passage of one wave of light. However, the correct quantum for light is the half-wave rather than the complete wave which is composed of two half-waves. This is because a photon is composed of transverse waves caused by an electron reversing directions regularly and thus creating opposing accelerations in the ether. These accelerations move outward at the speed of light. Each acceleration is created by a reverse in the electron's direction which reverses the rotation of the incoming ether. Two adjacent acceleration reversals create one light wave.
It is the electron's reversals in direction during the production of a "photon" that creates the energy in the photon. The passage of time the electron is moving between reversals in direction cause the length of the half-wave or wave.
Very near the center of the electron vortex, tranverse and radial velocity vectors of the incoming nether are equal to "c", the speed of light. The radius where this occurs is the "Schwartzchild radius" for the electron. The change in electron direction at this radius causes the nether tangential velocity vector change from its original direction to the opposite direction, for a total velocity change of "2c". This change happens over the period of time used for the electron to reverse direction, "ts".
This is not a true change in velocity for any particular volume of nether, but a can be likened to changing the direction of a flow in a hose used while watering a lawn. The direction change is quick, but applies to different volumes of water in the flow rather than the same volume. Of course, the electron is taking in a flow rather than sending it out. Although "2c/ts" appears to be an "acceleration" when using dimensional analysis, such an acceleration would far exceed the reaction speed of the nether. The highest actual acceleration for the tranverse vector of nether at the Shwartzschild radius is only "c/ts".
hf = EK = mad
m = electron mass, mts = Mass entering the electron in time
2c/ts = acceleration, and d = distance over which acceleration acts.
With a half-wave, the frequency is "1/2", so we will use "h(.5/t)" in the equation.
h(.5/t) = mad
h/(2t) = mts(2c/ts)d
h/(2t) = m(2c)d
Linear versus Angular Momentum
Electron spin is what 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 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 what the velocity is relative to. 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.
Because the half-wave is the correct place to begin, the usual equation should be
h/(2t) = (1/2)mv2.
Then by moving the divisor of "2" on the left side of the equation to right side (muliplying both sides by 2), we have
h/t = mv2 = 2mad.
The "m" in the following equation is the mass of the electron which is the flow measure of nether inward.
m = M/t
"ms" is the amount of Mass of nether entering the electron center in time "ts".
ms = mts
The "a" is the transverse acceleration "2c/ts" caused by the passage of a light half-wave and used in the production of a light half-wave. This is not a true acceleration of a Mass of nether but behaves mathematically as if it were. This is explained fully in Book Four on light. True acceleration cannot exceed "c/t". As shown above, this translates into "c/t".
The "d" is the the distance that the nether inflow of mass is moved in a tranverse manner by the acceleration "2c/ts", measured at radius "rs" which is the electron Schwartzschild radius.
"d" is actually not a straight-line linear distance. The "ring" of the outward moving transverse wave begins with "d" as many traversings of smaller circumferences, and becomes an arc measure within a single circumference as the light half-wave moves farther outward. As an arc measure it is both "cts/2" and "(2pi)rn/2". It is "cts/2" because the average velocity during the acceleration is "c" and "ts" is the tiny amount of time in which the electron changes direction at the end of each of its runs to produce the half-waves. The divisor of two is used because the average distance for all parts of the incoming Mass to move into the electron center in time "ts" is the greatest distance divided by two. The expression "(2pi)rn/2" is the arc distance using the circumference of the "ring" which is "(2pi)r" and the number of times around it which is "n". So the equation for photon energy when used for the half-wave becomes the following.
h/(2t) = ms(2c/ts)[(2pi)rn)/2]
h/(2t) = ms(2c/ts)[cts/2]
h/(2t) = msc2
h/(2t) = msc2
h/(2t) = (M/t)tsc2
h/(2t) = M(c/t)(cts)
h/(2t) = M(ts/t)c2
Equation 1. h/(2t) = M(ts/t)c2
Compton divided "hf " by "c" for the momentum of a lightwave. This was found experimentally and is correct. However, it appears to be either the result of an average velocity or "one side" of the transverse wave. Actually, the wave's momentum is not a good way to describe what happens to a lot of nether that is accelerating. In nether theory, it looks like this for the half-wave in which "f " equals one. Notice that rather than a divisor of "c", there is a divisor of "c/2".
[h/(2t)]/(c/2) = msc2/(c/2) = 2msc
Equation 2. hf/c = 2msc or 2M(ts/t)c
Compton's "hf/c" is absolutely correct for the the momentum imparted from electron spin during an electron reversal such as is the case with a half-wave. For a full wave the change in energy is double. Possibly because of this doubling for energy, the momentum of Compton appears to be half what is normal.
Or perhaps Compton was measuring half of the half-wave for his momentum. Because the two halves of the half-wave oppose to one another, this is about the only way that momentum can be measured. At least this is one theory.
Equation one can be re-written as follows.
h/(2t) = ms(2c/ts)[(2pi)rn)/2]
h/(2t) = mts(2c/ts)[(2pi)rn)/2]
h/(2t) = mc[(2pi)rn)]
h/(2t) = (M/t)c[(2pi)rn)]
h/(2t) = M(c/t)[(2pi)rn)]
Equation 3. h/(2t) = M(c/t)[(2pi)rn)]
Below is the correct general form of the energy equation.
E = mad
The mass "M" is nether Mass in one second of inflow into the electron. The acceleration is the acceleration "c/t" for a light "pressure wave". The distance "(2pi)rn" is the distance that the acceleration moves the nether Mass at the electron Shwartzschild radius.
Going back to momentum, it is the true electron momentum multiplied by two that furnishes the light half-wave momentum. This sounds confusing. It is the case because the half-wave is furnished by the electron reversing its momentum so that if the algebraic sum were used, there would be only a momentum of zero. First the electron vortex is "spinning" one way, then it is "spinning" the other way. The two spin directions relative to the surrounding nether cancel one another mathematically.
Dividing equation 3 by "c/2" provides momentum.
[h/(2ct)]/(c/2) = M(c/t)[(2pi)rn)]/(c/2)
h/(ct) = 2M[(2pi)r(n/t)]
Dividing by 2 provides the electron spin momentum as applied to a light half-wave during time ts.
Equation 4. h/(2ct) = M[(2pi)rn/t)]
This is electron Mass "M" multiplied by the distance that the nether inflow at the radius moves either tangentially or radially in one second - even though the velocity "[(2pi)rn/t]" applies to only time ts. (Remember that these are vectors.)
Perhaps this is why Compton had half the usual momentum for his equation.
These equations can be divided by "2pi" to put them in terms of the Planck unit of action, but to do so would only confuse what is actually happening. Later on this rather long page, this will be shown.
The electron is a vortex rather than a gyroscope. In case anyone still wishes to think of it as a particle, the following may cause him to pause.
Electron spin is, in reality, the means by which the vortex can exist. To those who think of the electron as a particle, it is angular momentum. By definition, the angular momentum, p, of a rotating body such as a gyroscope is
p = Iw = mrg2w
where I = moment of inertia, w = angular velocity,
rg = 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.
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.
rg = (I/m)1/2
It is best understood after discovering the nature of the moment of inertia.
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.
Moment of Inertia
The moment of inertia 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 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 [(1/2)mv2] the velocity squared part is not easy to average. However, if it were possible to have all of the parts move the same distance in the same length of time, 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. According one physics text, when translating to circular measure, in place of "v" we have "r(n/t)". This is squared to arrive at an energy of "(1/2)m[r(n/t)]2" and the "n/t" becomes "w" which is angular velocity. The equation is re-written as "(1/2)mr2w2". Then it seemed convenient to call "mr2" the "moment of inertia" because it is the moment of inertia when energy is used to cause rotation. This makes sense. But then it seems appropriate to divide the expression by "w" to have an expression for angular momentum. And mr2w becomes angular momentum, "I", just as linear energy divided by "v" becomes linear momentum. However, since it is "rw" which is used in angular measure to take the place of "v", it seems that it should be "rw" which is used to divide angular energy to arrive at angular momentum. So it would appear that what we have instead of true momentum is a bastard quantity which tends to create confusion. However, another explanation is better one and it follows.
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).
From this equation, we can easily arrive at the one for angular momentum by dividing both sides by "2pi". Now we have for angular momentum,
p = mrv/(2pi) = mr2(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 solve the equation "I = mrg2w" for "rg", we have the radius of gyration.
Rigid Body vs the Vortex
The foregoing has been used for the electron, treating it as a rigid body. Techically, 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 funnel causes its mass to remain the same at any distance from its center.
What is usually considered the vortex in contemporary science and has been treated as a rigid body, is actually the electron center. This is the part of the electron where the radius does not exceed approximately 1x10-56 meter and the exiting acceleration half-waves have not achieved lightspeed yet due to a very fast nether inflow. Outside 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.
Electron Angular Momentum
An electron has an innate tendency to maintain something which seems to be angular momentum even though a theoretical radius of gyration could not at first be found. However, a total value for angular momentum, possibly multiplied by something else, could be found. This product could be used as if it were angular momentum. And, indeed, it can function very well in this fashion, even creating a type of gyroscopic action which limits the rate at which an electron will turn about an axis that is perpendicular from its spin axis.
At the electron's theoretical radius of gyration is a theoretical circumference at which a theoretical mass moves perpendicular to the theoretical radius at a theoretical angular velocity. 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 re-orienting itself frequently, most of the vortex does not act like a body extending to infinity. Instead, it acts like a flexible disc or hemisphere with a theoretical radius. The area near the vortex center has a "radius of gyration."
Frankly, the use of the equation for a solid body may be improper for the electron angular momentum if another equation might be used, but that seems to be the only equation that we have for a vortex. Angular momentum is already known to be "-h/2", and the equation which describes it is of theoretical value.
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.
"S" is spin and "S = Msh".
"Ms" is the quantum number which can be "-1/2" for electron spin "up" or "1/2" for spin "down". Most of the time "Ms" and "h" are combined so that "h" is a spin of one and "h/2" is a spin of "1/2". The value of electron spin has been determined by math and experiment.
So for the electron, the unit of spin is "h/2" or "h/(4pi)".
Angular momentum, "p", is usually defined as the product of the moment of inertia, "I", and the angular velocity, "w".
p = h/2 = Iw = mrg2w
The gyration on the right is in revolutions. From this equation there is no way to tell what the value of "r" is,and "n/t" is equally elusive. Experiments have apparently shown that "h/2" is the correct total value. So we have the value for angular momentum without actually knowing what it is.
"w" can be expressed in linear terms as follows as [(s/rg)/t] where "s" is arc distance. "s" would be (2pi)rgn where "n" is the number of revolutions, and "(2pi)rg" is one circumference of a circle with radius "rg".
h/2 = mrg2w = mrg2[(s/rg)/t] = mrgs/t = (mrg)[(2pi)rgn]/t = mrg2[(2pi)n]/t
Dividing both sides by "2pi" gives us
Equation 5. h/[2(2pi)] = h/2 = mrg2(n/t)
Note that w = n/t where "n" is revolutions per second.
Equation 6. ng = ns (rs/rg)1/2 according to our research on gravity.
"ns" is the value of "n/t" at rs, the Schwartzschild radius for the electron. We know that it is equal to "cts/(2pi)rs" and is 1.4339x1043. rs" is equal to 1.352956x10-57 meter. Using equation 5 to solve for "rg",
Equation 7: rg = (h/2mns)2/rs = 1.22527x10-34 meter
For more about the the electron, light, and the Schwartzschild radius, see:
In nether theory, the equation for angular momentum is the usual angular momentum, but derived in the simple fashion of the cylinder analogy above. It is based upon the idea that the tangential vector of the inflow has a certain number of "rotations" in one second at the "rg". Actually, the rotations are merely the number of complete revolutions of the spiral about the center. What is not so apparent from the equation is that "mass" is a flow of "M/t".
h/2 = mrgvg where vg is the tangential nether velocity at "rg".
Equation 8. vg = (2pi)rg(ng/t)
p = h/2 = mrgvg/(2pi)= mrg[(2pi)rg(ng/t)/(2pi)] = mrg[rg(ng/t)] = mrg2w
This is the same equation used before and the value found for rg is the same.