LIGHT AND ELECTRON SPIN
(Light/Electron Theory Update)

Copyright (C) 1999, 2000, 2001, 2002, 2014
by Lew Paxton Price and Herbert Martin Gibson

Last updated April 2, 2014.

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Electron in Its Home

A lightwave is produced by an electron. The electron is a vortex that is bringing into its center many revolutions of dynamic ether (nether) all the time. Most electrons are found in atoms where each manages to exist within its own limited volume of space (space that is filled with nether). The atomic nucleus is about 10^-15 meter in diameter. Each atom is about 10^-10 meter in diameter. Each electron center is about 10^-57 meter in diameter. These measurements imply that there is a lot of room between an atomic nucleus and its outer most electrons.

Electrons reside within their own energy levels ("orbits"). The outermost energy level causes the valence part in chemistry. Electrons far away from the nucleus can generate light when activated with enough energy to rise outward within its residence much like an energetic rubber ball might rise within a funnel. When it is no longer provided with excess energy, it falls back into the bottom of its funnel while bouncing back and forth from one "side" of the funnel to the other.

As the electron bounces, it must move first in one direction, and then move back the way it came. This process continues as it moves from the top of its residence to the bottom. This is a vibrating electron that is creating a lightwave. As it rotates, its "mouth" turns from pointing in one direction to pointing in the opposite direction - and it generates a half-wave of light. For convenience sake, I will call the first direction in which it moved "north" and the second direction "south".

When the electron moves north, its nether may be incoming in a clockwise revolution. When it moves south, its nether may be incoming in a counterclockwise revolution. No one knows which is the actual direction of revolution of the incoming nether, but it changes according to the direction the electron is moving. So as seen from our viewpoint, when the revolution is clockwise and the electron is moving northward, the incoming nether direction is to the right. When the electron is moving southward, the incoming nether direction is to the left. This change in incoming nether direction moves outward as a half-wave of light.

Electrons prefer to move in the direction their mouths are pointing because it requires less energy to do so (there is less nether inertia to overcome). So the electron begins by moving north, rotates to create a light half-wave, moves south, rotates to create a second light half-wave, moves north again, and continues this cycle until it arrives back at the bottom of its residence within the atom. The half-waves combine to become full-cycle lightwaves and a "photon" of light is born.

The energy in the a lightwave comes from the electron rotations. The frequency comes from the number of times in one second that the rotations occur. The number of times in one second that rotations occur is a function of the time an electron requires to travel from one rotation to the next. Today, the energy in two rotations is Planck's constant divided by one second of time. This convention is a mistake. It should have been set up to have the time divisor incorporated into Planck's constant. But hindsight is always better. This will be explained in detail when we get into red shift.
 

A Short History

Planck introduced his constant in 1905 to explain the distribution in frequency of radiant energy in a cavity of a body as a function of the temperature of that body.   He found that he could derive the correct law of distribution with two assumptions: (1) each oscillator producing the radiant energy can possess only discrete amounts of energy or "nhf" where "n" is an integer, "h" is Planck's constant, and "f" is the frequency of that oscillator, and (2) the probability that an oscillator has the energy "nhf" is proportional to e ^{- nf / kT} where "k" is the Boltzman constant and "T" is the absolute temperature.

Bear in mind that Planck was experimenting with many oscillators (electrons) providing light in many frequencies over a period of time that was not exactly one second in duration.   He was using temperature to measure the energy.

In the 1880's, Wilhelm Hallwachs and Heinrich R. Hertz discovered the photoelectric effect.   This was analyzed further by later experimenters.   Incident light can eject electrons from metals.   The velocities of these electrons are independent of the intensity of the light but increase with its frequency.   The number of electrons ejected per unit time is proportional to the intensity of the light.

In 1905, Einstein proposed that the photoelectric effect was caused by light concentrated in bundles or quanta, of energy "hf", where "h" is Planck's constant and "f" is the frequency of the light.   Each of the bundles can be absorbed only as a whole and by an individual electron.   Thus the absorbing electron is given an additional kinetic energy equal to "hf".   In passing through the surface barrier of the metal, the electron loses from this energy a portion which can be designated as "hf_o".   The kinetic energy with which the electron emerges is then given by:

E_k = (1/2)mv² =   h ( f - f_o )

This gives the maximum energy of ejection, since electrons can also lose some energy inside the metal before reaching the surface. The equation indicates that unless "f" is greater than "f_o" the electrons cannot escape, so there exists a low frequency limit for the ejection of any electrons.   The equation gives no reference to the intensity of the light, but gives the energy of the ejected electrons in terms of frequency only.

This expression, when later modified to take into account the various energies possessed by the electrons before they absorb the light, agreed with the results of the experiments in detail.

The author of some paragraphs in Encyclopedia Americana states:   The equation itself, however, is completely paradoxical from the point of view that regards light as an electromagnetic wave and the electrons as charged material particles. [In nether theory, there is no such paradox.]

In the foregoing, neither Planck nor Einstein considered the possibility that in the energy they were attributing to "hf" they should have considered "h" to have "1/t" included as part of it and "n" to be separate.

Eddington published his book, The Expanding Universe, in 1933.   Hubble's work with red shift came even later.   The idea that "hf" is energy created the notions of energy being lost just because wavelength is lengthened.   The theories which followed were the result of a foundation in which math only was used to determine reality.   When "hf" is understood as being a what it actually is rather than just energy when applied to red shift, logic may again prevail.   We should always beware of the integer one which is our Achilles heel in math and which, when applied to time, can be very misleading.

According to the Encyclopedia Americana:
"The next extremely important fundamental contribution which came from the field of X-ray research was made by Arthur Holly Compton in 1923. It had already been observed by Joseph Alexander Gray (1920) that short wavelength X-radiation, after scattering from carbon and other low atomic number atoms, was somewhat more absorbable than the primary radiation, but still of a "hardness" so clearly related to the primary radiation as to exclude its being a characteristic fluorescent radiation from the scatterer.

"Compton gave the following daring explanation of this effect. He supposed the bundles of radiation energy, "hf ", instead of being associated with spreading waves, to be propagated through space from the source in the form of projectiles. When one of these projectiles (or "photons"), each with momentum "hf/c", was scattered by a loosely bound electron in some low atomic number scattering material such as carbon, the electron would recoil under the impact, the more so the larger the angle of scattering and the higher the quantum energy (and hence the momentum) of the projectile. The kinetic energy thus given to the electron at the expense of the photon explained the "softening" of the scattered radiation in a completely and quantitatively correct way.

"Using characteristic line radiation from a molybdenum target tube, Compton showed that in the spectrum of the scattered radiation there appeared lines each of which was shifted toward longer wavelengths than its corresponding line in the primary radiation by an amount in complete accord with his theoretical explanation.

"The recoil electrons were also detected and shown by Compton and Simon to have the requisite speeds and directions of recoil. Even more than this was ascertained, for Jesse W. M. Dumond and Harry A. Kirkpatrick succeeded in showing that the shifted line above referred to was notably broader than the unshifted line and this was satisfactorily explained by them (with complete quantitative verification in all respects), to be due to the randomly directed velocities possessed initially by the atomic electrons which were the agents that scattered the photons. The presumptively dynamic character of the electronic clouds in atoms both for gases and for solid metallic bodies was thus experimentally verified."
 

Enter Dynamic Ether (Nether)

The product of Planck's constant, "h", and frequency, "f ", equals the energy in a photon. The product of Planck's constant and a frequency of one is the kinetic energy, E_k, 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 nether. Two adjacent acceleration reversals create one lightwave.

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 that the electron is moving between reversals in direction cause the length of the half-wave or wave. One movement of the electron from one reversal to the next is what creates half of a wavelength of the light being produced. Two movements between consecutive reversals creates a complete wavelength of light.

Very near the center of the electron vortex, transverse 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 to 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, which is "t_s".

This is not a true change in velocity for any particular volume of nether, but 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/t_s" appears to be an "acceleration" when using dimensional analysis, such an acceleration would far exceed the reaction speed of the nether.

A single lightwave has a frequency of "1/t". So its energy is

h(1/t) = E_k = mad     (mad is the general formula for energy) This time, the specifics are
m_e = electron mass,   m_e(t_s/t) = Mass entering the electron in time "t_s",
2c/t_s = acceleration,   and   ct_s/2 = distance the acceleration pushes the average for the mass.

The distance is velocity multiplied by time. The velocity is "c" and the time is "t_s". It represents the length of the Mass that must be accelerated as it is entering the electron center. The distance "ct_s" is divided by 2 because the lead end of it moves into the center at the beginning of the electron reversal and the tail end does not move into the center at all during the electron reversal. The average is "ct_s"/2.     (0 + ct_s)/2 = ct_s/2.

With a half-wave, the frequency is "1/(2t)".

h/(2t) = mad
h/(2t) = [m_e(t_s/t)](2c/t_s)(ct_s/2)

which reduces to

Equation 1.       h/(2t) = [m_e(t_s/t)]c²
 

Moving Outward

The equation necessary to show the nature of Planck's constant is the one above. Planck's constant is a very strange creation considering what it is supposed to do. When physicists discovered that the energy in a "photon" can be found as "hf" where "f" is frequency, they made it possible to separate "h" and "f" so that "h" has the units "md²/t" in which "m" is mass, "d" is distance, and "t" is time. Frequency has always been "n/t" in which "n" is the number of events and "n/t" is the number of events in one second. So the product of "hf" is "m(d²/t²)" which is "mv²", kinetic energy.

When theoretical physicists created "hf" as energy and separated "h" and "f", the energy for a single lightwave became "h/t", forcing "h" to have the units "md²/t" which is neither energy nor momentum. Energy is "m(d²/t²)" and momentum is "m(d/t)". If theoretical physicists had incorporated "1/t" into "h" it would not be a bastardized hybrid and "hn" would be the energy in a photon of any time duration. This would remove the confusion caused by a photon that is limited to one second versus a natural photon which is never one second in duration. It would also eliminate the problems some physicists are experiencing with red shift.

The energy in a half-wave of light is that in the equation     h/(2t) = [m_e(t_s/t)]c².

The energy in a full lightwave is that in the equation     h/t = 2[m_e(t_s/t)]c².

By multiplying the above "h/t" by "n", we have the energy in a photon. But this energy must have a means of being transferred from one point to another through the nether. So momentum is employed as a means to do so. As the acceleration "2c/t_s" moves outward as a half-wave of light, it affects the momentum of the outward moving "ripple" that is the half-wave mass. The acceleration that is for the half-wave moves through each circumference of incoming nether at the speed of light "c" - and "c" is the velocity vector of the reactive speed of the nether itself, and does not change.

This acceleration moving outward at speed "c" is like a "thickness" for the mass that is accelerated at each circumference. This thickness (the "ripple") has the same dimension at all distances from the electron center. Unlike the theoretical spheres used to illustrate gravity in which nether compression is at work, with single electron inflow there is no appreciable compression of nether. So the half-wave mass of the outward moving ripple grows in direct proportion to its distance (radius) from the source electron center. The distance the mass of the ripple moves in a tangential direction decreases in direct proportion to its distance (radius) from the source electron center. The distance it moves tangentially is a function of the change in its tangential velocity. So the momentum "mv" remains constant for the light half-wave regardless of the distance of the ripple from its source.

Because energy is a function of velocity squared, the energy in the half-wave decreases as it moves outward because the tangential velocity of the half-wave decreases. This is not a problem. As the ripple approaches a receiver for the half-wave, the receiver's consequent ripple takes the momentum of the half-wave. This new ripple grows shorter with its mass decreasing, causing the tangential velocity to increase. Momentum remains constant, but the interchange between mass and velocity causes them to give the receiving electron the same amount of energy that was there at the start of the half-wave's journey.

See The Light Equation
 

Theoretical physicists agreed that the energy of a lightwave is "h/t" and that "h/ct" is the momentum of a lightwave. But energy is supposed to have the formula (1/2)mv² when momentum has the formula "mv". In the case of light, according to the experimental results momentum is "(1/2)mv" rather than "mv".

h/t = 2[m_e(t_s/t)]c² is energy.   And

h/ct = 2[m_e(t_s/t)]c is momentum.

These means that momentum is half the size that it should be. The question is why? This implies that either Planck's constant is half as large as it should be, or that Compton's momentum should be twice as large as it should be.

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 one another, this is about the only way that momentum can be measured.

Compton's work in discovering momentum has been satisfactorily verified and appears to be correct. The Hallwachs and Hertz experiment in discovering the photoelectric effect is based upon proportions rather then absolutes. The velocities of the ejected electrons increased with the frequency of the light. What if the velocities of the electrons were based upon half-waves of light providing their ejections? This might explain the paradox.

The answer is that all of the experimenters were correct. Momentum is "mv" and "v" is relative. As the half-wave passes by we see only the "v" relative to us. It can be to the left or to the right, but it must be one or the other. Between half-wave passages, and relative to us, the mass of the ripple is moving tangentially in one direction at velocity "v". Its momentum is "mv" relative to us. After the next half-wave passage, relative to us, the mass of the ripple is moving in the opposite direction at velocity "v" with momentum equal but in the opposite direction relative to us. We only see momentum as "mv" after each passage of a half-wave.

If we go back to the beginning of the momentum at the electron Schwarzschild radius, we find that it is equal to m_e(t_s/t)c relative to us. This is precisely the correct momentum relative to us, but it will be in only one of two directions that oppose one another. So what Compton measured was what we can see relative to us - which is half what it should be in the strictest sense. The actual change in momentum is

2m_e(t_s/t)c.

For more information, see:

Black Holes - More about the Electron

 

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 with 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 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.
 

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

 

 

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