MORE ABOUT THE ELECTRON
Advanced Electron Theory

Back - Main Menu - Confirmation of Light as Waves

The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

There are many types of units in the world for many purposes and few of them agree. The first step in working with units is to convert to one system. This can be very time-consuming and is made even more difficult in a system which uses the same word for two different things. Therefore, when applicable, I show which thing that a particular unit is.

See Radio for more details on how systems of measurement differ between electrical theory and other disciplines.

In the final summary, the "knowns" herein will not be given to the last computed digit to the right of the decimal. They will be given to only four digits to the right of the decimal. This is not the most accurate way to show them, but every book seems to have a slightly different version of each number (or of the inputs for each number) after the first four are shown. This makes the first four to the right the only dependable ones.

Knowns

Speed of Light = c = 2.9979x10 ⁸ meters/second

Electron Mass = m_e = 9.10956x10 ^-31 kilogram
where the *kilogram is a unit of mass

Planck's Constant = h = 6.6252x10 ^-34 joule second = 6.757704x10 ^-35 meter kilogram second
where the *kilogram is unit of force

The units for Planck's constant are flawed.   See Planck's Constant.

Planck Unit of Action = h = h/(2pi) = 1.0544x10 ^-34 Joule second = 1.075523x10 ^-35 meter kilogram second
where the *kilogram is a unit of force

Planck Area = A_p = 2.66412388x10 ^-71 meter ²

Planck Length = L_p = 5.16151517x10 ^-36 meter

Gravitational Constant = G = 6.6742x10 ^-11 meter³/kilogram second²
where the *kilogram is unit of mass

*The metric system has the same name for force as for mass, unlike the English system which uses pounds for force and slugs for mass. The metric system was devised to create a standard that was "natural". Actually, the metric system is erroneous as to the "natural" part and fails to properly address the difference between force and mass. Perhaps it could be improved by calling the force unit a "Kram" and keeping the mass unit as the "gram". But truthfully, all of our current systems should be converted to new system that is more acceptable to all of the scientific/engineering disciplines.

Introduction - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

The Schwarzschild radius is the radius for any particular mass from which light cannot escape. It was originally derived for black holes, and was derived in nether theory with much less effort. With one modification, it seems to be able to work for electron mass as well as the masses of larger entities.

At the vortex center (the "hole"), nether enters at the speed of light, so it is the electron r_s that is the approximate radius of the electron "hole" into the 4th dimension. It is true that the electron r_s is well above the necessary energy level that particle physicists can reach with their accelerators, but what could they find if they were able to reach this level? The electron r_s is computed via the equation above and is about 1.3529559x10 ^-57 meter.

New "Known"

Electron Radius at "c" according to the Schwarzschild Radius = r_s = 1.3530x10 ^-57 meter

Introduction - The Schwarzschild Radius

The Light Equation - Finding t_s - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

m = (M/t) multiplied by one second = Mass or mass for one second of flow.

At r_s, both the radial inward and the tangential velocity vectors of nether velocity equal the speed of light, "c". This means that the resultant of the two is equal to 2^1/2c.

The electron is a hole into the fourth dimension. It may be visualized by its construction. First think of a circular hole - just a circle hanging in the nether. If we look at the circle from its side, so that we see an infinitely small line, on one side of the line nether motion is essentially normal. On the other side, nether is flowing into the circle in the form of a vortex. The side with the vortex is the "mouth" of the electron.

The hole moves nether through it into the 4th dimension, so the mouth of the electron may point in any direction within our three-dimensional space and does so. When entering a magnetic field, the hole orients itself for minimum energy expenditure and its mouth pulls it to the right, left, up, or down, according to the way the magnets are set up. Less energy is expended in moving the electron toward the inflow than is expended in pulling all of the inflow toward the electron mouth. So in most cases, the electron moves in the direction that its mouth is pointed.

The vortex is formed of fluid elements moving at 45 degrees to any line (radial) from the vortex center. The speed of these elements, when near the electron center, is 2^1/2c, which is the square root of two multiplied by the speed of light.

As mentioned before, near the electron center the nether element velocity vectors parallel to the radials have a magnitude of "c", the speed of light. The nether element velocity vectors perpendicular to the radials are also equal to the speed of light. Kinetic energy equals (1/2)mv². So the kinetic energy of the incoming nether at r_s is (1/2)m_e2^1/2c² where m_e is the rest mass of the electron. When simplified, this becomes m_ec². This is based upon what would happen were the hole to close - which stops the inflow and releases the energy.

The speed of light is the incoming nether velocity because it is a vector pointing at 45 degrees from the resultant. The resultant of 2^1/2c is caused by the reactive acceleration of the nether moving from a place of nether higher pressure to place of nether lower pressure. In the kinetic energy equation, m_e is a measure of Mass flow and 2^1/2c is the actual resultant velocity.

The electron "vibrates" to create a natural "photon" of light. It moves back and forth along a path. The electron moves along the path with its "mouth" forward to conserve energy. At the end of the path, after each time that it turns to go back, it creates a wave of nether acceleration that we call a light half-wave. During the turning, the vortex is taking in nether at the speed of light and, at the same time, moving the nether tangentially at the speed of light. Of course, the resultant velocity is
2 ^1/2c.

Saying this in other words, as it vibrates to create a series of electromagnetic waves (EM), the electron accelerates in one direction with its "pole" or "mouth" turned forward. It next decelerates (accelerates in the opposite direction) to a stop and begins to accelerate in the opposite direction while rotating 180 degrees so that its mouth is pointed forward again. As it accelerates and decelerates in its directions of movement, it is still taking in nether at a constant rate at 90 degrees to its directions of movement. The number of coils of incoming nether, n, just after it begins to accelerate each time are what cause a half-wave of light to have its particular value for Mass.

Therefore, n = ct_s/[(2pi)r_t] is the number of vortex revolutions (circumferences) which can move into the "hole" in time "t_s".

BACK to Planck's Constant

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

Finding t_s - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

The light equation and the mass/energy equivalency equation, E = mc², are both kinetic energy equations.   It is true that
E = mc² is supposed to show the "rest" mass/energy for the electron, but the only thing that is resting in this equation is the movement of the vortex relative to the nether around it. The vortex itself is very active as it sucks in the nether.

There are two ways to show kinetic energy, shown here as "E".   The way that we are taught in school is with the equation
E = (1/2)mv². This equation is very misleading. Nothing that is moving ever squared its velocity. A baseball in flight has kinetic energy due to its velocity we are told. The fact is, that velocity is relative and the energy in the ball can only be known when the ball hits something. Due the fact that motion is relative, it is just as proper scientifically speaking to think of the brick wall the board hits as moving toward the ball while the ball is "at rest".

The energy that is supposedly due to the ball's velocity squared is removed when the ball hits the wall. The removal of the energy is a change. Change in this universe is accomplished only by acceleration, jerk, or a higher derivative of motion.

When the ball hits the wall it suddenly decelerates. Looking at it from another standpoint, the ball accelerates to a stop. The distance through which this acceleration occurs is very short, but nevertheless there is a distance through which it occurs.

The equation E = (1/2)mv² is a mathematical shortcut that is handy to use, but extremely misleading when it becomes a supposed major fact. It came from the more "truthful" equation E = mad where "m" is mass, "a" is acceleration, and "d" is the distance through which the acceleration is applied. The mass of the baseball was accelerated to a stop through a very short distance.

If we carefully examine E = mad, we can see what happened to make it become E = (1/2)mv².

E = m a d

Acceleration is distance divided by time divided by time.

E = m d/t/t d = m d/t² d = m d/t d/t = m v v

"v" is velocity which is d/t. But the second velocity is not the same as the first. It is average velocity during the ball's acceleration to a stop. It is the first "v" plus the ball's velocity after it stopped, all divided by two: (v + 0)/2. This can be shortened to v/2 and the equation looks like this.

E = m v v/2

This, of course, is E = (1/2)mv².

It is easier to use this shortcut when calculating because one need not worry about acceleration or distance. One need only worry about the mass and the velocity, both of which are much more easily measured.

The Mass/Energy Equivalency Equation
(Also called the Mass/Energy Equivalence Equation)

E = mc² is another energy equation that is a mathematical shortcut. It is derived from the fact that nether is moving at its maximum velocity at the electron vortex center. This maximum velocity is caused by the reactive speed of the nether when it accelerates from a vicinity of higher nether pressure to a vicinity of lower nether pressure. Because we are dealing with a vortex, this maximum velocity is at 45 degrees to the inward velocity vector that creates the mass of the electron. It is also at 45 degrees from the vortex tangential velocity vector which is also "c". So the resultant magnitude of the vortex velocity is the product of the square root of two and "c".

v_maximum = 2 ^1/2c

The mass of the electron is actually a flow rate of nether Mass (with a big "M"). What we call "mass" is "Mass" per unit of time. A flow rate is a little different from a other quantities. Mass is flowing into the hole that creates the vortex. If we choose an amount of Mass that flows into the hole in one second as a standard, then our electron mass, "m_e", can be measured by M_one divided one second.

m_e = (1)M / (1) second
Dimensionally, this is m = M/t

Now if we double the amount of mass going into the electron, we have:

m_e = 2M / 2 seconds.

Tripling the amount of mass, we have:

m_e = 3M / 3 seconds.

The Mass changes and time changes, but the flow rate, m_e, does not change. The fact that the mass is flow rate is important in understanding the equations of the electron.

The maximum inward velocity vector at the electron center is the speed of light "c". This is what creates the actual flow rate rather than the resultant velocity of the nether at the electron center. But this velocity vector is merely part of the mass flow equation m = M/t, and does not enter into the energy/mass equivalency equation E = mc² except as part of m.

It is best that we remember from the discussions on gravity, that the nether flow into the electron is actually an acceleration at all points within its little gravity funnel. The Mass has accelerated from zero velocity at a nearly infinite distance to a velocity of 2^1/2c at the electron center. So the average velocity is zero plus 2^1/2c all divided by 2.

Now we can better examine the energy equation for electron rest mass.

E = m a d

E = m (2^1/2c/t) (2^1/2ct/2)

E = m 2^1/2c ²/2

E = mc ²

The reason that electron mass can become energy according to the above equation is that the hole can close under certain circumstances and the kinetic energy of the incoming nether can be converted to electromagnetic energy (light), temporary smaller vortices, or other entities such as neutrinos. This energy is very different from the energy in the light equation because one is a stoppage of inflow and the other is a transverse acceleration of the inflow over a very short time.

Compton

BACK to Electromagnetic Radiation

Hallwachs, Hertz, and Einstein arrived at the "hf " as the correct value for the energy in a photon. In 1923, Compton performed several experiments which showed that "hf/c" is the momentum in a photon. "h" is Planck's constant and "f " is frequency. The value for Planck's constant was found via experiment and has proven to be correct.

The equation for the light half-wave, according to nether theory is:

(h/2)f = m a d

"t_s" is the time taken for an electron to reverse direction 180 degrees during light propagation. Two are necessary when speaking of a full wave of light. These short time intervals serve as limiters to m_e which is rate of nether flow, so that the correct flow for the period of electron turn-around is used in equations.

m = m_e(t_s) = M(t_s/t),   a = 2c/t_s,   and d = ct_s/2 = (2pi)r_sn/2

For a frequency of one, the full wave energy is "h(1/t)", and for the half-wave the energy is "h/(2t)".

h/(2t) = m_e(t_s)(2c/t_s)(ct_s/2).

When simplified, this is:

h/(2t) = [m_e(t_s)](c ²)

which can derived also from the other energy equation

E = (1/2)mv ².

The half-wave passage relative to the observer is in two parts, one on each side of what might be called a centerline. One part is half of the half-wave energy and the other part is the other half of the half-wave energy. If the average velocity were used with the two halves together, the result would be zero because one side is the mirror image of the other and the velocities cancel one another. So one side must be computed and then multiplied by two for the total. The equation for one-half of the half-wave energy is:

h/(4t) = (1/2)[m_e(t_s)](c) ²

which, when multiplied by two for the complete half-wave energy is

h/(2t) = [m_e(t_s)](c) ²

which when simplified is also

h/(2t) = [m_e(t_s)](c ²).

If both sides of the above equation were divided by "c" as would be the case with Compton's equation for momentum:

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

Which is the same as "mv", the equation for momentum.

From a similar perspective, the half-wave energy might be considered simply "mad" where
m is m_e       a is (c/t)       and   d is ct_s.   Then

h/2t = m_e(c/t)ct_s
h/2t = m_ec²(t_s/t)
h/2t = (M_e/t)c²(t_s/t)       where m_e = (M_e/t)
h/2 = M_e(t_s/t)c²

Since (t_s/t) is actually a dimensionless fraction, dimensionally h/2 and h are both a form of energy using nether Mass rather than mass as most of us think of it today.   Of course, dividing by c provides a form of momentum.

So in a strict sense, at the level of nether Mass, Planck's constant is energy and Planck's constant divided by "c" is momentum.   When frequency is introduced, Planck's constant is divided by time and becomes a form of power.   Click on the following for a more information.

BACK to Electromagnetic Radiation

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

The half-wave equation where dimensionally:

h/(2t) = mad

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

t_s = h/(2m_ec ²)

t_s = 4.12702x10 ^-22 second

If what I consider to be the correct Planck's constant is used, then dimensionally:

h/2 = mad

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

t_s = ht/(2m_ec ²)

t_s = 4.12702x10 ^-22 second

Either way, t_s is the same.

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings

h/(2t) = (m_e)(2c/t)d

Solving for d:

d = h/(m_e2c)

d = 6.1862x10 ^-14 meters

d = n(2pi)r_s/2 = n(pi)r_s   at the starting radius for light generation.

n = d/[(pi)r_s]

n = 1.4554x10 ⁴³

New "Knowns"

Turn-around time for the electron = t_s = 4.1270x10 ^-22 second

Number of vortex revolutions in time t_s = n = 1.4554x10 ⁴³ revolutions

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n

Discussion and Conclusions - Summary of Mathematical Findings

"The Planck length, L_p is estimated (to an uncertainty of 1/13 of a percent) to be 1.6160x10 ^-35 meter. [This is incorrect but typical.] This is based upon the joule second version of Planck's constant. [Any version that is correct is supposed to obtain the correct answer.   I discovered that by using the joule second version of Planck's unit of action with an incompatible version of the gravitational constant, one can arrive precisely at this same incorrect answer.] In general relativity, it is the natural unit of Planck force giving unit acceleration to unit mass, and in general relativity, it is a key to how gravity works. It is the square root of "bar h", shown here as h, multiplied by "c" for the natural force area unit, hc, divided by the natural unit force, c⁴/G. According to John Baez, a physicist, Planck area, Gh/c³ is even more fundamental than Planck length."

Although poorly written, I believe that the above means
(1) Planck length is supposed to be equal to 1.6160x10^-35 meter[not true],
(2) Planck length is the natural unit of Planck force,
(3) Planck force is the key to how gravity works (in general relativity),
(4) Planck force gives acceleration to unit mass,
(5) hc is the natural force area unit,
(6) the natural unit force is c⁴/G,
(7) Planck area is (hc)/(c⁴/G),
(8) Planck area is, therefore, equal to hG/c³,
(9) Planck length is the square root of Planck area.

Frankly, I don't trust that book very much as I have found errors in it before.
 

The value given for

The half-wave equation above can be used with r_s in a derivation as follows.

h/(2t) = m_e(2c/t)d

h/2 = m_e2cd

Solving for d where n_s is revolutions at r_s :

d = h/4cm_e

Going back to the equation for the Schwarzschild radius,

r_s = 2Gm/c²

Solving for m:

m = r_sc²/2G

Substituting:

d = h/[4c(r_sc²/2G)]
d = Gh/(2r_sc³)
d(2r_s) = Gh/c³

d = n(2pi)r_s/2 = n(pi)r_s

Substituting:

[n(2pi)r_s/2](2r_s) = Gh/c³
n(2pi)r_s² = Gh/c³
nr_s² = Gh/[(2pi)c³]

nr_s² = Gh/c³

The above equation has the Planck area on the right.

r_s² = Gh/(nc³)

The above is an actual area devoid of any other factors. Perhaps it should be the correct Planck area except that n is peculiar to the electron and would not have the same value if found elsewhere.

If we multiply both sides of the equation by pi, we have the cross-sectional area of the electron at its Shwarzschild radius on the left, and on the right, in lieu of the planck unit of action, we have Planck's constant divided by two.

(pi)r_s² = G(h/2)/(nc³)

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n - The Planck Area

Summary of Mathematical Findings

The question arises as whether or not there is a way to crosscheck the value of "t_s".

The half-wave energy passes into the receiving electron in about 2x10^-22 second. This is a distance of about (3x10⁸)(2x10^-22) which is approximately 1x10^-14 meters or a ten-thousandth of an angstrom.

The highest known frequencies are about 1x10²². These have half-wavelengths that are essentially the same (within the limits of our ability to measure them) as the distance for the electron to travel after its turn each time. Apparently, the electron requires a certain space or time to make its turn and that is the reason for the time used which is called "t_s" here.

"t_s" should be the time used to make one half-wave of the highest possible frequency. Therefore, the inverse of the highest known frequency multiplied by 2 should be equal to t_s. The inverse of the frequency for the highest known gamma radiation appears to be very close to the correct value.

It should be remembered that the half-wave of acceleration, that is part of what we call a photon, moves outward at what is literally a crawl at the beginning and builds up speed as the distance from the electron center increases.

It seems that when producing a typical series of light waves (not the highest frequencies) the source electron sends a light half-wave just as it changes direction, moves a distance and changes direction once more, sends another half-wave, and so on. The portion of the half-wave of acceleration that is received is the same for any frequency and is caused by n complete revolutions of nether entering the vortex. The distance the electron travels between sending the new acceleration through the nether is what governs the frequency or distance between half-wave receptions.

The Schwartzschild radius for the electron may not show the true radius where the incoming nether is to equal to "c". The electron is a vortex creating a tiny gravity funnel with a cross-section, at the magnitude of r_s, that is a hemisphere. The usual gravity funnel has a cross-section that is spherical. So the electron must have a vortex radius at incoming nether velocity "c" that mimics the effect of a spherical cross-section. In other words, the cross-section at incoming nether velocity "c" may be required to have the same area as would a spherical cross-section at incoming nether velocity "c". This means that the actual r_s of the electron is probably close to the product of the square root of two and its supposed r_s. This radius can be called r_e.

Regardless, it is the r_s rather than the r_e or the actual hole radius that should be the basis of the flow into the hole for purposes of these calculations.

According to my experiments with vortices, the actual radius of the hole into the 4th dimension should be double the value of r_e and can be called r_h.

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n - The Planck Area

Discussion and Conclusions

Speed of Light = c = 2.9979x10 ⁸ meters/second

Electron Mass = m_e = 9.1096x10 ^-31 kilogram
where the *kilogram is a unit of mass

Planck's Constant = h = 6.6252x10 ^-34 Joule second = 6.7577x10 ^-35 meter kilogram second
where the *kilogram is unit of force

The units for Planck's constant are flawed.   See Planck's Constant.

Planck Unit of Action = h = h/(2pi) = 1.0544x10 ^-34 Joule second = 1.0755x10 ^-35 meter kilogram second
where the *kilogram is a unit of force

Planck Area = A_p = 2.6641x10 ^-71 meter ²

Planck Length = L_p = 5.1615x10 ^-36 meter

Gravitational Constant = G = 6.6742x10 ^-11 meter³/kilogram second²
where the *kilogram is unit of mass

Computed electron Schartzschild radius = r_s = 1.3530x10 ^-57 meter

Possible actual electron Radius at "c" = r_e = 1.9134x10 ^-57 meter

Possible hole Radius = r_h = 3.8267x10 ^-57 meter

Time for incoming nether Mass to create the light half-wave = t_s = 4.1270x10 ^-22 second
(The time for one turn-around of the electron when creating light.)

A product that remains constant = nr_s = n_er_e = 1.9661x10 ^-14 meter revolutions

Number of vortex revolutions at radius r_s in time t_s = n = 1.4554x10 ⁴³ revolutions

Number of vortex revolutions at radius r_e in time t_s = n_e = 1.029x10 ⁴³ revolutions

Incoming Mass seconds in time t_s = M_s = 3.7595x10 ^-52 kilogram second
where the *kilogram is a unit of mass.

Incoming Mass seconds in one electron vortex revolution at r_s = M_as = 2.5832x10 ^-95 kilogram second
where the *kilogram is a unit of mass.

Incoming Mass seconds in one electron vortex revolution at r_e = M_ae = 3.6531x10 ^-95 kilogram second
where the*kilogram is a unit of mass.

*The metric system has the same name for force as for mass, unlike the English system which uses pounds for force and slugs for mass. The metric system was devised to create a standard that was "natural". Actually, the metric system is erroneous as to the "natural" part and fails to properly address the difference between force and mass. Perhaps it could be improved by calling the force unit a "Kram" and keeping the mass unit as the "gram".

When working on this part of the website, I was constantly spending more time converting units, checking and re-checking the conversions, than I was spending with the theory itself. Our systems of measurement came about from different branches of science in different countries at different times and they do not easily work with one another. In fact, measuring systems are much like committees. The more there are, the more is the obstruction of progress and the obfuscation of thought. It may be said that what we have created is an abomination that is a non-system. Perhaps we can eventually find a way to have a reasonable standard system of measurement that works with all disciplines of science and engineering.

BACK - Main Menu - Confirmation of Light as Waves

Introduction - The Schwarzschild Radius - Vortex Coils and Mass

The Light Equation - Finding t_s - Finding n - The Planck Area

Discussion and Conclusions - Summary of Mathematical Findings