Electron Radius Calculated from Gravity
Posted: Tue Sep 16, 2014 5:42 pm
Executive Summary
The radius of an electron is calculated to be 10^-42 meters by using the gravitational force between two half-electrons that orbit a common center.
Summary of Part One and Part Two
An electron is modeled in Part One as two uncharged masses and the gravitational force between them is calculated using a spin rate of the inverse Planck Time. By setting the gravitational force equal to the centrifugal force of a rotating pair of half-electron masses, the radius is calculated to be 10^-42 meters. That radius is less than a Planck Length, which is permissible.
In Part Two, these uncharged masses are modeled as two bar magnets that repel. The spinning magnetic object generates an electric field which is perceived at a larger scale to have an electrical charge of -q.
By adjusting the magnetic repulsion force inside the electron, and by adjusting the spin rate to be slower, the radius can be changed. The gravitational attraction is balanced by the magnetic repulsion so that the electron does not collapse. Bar magnets are used as a model for a general repulsive force, but that can be modified.
Background for Part One
Classical physics are used to calculate the radius of an electron. The basis for this calculation is done with the simple equations:
F=Ma
Force equals Mass times acceleration. Units kg*m/(s*s)
F=G(M1*M2/(r*r)
Force of Gravity from Issac Newton
G is 6.673*10^-11 (m*m*m)/(s*s*kg)
M1 is half Mass of an electron = 4.555*10^-31 kg = M2 = M
F=M*r*w*w
w is omega, the angular velocity in radians per second
r is the radius of an electron = unknown
F is centrifugal Force
The Calculation When Charge is Not Considered (Part One)
Set force of gravity equal to the centrifugal force of the spinning pair of half-electron masses.
M*r*w*w = G(M*M/(r*r) = F (Equation 1)
divide by M
r*w*w = G*M/(r*r) = F (Equation 2)
multiply by r*r
r*r*r*w*w = G*M
divide by w*w
r^3 = G*M/(w^2)
therefore the radius is
r = cube root(G*M/(w^2))
G is 6.673*10^-11 (m*m*m)/(s*s*kg)
M is 4.555*10^-31 kg
f = inverse Planck time is 1/(5.4*10^-44 seconds) frequency
Assume w is f radians per second as a starting approximation.
r = cube root((6.673*10^-11 * 4.555*10^-31 )/((1/(5.4*10^-44))^2) meters
simplify
r = cube root((6.673*10^-11 * 4.555*10^-31 )*(5.4*10^-44))^2) meters
coefficients 6.673*4.555*5.4*5.4 = 886
powers of ten -11-31-44-44 = -130
r = cube root(8.86*10^-128) meters
r = 3*10^-42.7 meters
simplify exponent
10^-42.7 = 10^-42 * 10^-0.7
10^-0.7 = 0.2
r = .6* 10^-42 meters
r = 6*10^-43 meters
$$$$$$$$$$$$$$$$$$$
The Planck Length is 1.6*10^-35 meters
So the calculated electron radius is 27 million times smaller than a Planck Length when the electrical charge is ignored.
Part Two
Electron Radius Calculation using Gravity Plus Electromagnetic Effects
(to be finished later)
The gravity attracts the two masses and here in Part Two, a magnetic repulsion is added to the model. To increase the radius of the electron, the repulsion can be increased or the w angular frequency can be increased. But this dos not seem to result in the radius increasing to a Planck Length.
To be continued... maybe.
Part Three
Relativistic Effects on the Calculated Radius
The two masses are moving quickly. If they approach the speed of light, the masses increase. In Equation 1, the gravity increase with the square of the mass, but the centrifugal force is linear with mass. So increased mass makes the radius larger.
The radius of an electron is calculated to be 10^-42 meters by using the gravitational force between two half-electrons that orbit a common center.
Summary of Part One and Part Two
An electron is modeled in Part One as two uncharged masses and the gravitational force between them is calculated using a spin rate of the inverse Planck Time. By setting the gravitational force equal to the centrifugal force of a rotating pair of half-electron masses, the radius is calculated to be 10^-42 meters. That radius is less than a Planck Length, which is permissible.
In Part Two, these uncharged masses are modeled as two bar magnets that repel. The spinning magnetic object generates an electric field which is perceived at a larger scale to have an electrical charge of -q.
By adjusting the magnetic repulsion force inside the electron, and by adjusting the spin rate to be slower, the radius can be changed. The gravitational attraction is balanced by the magnetic repulsion so that the electron does not collapse. Bar magnets are used as a model for a general repulsive force, but that can be modified.
Background for Part One
Classical physics are used to calculate the radius of an electron. The basis for this calculation is done with the simple equations:
F=Ma
Force equals Mass times acceleration. Units kg*m/(s*s)
F=G(M1*M2/(r*r)
Force of Gravity from Issac Newton
G is 6.673*10^-11 (m*m*m)/(s*s*kg)
M1 is half Mass of an electron = 4.555*10^-31 kg = M2 = M
F=M*r*w*w
w is omega, the angular velocity in radians per second
r is the radius of an electron = unknown
F is centrifugal Force
The Calculation When Charge is Not Considered (Part One)
Set force of gravity equal to the centrifugal force of the spinning pair of half-electron masses.
M*r*w*w = G(M*M/(r*r) = F (Equation 1)
divide by M
r*w*w = G*M/(r*r) = F (Equation 2)
multiply by r*r
r*r*r*w*w = G*M
divide by w*w
r^3 = G*M/(w^2)
therefore the radius is
r = cube root(G*M/(w^2))
G is 6.673*10^-11 (m*m*m)/(s*s*kg)
M is 4.555*10^-31 kg
f = inverse Planck time is 1/(5.4*10^-44 seconds) frequency
Assume w is f radians per second as a starting approximation.
r = cube root((6.673*10^-11 * 4.555*10^-31 )/((1/(5.4*10^-44))^2) meters
simplify
r = cube root((6.673*10^-11 * 4.555*10^-31 )*(5.4*10^-44))^2) meters
coefficients 6.673*4.555*5.4*5.4 = 886
powers of ten -11-31-44-44 = -130
r = cube root(8.86*10^-128) meters
r = 3*10^-42.7 meters
simplify exponent
10^-42.7 = 10^-42 * 10^-0.7
10^-0.7 = 0.2
r = .6* 10^-42 meters
r = 6*10^-43 meters
$$$$$$$$$$$$$$$$$$$
The Planck Length is 1.6*10^-35 meters
So the calculated electron radius is 27 million times smaller than a Planck Length when the electrical charge is ignored.
Part Two
Electron Radius Calculation using Gravity Plus Electromagnetic Effects
(to be finished later)
The gravity attracts the two masses and here in Part Two, a magnetic repulsion is added to the model. To increase the radius of the electron, the repulsion can be increased or the w angular frequency can be increased. But this dos not seem to result in the radius increasing to a Planck Length.
To be continued... maybe.
Part Three
Relativistic Effects on the Calculated Radius
The two masses are moving quickly. If they approach the speed of light, the masses increase. In Equation 1, the gravity increase with the square of the mass, but the centrifugal force is linear with mass. So increased mass makes the radius larger.