Fine Structure

Potential Energy

Total, or Potential, Gravitational Energy from Infinity to Radius, or Continuous Orbital

Although a gravity system, there still exists a type of "Fine Structure Constant".
When done with this analogy, I will derive the real Fine Structure Constant as is common usage.

In this scenario, only the smaller body falls, and only the smaller body is allowed to gain speed. Mass big M >> Body m.
This requirement is only for the calculations. As perplexities increase in real solar systems and galaxies, the mathematics becomes more involved. But the "Fine Structure Constant" still holds.

We begin by visualizing all the energy from a falling body unto a future planetary system. The future planetary system will consist of a planet and now a moon.

RULERMAR.GIF, 1.6kB

Stable Kinetic Energy

Kinetic Energy of a stable body in orbit, at Orbital R.

Viral Rejected Energy

ViralReject is rejected Energy, not used for matter condensation.

Half the Energy is thrown away as heat and light.

RULERMAR.GIF, 1.6kB

The process can be visualized by Stepped orbits or Continuous orbits.
The Orbiting body and the Falling body are, more or less, the same body, and definitely the same mass.
If stepped: At each orbit closer to big M, the speed of the Orbital body increases, as well as when the body is in the Falling form.
The Orbiting bodies velocity will be increased by 1/sq2, or 0.707 of the increase in the falling bodies vertical speed.
Or Instead of stepped or Continuous, you get the same result if you use one step from infinity to Max R: R1. The lowest obit possible.
Here, there are no obits in between, or I should say they were "skipped" and not used.
Here the final velocity of the Orbital is 0.707 of the velocity of light, 0.707 c.

This is by definition a "Fine Structure Constant".
However, and especially in this instance, The Fine Structure Constant is not a good name.
A better name would be a "Virility Constant".
It seems - again - that I have invented a Constant. I can not help it if it encompasses an already named constant: The Fine Structure Constant. I invisioned a different domain: One of infinite radius. A Virility constant of Cosmological significance.

Here the Radius R1 is at the outer Event Horizon.
The First Event Horizon is at R0.
In between these two Event Horizons is a lot of plasma.
In between these two Event Horizons are several xray spectral bands.
This band of the "Outer" Event Horizon has the least energy.
This Outer band represents atoms, and pieces of planets.
All of the bands will be red shifted with the xrays produced in heavy gravity as they leave the black hole.
The amount of red shift may be used to calculate the mass of the black hole.

This is an energetic band, the nucleus band:
The band is at 1/2m(alphag*c)^2, m=mass of lightest atom: a neutron or proton, minus red shift.
Nucleus Band = 3.76E-11J = 2.34E8 eV = 2340KeV , WaveLen=3.52E-23m
There will be a band for each atom and isotopes, up to about Fe. Then they will smear together, and not be practacal to resolve.
The xrays will start at a rediculously high level and just get worse.

There should be another band composed of free Charged particles: electrons.
I have already developed the charged particle section down below, but I will show some derived data here...
This band will be lighter in visable contrast due to a sharper line, but because lighter in energy, detector aparatuses should be able to detect it sooner someday.
They travel at velocity alphag*c, but they convert their Charge energy to light with alphac, or FineStructure contrast.
Their energy is 1/2m((alphag+alphac)c)^2, - minus red shift.
Free Charge band energy is 2.09E-14J = 1.30E+5eV = 130KeV, WaveLen=6.34E-20m

These are my predictions...

Charge

Fine Structure Constant

With gravity, any orbital or radious is permitted.
A proton or electron in a gravitational orbit, can have any radius, any energy and speed.
And is governed by my 0.707 ratio of speeds.
And this 0.707 speed ratio will be the case with Charge too, in specific cases.

Consider an ionized hydrogen atom with no electron.
Consider a charge of one electron falling from deep space.
It can also fall from a specific Orbital as well.

The obital energy will only be specific energies as dictated by the structure of an atom.
The Reject energy will be the same as the Obital energy.
The Reject energy will be quantized, and be one photon, and be one specific energy and color.

Potential Energy

Total, Potential Energy

Kinetic Energy

The over simplified Bohr orbit works perfectly.

A Bohr Centripetal requirement for bound rotational orbit.

Notice that the Orbital Electron Kinetic energy, in an equivalent Bohr orbit or in a quantum Orbital, is half the Total energy.
This "Virility" feature is the same as Gravity.

Also, the equation does not talk about the difference between an "Obital" and a "Radius".
In hydrogen, a complete description is not necessary, and does not effect my topic of Virility.

Reject Energy

This is the Reject Energy.

And it is equal in magnitude to the Kinetic Energy.

Here I measure the Bohr radius.

With the radius, here I measure the Energy, in eV.

I will not use the explicit value in my calculations. I just like to "feel" the immediate value, digested and available, as I progress along the way. I will keep the equations implicit, with full variable disclosures, and few abbreviations.

There are several forms for the Kinetic Energy of the electron bound in the atom.

I have spent some time developing the Reject Energy. As it is so important to the next section. This energy will leave the atom.

This energy will be known and measured in another way: Line Spectral Energy.
Accurately known quantity is the Spectral Line Energy for this orbital E(R).
This is the Reject Energy. The energy emitted and thrown away between bands. This is a one time event; Of a radiation emission .

And I will equate this Rejected energy, which is in the form of light, to the energy of Line Spectra. And I will derive the Fine Structure Constant in the next section: Virility.

Virility

As the electron vibrates or travels in an orbit with an electron speed of v, it produces a frequency f of charge change. This f is exactly the same f frequency as if, or when, it is radiated as electromagnetic radiation with a velocity of c. The alpha will compensate for the slower speed of the electron, compared to a photon at the speed of light, with the same frequency. The alpha will compensate and equate the same energy for an electron in orbit, to the energy of a radiated photon.

Same frequency.

WaveLengths are different.
WaveLength of electron will be way less than WaveLength in free space.

Velocities are different.
The velocity of electron is v, and velocity of photon is c.

Once we have established the fact that the frequency is the same between the electron obital and the emitted light, we necessarily have created a conversion factor: alpha, the Fine Structure Constant. And it is not hard, as many have stated. I have shown each and every little step. It is easy. The Fine Structure Constant allows us to conveniently change from one energy form to another. We can convert a changing-charge Energy to Light Energy.

Virility Constant is a better name. Virility is a more General term expressing Causality and Entropy.

It has to be dimensionless.

And involved in the creation of Matter. Which is the allocation of Mass, and condensation of Mass.

RULERYEL.GIF, 4.2kB

Some constants that I used in this work.

Wikipedia, and other sources, have the Dimension of Time as -4. This is wrong! Should be -2.