Derivation of Gravity

Derivation of the gravitational constant, G

This page is a continuation of the last page. But here I have clarified, made it simpler, and discovered that I can eliminate the Kodi explanation. RULERMAR.GIF, 1 kB
EqComptonWave.gif, 2 kB
I will start, as before, with the Compton Wave Length.

EqrComptonNeutron.gif, 2 kB
The compton wave length can be used with any mass.
For example: the neutron wavelength.

And I have chosen the neutron for a reason. The neutron has no charge. It is relatively stable, half life of minutes. And no spin. I want no compositions, unless they are complete.
The compton length is an energy length, that when converted to photonic light can be visualized in one dimension. But, at rest can be visualized in a static sense as a circle in two dimensions.

EqrPlankLength.gif, 3 kB
Gravity is three dimensional. And any "length" must be converted to three dimensions. The planck length is a "gravity" length, and as such can be visualized in three cartesian dimensions.

(Planck-length is simply derived from "compatible-units".
and I will later use it to find G.)

PlanckLength, 3 kB EqrPlankGrav.gif, 2 kB

Two lengths:
RulerGrn4.jpg, 12kB EqPlankLengthGrn.gif, 2.5kB
Planck Length: a Gravity length, a Mass length
RulerPur4.jpg, 11kB EqComptonWavePur.gif, 2.0kB
Compton Length: an Inertial length, momentum, energy

I reasoned that I needed a specific mass type unit to put into the compton wave length equation. mQuestion.gif, 666B

Most of the mass of substances can be represented by the nucleus with its neutrons, and Protons-plus-electrons.

Eq-PlankAndCompt.gif, 3.0kB
This is true whether measurements have been made using the iron and nickel of the earths core, platinum-iridium in experiments, or brass balls in experiments. A "nuetron-mass-unit" is just as easy and comparable as the atomic mass unit based on carbon-12.

EqrPlankCompton.gif, 2.9kB
The mass of the neutron was substituted into the planck equation.
And the two lengths were set equal to each other in principle.
I told the computer: "Make them equal."
And I did not care HOW it did it!
I stood back and let the computer run with it.

My computer came back, and said there was a simple relationship between Planks gravity Length (of the Neutron) and Comptons Wave Length (of the Neutron). That relationship was a simple factor of the square root of three halves times 10 minus 20. My computer had mined its data base with countless permutations, and presented me with this...

EqrPlankCompton.gif, 2 kB VectorSqr3.gif, 2.9kB
A unit length in three dimensions is sqrt three.
A unit length in two dimensions is sqrt two.
The gravity length must be multiplied by sqrt three.
At the same time, divided by the "two dimensional" sqrt two.

I have no explanation for the E-20.

EqKkodieP1.gif, 3 kB EqKodieP2.gif, 2 kB Equation NeutronG, 3 kB
Combining the two equations...
Solving for G...

Dividing up the coefficients a little differently...
(The 8 pi has a nice look.)

Eq-GNeutron.gif, 3.5kB
I will call it the "Neutron-G equation", and it is for only ONE mass.
...Which brings up an interesting point:
According to the equivalency principle, this equation should not exist: There is no difference between inertial mass and gravitational mass. Gravity should not depend on an arbitrary mass.
Perhaps the Neutron is "representative" somehow.

Here is my formula value of the formula Gravitational constant for the neutron.
EqrGravNuetron.gif, 3 kB
Which is close to the G=6.67387(0.00027)E-11 Armstrong2003

The last accepted empirical value of Codata - 2006.
EqrGravCodata.gif, 3 kB
A few years have passed. Here is the Codata-2010.
EqGravCodata2010.gif, 2.3kB

All in agreement to all known digits of accuracy.

There are two ways to get this value.
Left: Keplerian, Real World example ______________________ Right: Units, Dimensional Analysis
Kepler.gif, 13kB
UnitsPlanck.gif, 15kB

There are two ways to get this value.
I guess I will call one the "Newtonian" way, and the other the "Units Derived" or "Dimensional Analysis" way.
And they are exactly the same if you only conceder the total energy:
both kinetic and potential.
We are only dealing with a handful of variables, but it still always nice that they agree!

Eq-PlancksMass.gif, 4.3kB
To be fair; Coefficients are not explicit in the Dimensional Analysis way. And, consequently, the choice of the neutron is arbitrary.

However, the Newtonian way from known physics is explicitly "complete".

Along the same lines...
You can see the Planck Mass.

Although all this is very exciting...
Please; Do not take what you see above as gospel.
I am the first person, that I know of, to conceder the neutron in this light.
You know that I could be wrong...
And that is exactly what I need to talk about next.

Miners.jpg, 75kB
A Great Artist: Alfredo Rodriguez
Mining data...

It is not in the spirit of science; it is total HERESY!
I have degraded myself to an opportunistic vagabond, freely skating around in the realms of science.
Most would object to the ethics - and very intensely.

BadDog.jpg, 42kB
Irreverent, disruptive - Bad dog.
The fabric of the science being assaulted!
I continually insist that it is not my fault.
Before computers, the issue never would have even came up.
If it is not now happening with me, it will - for sure - be happening in the future with the advancement of super computers.

Science: A most sacred art, and those in it's presents are honorable. The most sacred of all disciplines; NEVER cheapened by cutting corners.

I love science, and would never do anything to hurt it, if I could not help it. Admittedly, there are some things that I can not help.

How reasonable is it?

For example:
BBALLBLU.GIF, 139B What are the odds of a match of "6673", in all 4 digits,
BBALLBLU.GIF, 139B with 1,000 tries,
BBALLBLU.GIF, 139B from a replenished (equal) pool?

What are the odds to find "Fools Gold"?

Eq-BDistribution.gif, 2.7kB Eq-BDistCoefecient.gif, 2.1kB
I am going to search approximately a Thousand Times for a single match. That single match is composed of four digits, and that criteria has exactly a ".0001" odds of being a match.

Eq-BDistribution-n.gif, 2.7kB BBALLBLU.GIF, 139B Tries or events, n=1000
This is hard to estimate. In the computer, the search targets are recursive and convoluted. Precision criteria is not always the same, and the "tries" are not always the same.

Eq-BDistribution-p.gif, 2.7kB BBALLBLU.GIF, 139B 1 in 10000 odds for all 4 digits, p=1E-04
I have another digit of accuracy, but the experimental criteria, which it is compared, is only four digits.

Eq-BDistribution-k.gif, 2.8kB BBALLBLU.GIF, 139B The 4 digits are lumped together and taken as all at one time, k=1
I choose this for simplicity.

Eq-BDistCoefecientE.gif, 2.6kB Eq-BDistributionE.gif, 2.6kB
Substituting the values from above into the equation...

The odds are VERY high (9%) of accidently hitting pay-dirt!
Actually, Fools Gold.
It is relatively easy to obtain Fools Gold.

But... "Thats my story and I am sticking to it."