Solution to Proton Radius Puzzle and 8 Fundamental Physics Constants from Theory/Algorithm- Narrated

YouTube narration of solution

The Surfer, OM-IV
©2021 Mark Eric Rohrbaugh & Lyz Starwalker © 2021

"This is How We Do It"

"I'm So Paid"

Send your extra bitcorn to: 19oBJbAMmpkz5n47AfDuLDaBikBBQrFPyy

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This Is How It's Done - Basic Code - Full Rydberg Equation Roots, part 3

Basic Program  <-- Load this basic program into the online basic interpreter at: http://www.calormen.com/jsbasic/ or use your own basic interpreter.  Will use this code to create the MS Excel macro/VBA document later.  It's a BASIC numerical iteration program that uses the sign-flip algorithm to solve for the roots of the Full Rydberg Polynomial. Erdos number TBD (IEEE references, Patents?).

Click the "Show output" button for more readable and total output log.

Full Rydberg Polynomial

For now, the results for the roots for our most recent re-derivation:

(mks units)

elementary charge, e=1.6022514387454(393)e-19  

Planck's constant, h=6.6257738721130(28)e-34  

electron mass, m_e=9.1097907336274(77)e-31  

Proton radius, r_p=8.4119972191308(31)e-16  

Rydberg constant, R_H=10973241.071596(634)  

Permittivity of free space, epsilon_0=8.8537920581144(05)e-12  

Speed of Light, c=299779058.06636(304)  

Fine-structure constant, alpha=0.0072976787382677(79)  

Digits resolution 14

Calc'd proton mass= 1.6726933172773(2)e-27

NIST   proton mass= 1.67262192369(51) x 10-27 kg

Final  fine-structure constant= 0.0072976787382677(79)

Input  fine-structure constant= 0.00729735256  (compare to above line)

Proton/electron mass ratio=1836.1490029653(637)

The Surfer, OM-IV
©2021 Mark Eric Rohrbaugh & Lyz Starwalker © 2021

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This Is How It's Done - FRED* - Full Rydberg Equation Derivation, part 2

Goog calc link for Rydberg Poloynomial

Notice the Rydberg Polynomial only adds up to 0.999455406 

$1={{m_ee^4\over 8{\epsilon_0}^2h^3cR_H}}-{\pi r_pR_H\over \alpha^2}$

This is due to the orignal Rydberg Constant equation, which is incomplete, has adjusted ALL of the constants so that it equals 1:

Goog calc link for Rydberg Constant Equation

This ignores the proton radius and how it is connected/correlated to the other fundamental constants.

Note that it is tuned (ignoring precision of value used for proton radius for the moment) to:

Goog calc link for closeness to 1

...within 1.862e-10 of 1.0, thus, mainstream's most prized constant is a tweaked hack of theoretical and emperical work and measurements.

Once the correction is made to the equation to account for the proton radius, then the theory agrees with measurements more closely and some anomalies are simulatenously resolved. 

Still to be peer reviewed, however, by inspection, dropping the electron mass to proton mass ratio from the derivation like the mainstream does with their reduced mass assumption (to allow for an analytical solution to the wave equaitons and the creation of the Solid-State theory, which is of major practical importance and for all practical purposes works but for all of the finest of measurements) was a bad idea. Good for technology, not so good for theory.

The stabilty and uniqueness of the solution is being revisited, and plan to present a working Excel spreadsheet to demonstrate this numerical methods solution. So, the error can be kind of forgiven since it requires iteration on a computer, computers which were not available (or readily available) when the original work was done back in the 30s, 40s, 50s. No excuse in the 60s and 70s when some of the theory was "finalized". It hardly seems like science, more like a captured dogma.

*Fred gets credit for asking me if I could solve for what mass is, a Feynam problem, which happened to coincide with my search for a derivation of the proton to electron mass ratio.

Moar later.

(forgive the repeats from earlier posts, however, this approach is more concise and less scattered)

The Surfer, OM-IV

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This Is How We Do It - FREE - Full Rydberg Equation Extracted, part 1

The Rydberg constant for hydrogen, from:

https://en.wikipedia.org/wiki/Rydberg_constant

$R_M=$ Rydberg constant for reduced Mass(?)

$R_\infty=$ Rydberg constant for heavy atoms

$R_H=$ Rydberg constant for Hydrogen

$m_e=$ mass of electron

$M=$ Mass of nucleus

$m_p=$mass of proton

$\alpha=$ Fine structure constant

$r_p=$ proton radius

$\epsilon_0$ = Permittivity of free space

$h=$ Planck's constant

$c=$ speed of light

$e=$ electron charge, fundamental charge

$\pi=$ 3.1415926535897932384626433...

$1=$  1.0000000000000000000000000...

From wikipedia page on the Rydberg constant:

$R_M={R_\infty\over {1+{m_e\over M}}}$

$R_H=R_\infty{1\over {1+{m_e\over m_p}}}$

$R_H=R_\infty{m_p\over {m_e+m_p}}$

$R_H=R_\infty{1\over {1+{m_e\over m_p}}}$

https://en.wikipedia.org/wiki/Hydrogen_spectral_series

This post is simply to show how to derive the Full Rydberg Equation (FRE), a polynomial that has been solved via the sign-flip numeric iteration algorithm for all terms in the equation.  This solution can only be performed with the Full Rydberg Equation as the equation for the Rydberg constant is incomplete and not solvable for the terms which compose the equation. The stabilty and uniqueness of the solution can be shown via computer numeric solution and will be available soon in The Excel VBA / macro spreadsheet.

This derivation makes use of, as a starting point,: $$R_M={R_\infty\over {1+{m_e\over M}}}$$ however, it can also begin with the wave equation, Schrödinger's wave equation, as done in previous posts and whitepapers linked throughout this blog. For simplicity and clarity, this is how we do it:

$R_M={R_\infty\over {1+{m_e\over M}}}$

$R_M(1+{m_e\over M})=R_\infty$

$(1+{m_e\over M})={R_\infty\over R_M}$

$1={R_\infty\over R_M}-{m_e\over M}$

For hydrogen, 1H @ 0°K:, $M=m_p$

$1={R_\infty\over R_H}-{m_e\over m_p}$

${m_p\over m_e}={\alpha^2\over\pi r_pR_H}=1836.15267$ - see derivation-of-proton-to-electron-mass-ratio

$1={R_\infty\over R_H}-{\pi r_pR_H\over \alpha^2}$

$R_\infty={m_ee^4\over 8{\epsilon_0}^2h^3c}$

$1={{m_ee^4\over 8{\epsilon_0}^2h^3cR_H}}-{\pi r_pR_H\over \alpha^2}$

To be continued... https://en.wikipedia.org/wiki/That's_All_She_Wrote

https://phxmarker.blogspot.com/2022/09/thats-all-she-wrote-one-equation-to.html

The Surfer, OM-IV

http://goldenmean.info/kit/

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