Convergence!

The waveforms of the constants as the algorithm converges are shown here, starting with the ERROR versus Iteration#: (from Excel file, data generated from BASIC program*)

Error, log scale Y-axis, Iteration# X-axis

Elementary charge, e

Electron mass, m_e

Fine-structure constant, α

Permittivity of free space, ε_0

Planck's constant, h

Proton radius, r_p

Rydberg constant, R_H

Speed of Light, c

The Full Rydberg polynomial is in the upper right of this image:

The final values to about 14 digits accuracy are:

(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).                        (1/137.029874274)  

Input  fine-structure constant= 0.00729735256  (compare to above line) (1/137.035999084(21)) 

Proton/electron mass ratio=1836.1490029653(637)

More about final values later... ...(need to do a little more checking before replacing NIST/CODATA)

From https://en.wikipedia.org/wiki/Dimensionless_physical_constant:

“Fundamental physical constants cannot be derived and have to be measured. Developments in physics may lead to either a reduction or an extension of their number: discovery of new particles, or new relationships between physical phenomena, would introduce new constants, while the development of a more fundamental theory might allow the derivation of several constants from a more fundamental constant.

A long-sought goal of theoretical physics is to find first principles (theory of everything) from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.”

Also see https://en.wikipedia.org/wiki/Physical_constant

Looks like they might have to update their information.  

https://en.wikipedia.org/wiki/Dimensionless_physical_constant#Examples

Comment on the solution (which was derived and discussed in previous posts and papers):

The constants are the roots of the Full Rydberg polynomial - for a single hydrogen atom. Do not reduce the "two wave/particle" system into simply examining the electrons like Feynman did in QED or like Squalid-State (Solid-State for those in Rio Linda)

"The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation.", from:

https://en.wikipedia.org/wiki/Characteristic_equation_(calculus)

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

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book:_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/02:_Foundations_of_Quantum_Mechanics/2.07:_Derivation_of_the_Rydberg_Equation_from_Bohr's_Model

*modified to print out ALL intermediate values instead of simply the error and final results (see link)

The Surfer, OM-IV (Ω4)
©2021 Mark Eric Rohrbaugh & Lyz Starwalker © 2022

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LaTeX Reference

https://en.wikibooks.org/wiki/LaTeX/Mathematics

The Surfer, OM-IV

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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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Ratio of Speed Limit of Sound to Light Speed Squared - Profound Relationship

Crystalline Lattice Analysis of the Speed of Sound in Metallic Hydrogen (Simple Version - WIP) Sound to Light Sonoluminescence

credit

from: https://forums.autodesk.com/t5/inventor-forum/3d-array-of-spheres/td-p/8054413

The spacing of the protons, center to center, is $2r_p$. For a standing wave phononic vibration in the crystal, proton to proton spacing is $1\over2$ wavelength, so the shortest standing wave wavelength is $4r_p$, thus the $\pi\over2$? in:

https://phxmarker.blogspot.com/2021/05/speed-limit-of-sound-fine-structure.html

$$f_u={v_u\over\lambda_u}$$
$$v_u=c\sqrt{{\pi\over2}r_pR_H}$$

$$\lambda_u=4r_p$$

$$f_u=c\sqrt{{\pi\over32}{R_H\over r_p}}$$

Max Speed of Sound Google Calc link

Google Calc Link: c*sqrt(pi/32*(Rydberg constant)/0.8414femtometers)=

The frequency would be a subharmonic of this.

Wavelength of the sound is $4r_p=3.3656 femtometers$

A subharmonic of a factor 178,274,305 would bring the frequency down to the middle the visible spectrum:

Google calc link to divide frequncy by 178274305

Vibrating a crystal of metallic hydrogen at 60GHz would make it radiate in the visible spectrum?

(need to revisit basics - Work In Progress -WIP)

(I would imagine there is a lot of noise in space)

Modifications for Tension-Pressure and density:

$$f_u={v_u\over\lambda_u}\sqrt{T\over\mu}$$

$$v_u=c\sqrt{{\pi\over2}r_pR_H}$$

$$\lambda_u=4r_p$$

$$f_u=c\sqrt{{\pi\over32}{R_H\over r_p}}\sqrt{T\over\mu}$$

Might have to review crystal resonators to progress:

https://en.wikipedia.org/wiki/Crystal_oscillator#Mechanical_stress

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

Once the equation is corrected for Pressure/density/elasticity/temperature or whatever, perhaps Jupiter's 22.3MHz emmissions can be simply explained. 

Moar coming.

sauce

source

Goog calc link for maximum possible sound frequency

Some effect like this, however, with the protons+ moving via phonon standing wave in a periodic 3D metallic crystal, for when the phonon frequency equals the photon frequency, however, even that assumption may be wrong... (this is LIVE derived crash and burn, results will verify over time):

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

The Surfer, OM-IV

https://radiojove.gsfc.nasa.gov/library/sci_briefs/discovery.html

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Simply For LaTeX Practice: Defintion of Derivative

$${df\over dt}=\displaystyle{\lim_{h \to 0}}{{f(t+h)-f(t)}\over h}$$

How?

Navy. USN, United States Navy, that's how.

and https://en.wikipedia.org/wiki/Leslie_Lamport for LaTex!!!

Speed Limit of Sound - Fine Structure Constant and the Proton to Electron Mass Ratio

Speed limit of sound is limited by the speed of light, proton radius, and the Rydberg constant:

(this defines a new experiment / series of experiements to determine the proton radius)

https://advances.sciencemag.org/content/6/41/eabc8662*

$$v_u=\alpha({m_e\over{2m_p}})^{1\over2}c$$

using for the proton to electron mass ratio:

$${m_p\over m_e}={\alpha^2\over\pi r_pR_H}$$

$$v_u=c\sqrt{{\pi\over2}r_pR_H}$$

Google Calculator Link

Google Calc link with Phi equation for mass ratio

$$r_p={2\over{\pi R_H}}{({v_u\over c})}^2$$

Google Calc Proton Radius

Tinkering and Hammering Out Equations verifies!

And there you have it, another simple result from good old fashioned work!

It looks like you have a sort of Rydberg Molasses™ that slows the speed of light down as it traverses the proton radius a quarter wave at a time, thus the ${\pi\over2}$ quarter wave phase-factor, or some rms $\sqrt2\over2$ crystal lattice averaging factor.

* "Our result expands the current understanding of how fundamental constants can impose new bounds on important physical properties."

Other notes:

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

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

https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_solids

One more for the road:

$$({v_u\over c})^2={\pi\over2}r_pR_H$$

This clearly sheds Light on the geometric reality of the Universe.

™=That's Mine

Addendum:

Assuming the photon and phonon are the same frequency:

$$f_{phonon}=f_u$$

$$f_{photon}={c\over\lambda}$$

$$f_u={v_u\over\lambda_u}$$

$${c\over\lambda}={v_u\over\lambda_u}$$

$${v_u\over c}={\lambda_u\over\lambda}$$

$$({v_u\over c})^2=({\lambda_u\over\lambda})^2$$

$$({\lambda_u\over\lambda})^2={\pi\over2}r_pR_H$$

Moar later to check correlation in k-space/momentum space.

https://en.wikipedia.org/wiki/Metallic_hydrogen#Claimed_observation_of_solid_metallic_hydrogen,_2016

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

The Surfer, OM-IV

Cannon Fire!

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Proton Radius: Willfully or Ignorantly a Puzzle?

A simple review of the existing derivations of the foundations of Solid-State theory, and examination of the derivation for the Rydberg constant/equation that puts constraints on the other constants, one can see it appears willful that the terms involving the electron mass and proton mass ratio are dropped. 

The reduced mass approximation is an approximation to a 2 "body" problem.  $\mu$, reduced mass, 

$$\mu={m_pm_e\over{m_p+m_e}}$$

$$\mu={m_e\over{1+{m_e\over m_p}}}$$

$$\mu=m_e^*$$ reduced mass or effective mass of electron*

$$\therefore m_e^*<m_e$$

Just** turning the terms for the mass ratio into an effective mass ends up dropping the proton radius from the equation,the Rydberg equation, the equation that puts constraints on MANY other key constants.

*effective mass can be determined via experimental or theoretical techniques for periodic arrays of atoms, energy wells, created by crystals (physical atom placement, nanotechnology, EM periodic, or phonon (sound vibration) periodic, HOWEVER, we are talking about a single hydrogen atom for the purpose of solving for some constants of a solution of a characteristic wave equation for a single atom in the aether that is a simultaneous solution simply for determination of the constants BEFORE everyone runs off crazy with ill thought out experiments and missing the boat and ending up with all kinds of puzzles and unsolved physics problems. (I'm talking about the mainstream funded science flow, so yes, that means (You)).  Once the theory is mathematically fully solved, then it's time to compare to experiments where necessary for verification and investigative purposes.

**In other words, do not confuse the solution of one problem with the solution of another, i.e., solid-state periodic array assumptions so one can just treat the electron motion in the anlaysis, very similar to QED, is an approximation to the free atom. Fully solve the single free atom with the constants from the boundary conditions - just like real mathematicians*** do.

***Mathematicians would fully solve the general case for the wave equation and the physicist would point out the boudary conditions which enforce a set of equations that define the specific problem being solved since the general case for a second order fully complex wave function (prior to being reduced to the Schrödinger Wave Equation) is not close form solveable (if the general case actually is then all of what this blog is talking about has already been solved and there is no proton puzzle)

In other news, a double witching or whatever with silver 3/28 & 4/1 with deliveries a month later.  Will they have the silver?

The Surfer has been watching Silver since the 60s...

PS: Reduced mass concept works for technology such as the Solid-State devices we have and the Weyl fermion ideas thrown about, however, approximation techniques have to be CAREFULLY applied and used when doing Fundamental Fysiks!

The Surfer, OM-IV

Ag

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Throwing in a Pi ($\pi$) Versus Throwing in the Tau ($\tau$) or "Who Threw Those Pies?" (Never Give Up)

Three Stooges - Who Threw Those Pies?

@3:21 "Somebody give me a pie!"

Don't forget to bring a tau!

(the best thing about this post is what it doesn't say, and that is what proton radius is required to get the correct mass ratio, i.e., -4% solution) https://phxmarker.blogspot.com/2016/03/derivation-of-proton-to-electron-mass.html

Approximate work here: https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/video-lectures/part-3/

The Surfer, OM-IV

"Throwing In The Towel"

Pie Throwing

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Explanation of Why Mainstream Analysis & Thinking CANNOT Resolve Measurement Versus Theory for The Proton Radius Puzzle

Here* is why the standard model, QFT, QED, QCD or whatever, cannot calculate a proton radius that agrees with measurement.

It has to do with reductionism and reduced mass. Simply, more precisly and concisely than before, examine the way the terms are added to the ground state energy (from wave equation analysis), for example,  from Pohl's recent video on the proton radius puzzle:

Bohr Quantization

2 particle problem, the proton and electron of the $^1$H atom, reduced to Solid-State (Squalid State) analysis:

Simple case: parabolic, isotropic dispersion relation

Intermediate case: parabolic, anisotropic dispersion relation

 

Adding the radius term and other 
(measurement analysis is correct, however, the theory has to wholly solve to give a prediction such as this blog and Haramein's work which correctly predicts the proton radius)

 

These are parts the terms, formulations,  and coefficients of the Schrödinger Wave Equation where as the Full Wave Equation for a single hydrogen atom (2 particle problem, closed form analytical solution for a single hydrogen atom exists and is the only atom with a complete analytical solution) may be  needed to be used for a more precise mathematical treatment to derive the proton radius (as already done by this blog and by the author circa 1991).

Note how the terms are ratios of Energy to Mass AND, a starting point is the Bohr model, and since the Bohr model is incorrect, that's where the Standard Model comes in and can add more terms for newly discovered effects.

So, from the Bohr model, more and more terms are added.

Note, again, however, the inverse relationship wrt to MASS being in the denominator. Since the effective mass / reduced mass of the electron is slightly less than the actual rest mass of the electron, 1 over the effective mass term will always be greater than the 1 over electron rest mass term.  No matter how many terms one adds (assuming positive mass, positive energy as negative may not be reality) the effective mass will always diverge from the actual electron mass, thus any other derivations, like for the proton radius, will diverge from measurements. A full analysis must be done to extract the proton radius as well as the other constant in the Rydberg equation.  In other words, do not drop the ${{m_e}\over{m_p}}$ term simply because it is less than experimental error and allows a closed form solution.  Keep the term and do a numerical solution via iteration - Numerical Methods solve precisely.

$${1\over{m^*_e}} + {1\over{N}}>{1\over{m_e}}$$

where

$m_e=$ mass of electron

${m^*_e}={{m_pm_e}\over{m_p+m_e}}=$ reduced mass (effective mass)

$N=$ New terms from "more accurate standard model"

This can easily be seen by realizing:

$$m^*_e<m_e$$

$${1\over{m^*_e}}>{1\over{m_e}}$$

Therefore, the way to solve the problem is to carefully consider the 2-body problem before reducing it via reductionism into a 1-body problem.  I.e., more carefully derive the Rydberg equation from the Full Wave Equation.  All in the framework of 0°K absolute zero, no phonons, since we are establishing a reference, the proton, the instrument with which the characteristics of the single hydrogen atom and its vacuum environmental dynamic can be predicted & extracted.

This is the best example of an experimental approach (measurement & technology) dominating over an actual well thought out application of the theory and thus clouding the discussion and results.

And it has been cloudy since that proton work in Stanford in 1968 and before...

4/2/2021 update -MR Proton, aka, The Surfer:

A recent attempt, using QCD, at the proton radius:

https://idw-online.de/de/news766082

https://www.uni-mainz.de/presse/aktuell/13367_ENG_HTML.php

*I've been doing this kind of analysis since 1984 - 1989 where I wrote a process manual or two  at Texas Instruments headquarters for an advanced Integrated Circuit (IC) analog process. Some of my calculations or thoughts on the proton to electron mass ratio may be in my engineering notebooks in the TI library in South Building(?) Dallas, Tx.

The Surfer, OM-IV

Randolf Pohl, "Myonic Hydrogen and the Proton Radius Puzzle"

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