Summary of (Scientific) Proton to Electron Mass Ratio Equations

The proton to electron mass ratio equations:
List:
$$\mu_{NIST}={m_p\over m_e}=1836.15267343(11)$$
$$\mu={electronChargeToMassQuotient\over protonChargeToMassQuotient}={{e\over m_e}\over {e\over m_p }}={m_p\over m_e}=1836.15267343(11)$$
$$\mu_{Surfer}={m_p\over m_e}={\alpha^2\over\pi r_pR_{H}}=1836.15267$$
$$\mu_{Nature}={2903\over \Phi}+42=1836.15266934\dots$$ **

The proton to electron mass ratio, $\mu$, is needed to solve the full Rydberg equation derived from the full analytical model of a single hydrogen atom, the only atom that has such a solution:

$$F\left(x,\cdots,x_n\right)\equiv1\equiv{m_e}{e^4\over8c\epsilon_0^2h^3R_H}-{{\pi r_pcm_e}\over2h}$$
$$F\left(x,\cdots,x_n\right)\equiv1\equiv{m_e}{e^4\over8c\epsilon_0^2h^3R_H}-{{m_e}\over m_p}$$

The full Rydberg equation has a stable numerical solution that converges on a harmonic solution for ALL the constants in the equation using a sign flip numerical method. *
(see previous post: https://phxmarker.blogspot.com/2017/11/the-oracle-toppcg-beta-2-included-basic.html, also, the derivation paper(s) using same wave equations as mainstream:
https://drive.google.com/file/d/14ZUyxi1GRkT-n3MphJ7whz-2FYTHjSXx/view?usp=sharing
https://drive.google.com/file/d/1MjQSu-ldDiwC85tqtEr9S3cbgmq3oUst/view?usp=sharing)

This defines the masses and constants of the standard model to any precision required, by using the 0°K hydrogen atom as a reference.  The full wave equation solution to the single hydrogen atom  then is the reference for defining mass, speed of light, etc.  Still a correlation to the absolute it needed, so a definition of time is needed for completeness.  Defining mass using Planck's constant by using a harmonic solution to single resonating hydrogen atom continues the theory to also define the basic physics constants.

Since the Standard Model is incomplete, a more complete science is in our future, one that describes Nature more fully, thus the Golden ratio equation , $\phi$.  It is accurate and matches NIST to 9 digits if rounded. This $\phi$ equation for $\mu$ links Dan Winter's work to mainstream science, as the phase conjugate solution involves $\phi$ ratios.

NIST=link to NIST/CODATA
$\mu=$ proton to electron mass ratio
$m_p=$ proton mass
$m_e=$ electron mass
$r_p={0.841235640294664fm}$ proton radius
$\alpha=$ fine-structure constant
$h=$ Planck constant
$c=$ speed of light
$R_{H}=$ Rydberg constant
$\ell=$ Planck length
$m_{\ell}=$ Planck mass
$\phi=1.61803398875$
$c=$ speed of light
$\epsilon_0=$ permittivity  of free space
$e=q=$ elementary charge
$\pi= 3.14159265358979323846$


Solved by this blog.

* the equation does not have a stable solution if the electron to proton mass ratio term is dropped.
(verified by author in 1981/2 using IBM mainframe on campus of University of Cincinnati, and in the 90's on my PC, awaiting others to verify); mainstream drops the ${m_e\over m_p}$ term since it's less than measurement error and very small, however, this prevents finding the full solution.

** Only a prime, integer, and phi constant, thus significant
note:
$\mu_{Surfer}$'s equation is the same as Nassim Haramein's, as shown previously in this blog.
Key note: Even the proton radius is modified to a refined value when the iterative numerical solution converges to harmonize all constants with unity.

The Surfer, OM-IV

Ω