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Sunday, June 21, 2020

Summary of (Scientific) Proton to Electron Mass Ratio Equations


J.J. Thomson's Experiment and Discovery of Cathode Ray, Electrons
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

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