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Tuesday, March 1, 2016

Derivation of Proton to Electron Mass Ratio Equation from the Rydberg Equation



\mu={m_p\over m_e}=1836.15267\dots

m_e={2R_{\infty}h\over c\alpha^2}
m_e{\alpha^2\over R_{\infty}}={2h\over c}
m_e{\alpha^2\over \pi R_{\infty}}={2h\over \pi c}
Let r_e={\alpha^2\over\pi R_{\infty}}, then:
m_er_e={2h\over\pi c}
Now, because for every action there is an equal and opposite reaction, for every force there is an equal and opposite force, for every torque, there is an equal and opposite torque, equate m_pr_p to m_er_e to balance torque/spin between proton and electron:
m_er_e={2h\over\pi c}=m_pr_p
\therefore {m_p\over m_e}={r_e\over r_p}={\alpha^2\over\pi r_pR_{\infty}}=1836.15267
Where:
m_pr_p={2h\over\pi c}=4\ell m_{\ell}
r_p=0.841235640294664\;fm

Compare to TOP_PCG calculated r_p:
r_p=0.841235640294664\;fm
r_p=0.841235640479985\;fm <~~ TOP_PCG


m_p= proton mass
m_e= electron mass
r_p= proton radius
r_e= effective torque arm radius for electron
\alpha= fine-structure constant
h= Planck constant
c= speed of light
R_{\infty}= Rydberg constant
\ell= Planck length
m_{\ell}= Planck mass
QED.

The Surfer, OM-IV

7 comments:

  1. https://en.wikipedia.org/wiki/Q.E.D.

    ReplyDelete
  2. Years are passing by as the mainstream FLOUNDERS!
    Ha ha
    🤡🤡🤡 <--- Rare Triple CLown!!!

    ReplyDelete
  3. NASA's having trouble with the Hubble constant.
    Ha ha
    🤡🤡🤡 <--- Rare Triple CLown!!!
    (usually comes in pairs)

    ReplyDelete
  4. What is "TOP_PCG"?

    PS: By using your formula for rp I get:

    8.41235641(34 ±26)e-16 m

    I obtained the calculated result's uncertainty by using Mathematica's "Around" function to do error propagation of the uncertainties in the constants retrieved from Mathematica's CODATA database.

    This is of course within Mathematica's CODATA rp ("ProtonRMSChargeRadius") of:

    8.414 ± 0.019 e-16 m

    ReplyDelete
    Replies
    1. TOPPGP is a program I wrote to solve the polynomial for the minimum error - Top Physics Constant Generation. I have a copy of it in the blog: https://phxmarker.blogspot.com/2017/11/the-oracle-toppcg-beta-2-included-basic.html

      Delete
  5. This is a fascinating explanation of the relationship between proton and electron spin.

    ReplyDelete

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