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:
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| Simple case: parabolic, isotropic dispersion relation |
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| Intermediate case: parabolic, anisotropic dispersion relation |
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| 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 Schrรถdinger 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:
*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.
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