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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