Mark Rohrbaugh may be some kind of on-the-spectrum genius with a professional background in mix-signal (analog-digital) integrated circuitry. For some time, based on a semi-classical relation involving a reasonably intuitive assumption about angular momentum in the Bohr model of the hydrogen atom, he’s been pursuing a derivation of the proton radius that presaged the major correction in that “constant” by the wider physics community.

Since then he’s been working on a kind of minimalist algorithm calculating predictions for significant digits of physical constants. In his latest blog post he describes his use of Newton-Raphson Iteration to derive 5 physical constants using only his semi-classical ration and the proton/electron mass ratio.

Those constants are:
e
ϵ0
h
c
RH

He describes the semi-classical relation and resulting algorithm in this post:

Obviously, since Mark Rohrbaugh doesn’t use a Dvorak keyboard, I’ll have to admonish him to please not torture us with his crackpottery further. You can only trust those who permit typos to appear in public if they misspell Rydberg as either Rpdberg or Rfdberg or Ridberg. A diagonal slip of the finger to Rudberg is so unlikely on a Dvorak that we can surely classify Mark Rohrbaugh as a QWERTY crackpot.

Besides checking his spelling, Mr Rohrbaugh could help himself by doing some algebra to simplify his formula. Specifically, it reduces to
r_p = 2h/(pi c m_p),
where
r_p = proton radius
m_p = proton mass c = speed of light
h = Planck’s constant
Thus, there are only two independent physical constants involved, not five. (Speed of light is now a defined value.)

Mr. Rohrbaugh’s overly complex expression obfuscates the relation of r_p to fundamental constants, not to mention making the computations subject to the propagation of errors. Quantities such as the hydrogen Rydberg constant (R_H) and the fine structure constant (alpha) are defined in terms of fundamental constants, not determined independently. The permittivity of free space cancels out.

To the substance of the equation, it results in a value of r_p of 0.8412 fm. Some measurements are consistent with this value, while others are not. Since it’s unclear where Mr. Rohrbaugh’s equation comes from, it’s hard to assess its relationship to conventional theory, if any.

It’s merely indicative of low consciousness, which is an important personality trait for someone working in mathematics and science. Let’s hope he’s more careful with his math than he is with his spelling, especially when it comes to the name of a famous physicist and well-known physical constant — at least famous and well-known to physicists.

If you wish to admonish him, may I suggest that you urge him to check his work for obvious errors before posting to his blog.

He assumes a proton-electron torque balance in the Bohr model (which above I mischaracterized as momentum):

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 mprp to mere to balance torque/spin between proton and electron

At my suggestion he’s pursuing a calculation with c set to the SI exact value, but also seems to think the standards committee should consider a different approach to that taken in the 2019 revision.

Here’s what he said:

As well as correcting the intial values and tolerances, I’m planning on running a version with c set to SI unit value of 299792458 m/s. In this way, four constants can be solved for and a more fair comparison made to NIST/CODATA. Addressing the idea of setting c will be saved for a later post. Perhaps c should be set according to the polynomial AND a timebase reference created. I think that, combined with re-defining mass, could carefully set the constants to be in harmony with mks SI units ideas.