Speed Limit of Sound - Fine Structure Constant and the Proton to Electron Mass Ratio

Speed limit of sound is limited by the speed of light, proton radius, and the Rydberg constant:

(this defines a new experiment / series of experiements to determine the proton radius)

https://advances.sciencemag.org/content/6/41/eabc8662*

$$v_u=\alpha({m_e\over{2m_p}})^{1\over2}c$$

using for the proton to electron mass ratio:

$${m_p\over m_e}={\alpha^2\over\pi r_pR_H}$$

$$v_u=c\sqrt{{\pi\over2}r_pR_H}$$

Google Calculator Link

Google Calc link with Phi equation for mass ratio

$$r_p={2\over{\pi R_H}}{({v_u\over c})}^2$$

Google Calc Proton Radius

Tinkering and Hammering Out Equations verifies!

And there you have it, another simple result from good old fashioned work!

It looks like you have a sort of Rydberg Molasses™ that slows the speed of light down as it traverses the proton radius a quarter wave at a time, thus the ${\pi\over2}$ quarter wave phase-factor, or some rms $\sqrt2\over2$ crystal lattice averaging factor.

* "Our result expands the current understanding of how fundamental constants can impose new bounds on important physical properties."

Other notes:

https://en.wikipedia.org/wiki/Hydrogen

https://en.wikipedia.org/wiki/Hexagonal_crystal_family

https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_solids

One more for the road:

$$({v_u\over c})^2={\pi\over2}r_pR_H$$

This clearly sheds Light on the geometric reality of the Universe.

™=That's Mine

Addendum:

Assuming the photon and phonon are the same frequency:

$$f_{phonon}=f_u$$

$$f_{photon}={c\over\lambda}$$

$$f_u={v_u\over\lambda_u}$$

$${c\over\lambda}={v_u\over\lambda_u}$$

$${v_u\over c}={\lambda_u\over\lambda}$$

$$({v_u\over c})^2=({\lambda_u\over\lambda})^2$$

$$({\lambda_u\over\lambda})^2={\pi\over2}r_pR_H$$

Moar later to check correlation in k-space/momentum space.

https://en.wikipedia.org/wiki/Metallic_hydrogen#Claimed_observation_of_solid_metallic_hydrogen,_2016

https://en.wikipedia.org/wiki/Delocalized_electron

The Surfer, OM-IV

Cannon Fire!

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