Crystalline Lattice Analysis of the Speed of Sound in Metallic Hydrogen (Simple Version - WIP) Sound to Light Sonoluminescence

credit

from: https://forums.autodesk.com/t5/inventor-forum/3d-array-of-spheres/td-p/8054413

The spacing of the protons, center to center, is $2r_p$. For a standing wave phononic vibration in the crystal, proton to proton spacing is $1\over2$ wavelength, so the shortest standing wave wavelength is $4r_p$, thus the $\pi\over2$? in:

https://phxmarker.blogspot.com/2021/05/speed-limit-of-sound-fine-structure.html

$$f_u={v_u\over\lambda_u}$$
$$v_u=c\sqrt{{\pi\over2}r_pR_H}$$

$$\lambda_u=4r_p$$

$$f_u=c\sqrt{{\pi\over32}{R_H\over r_p}}$$

Max Speed of Sound Google Calc link

Google Calc Link: c*sqrt(pi/32*(Rydberg constant)/0.8414femtometers)=

The frequency would be a subharmonic of this.

Wavelength of the sound is $4r_p=3.3656 femtometers$

A subharmonic of a factor 178,274,305 would bring the frequency down to the middle the visible spectrum:

Google calc link to divide frequncy by 178274305

Vibrating a crystal of metallic hydrogen at 60GHz would make it radiate in the visible spectrum?

(need to revisit basics - Work In Progress -WIP)

(I would imagine there is a lot of noise in space)

Modifications for Tension-Pressure and density:

$$f_u={v_u\over\lambda_u}\sqrt{T\over\mu}$$

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

$$\lambda_u=4r_p$$

$$f_u=c\sqrt{{\pi\over32}{R_H\over r_p}}\sqrt{T\over\mu}$$

Might have to review crystal resonators to progress:

https://en.wikipedia.org/wiki/Crystal_oscillator#Mechanical_stress

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

Once the equation is corrected for Pressure/density/elasticity/temperature or whatever, perhaps Jupiter's 22.3MHz emmissions can be simply explained. 

Moar coming.

sauce

source

Goog calc link for maximum possible sound frequency

Some effect like this, however, with the protons+ moving via phonon standing wave in a periodic 3D metallic crystal, for when the phonon frequency equals the photon frequency, however, even that assumption may be wrong... (this is LIVE derived crash and burn, results will verify over time):

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

The Surfer, OM-IV

https://radiojove.gsfc.nasa.gov/library/sci_briefs/discovery.html

Ω

Simply For LaTeX Practice: Defintion of Derivative

$${df\over dt}=\displaystyle{\lim_{h \to 0}}{{f(t+h)-f(t)}\over h}$$

How?

Navy. USN, United States Navy, that's how.

and https://en.wikipedia.org/wiki/Leslie_Lamport for LaTex!!!

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!

Ω