Rough-deriving rest-masses of 0.5, 938, and 105 MeV. Of course those are electron, proton and muon respectively.
What follows is some rough play calculations to see if I can come at all close to the numbers. And keep in mind that the calculations are counting of the ridges and troughs of standing waves that have looped back around creating a standing wave. A photon has no rest-mass because the wave has no circles or loops in it but is more or less a straight line wave. A particle that has rest mass has part of its wave circling around into forming a circle or surface area or volume.
I am working with just plain spheres and circles but I need to work with ellipsoids for more precision.
Now I need all three formulas of circumference, surface area and volume: (a) C = pi(2r) (b) S.A. = 4pi(r^2) (c) V = 4/3(pi)(r^3)
Now I have not found out the characteristics of the wavelength of the hydrogen atom electron or proton so I am going to assume with a hypothetical number, the number 300 as a unit of measure, purely hypothetical to see if 300 gives me 0.5, 938, and 105 MeV.
For the electron we have 300 x 300 = 90,000. And if the radius is 90,000 then pi(2r) is 540,000 and for this hypothetical 540,000 is close enough to 0.5 MeV
For the muon we have (300)^3 = 27,000,000. So if the radius is 300 then the volume is 4/3(pi)(r^3) so that 4 x 27,000,000 is 108,000,000 which is close enough to 105 MeV for the muon.
Now for the proton we have surface area but the inverse of the electron so we have (90,000)^2 = 8,100,000,000 divided by 6 from 2pi of circumference since inverse we have 1,350,000,000 which is not a good estimate of the proton rest-mass of 938,000,000 eV.
Now if I was working with ellipsoids for the proton I believe I could easily get 938,000,000 rather than get 1,350,000,000 with spheres. Now I do recall the physics literature has the tear drop shape for the nucleus of radioactive elements. The tear drop shape is an example of ellipsoids. Now I have to investigate whether the tear drop shape has some exacting numbers or whether it is just a qualitative description with no quantitative backing.
The reader must keep in mind that leptons are hyperbolic geometry and the rest mass is the counting up of ridges and troughs of the standing wave, whereas the baryons of protons and neutrons are elliptic geometry and the counting up of ridges and troughs of standing waves.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: