# Thread: Coefficient free planck constant and elementary charge in square per proton mass ratio

1. 1.Mass coupling. The elementary charge is between a proton and a electron. The electro motoric force F and electric field E are "connected" to physical objects and thereby mass via the proton , and are actuated or actuating with a force relative to the proton mass (Newton/proton mass). Because of inverse square law the force at distance r is F=f*Q1*Q2/r^2/proton mass. Here f is a factor (the relation), Q1 and Q2 charges in a applicable unit that I call indifferent Coulomb Ci that is different from SI Coulomb indexed i. Rewriting mass in nuclear units give F=f*Q1*Q2/(r^2*mpi*c^2) The proton mass mpi is key to the by me used i-units.

2.Geometric Coulomb constant. For two identical spheres the electric fields meet at halfway their distance r/2. Using the radius of the sphere as distance unit (for math reasons) a proportional distance p=r/R. A "geometric" integral over the sphere surface A from distance p give f*A=INT 2*|R|sqrt(1-R^2)/(p+R)^2 dR => f*A=(4pi*sqrt(p^2-1)*(2p^2-1)*arcsin(1/p)-2p^2+2)/(p^2-1). This equation have a limes value 4/3 at infinity, f=4/3. This give full formula for Coulombs constant (macroscopic squares) F=ks*Q1*Q2/r^2 where ks= 4/(3*mpi'c^2) =8,9*10^9 Nm2/Ci2.

3.Stoichiometric correction. When going from weighed (kg) laboratory spheres to atomic scale, I realized that the ratio kg/g (kmol/mol) have been "unnoticed". (The detail evaded me for quite long even though I am a chemist) This mean macroscopic is N/kg and atomic scale is N/g (N/mol). To get this on same magnitude for force and E, using atomic N/(kg/1000) =N*1000/kg. The force (field) is the same N but impact a target of a 1/1000 units.

4.Atomic Coulomb constant. "Adding a spheric (proton) field to a point (electron) field was in the end straight forward (4/3+1)=7/6 because it is about ONE charge not two halves, I realized half a year later. This give a feature I call the atomic Coulomb constant ka=7*1000/(6*mpi*c^2) =7,8*10^12 N/m2Ci2. This also mean that (alpha) the fine structure constant is part of "compensating" for the 1000 times mishap. The balance equation e^2=2(alpha)*(epsylon0)*h*c, I rewrite to ka*ei^2=hi*c, where ei is elementary charge and hi Planck constant. Indexed i to separate from CODATA and those mainstream constants.

5.The ratio. To the theory rigid, the amount n of elementary charges need to match protons (and kg:s) Deploying Avogadro type of number NApi=1kg/(1000*mpi). This give a Faraday constant Fi=NApi*ei=sqrt(ks) =94150 Ci/mol protons. The correction is not because coulomb being in mols, but having mpi having mpi kg: as common factor. This give ei=sqrt(4*1000^2*mpi/)3*c^2))= 1,5757*10^-19 Ci (indifferent coulomb). The charge mass coupling is "exactly" ei^2/mpi=4*1000^2/(3*c^2) = 1.4835*^10^-11Ci2/kg. This regardless of what proton mass "turn out to be".

6.Planck constant. Further can be derived Planck constant for Ci and kg compatible units hi=ei^2*ka/c= 14*1000^3/(9*c^5)= 6,4236*10^-34 Js. This in classic (mecanical) Joule.

7.Proton mass (mainstream /i blend calculation). Since Rydberg has worked around the 1000 times mishap I use his formula R(inf)=me*e^4/(8*(epsilon0)^2*h^3*c) and classic (epsylon0)=1/(4*pi*k) and my ka*ei^2=hi*c. From these can be derived R(inf)=2*mei*pi*ks^2/(hi*ka^2) =mei*576*pi^2*c^6/(343*1000^5). mei =indexed mass of electron. Mass of proton /mass of electron 1836,15 and Rydberg constant for hydrogen RH=1,09678*10^7 /m give mei =9,1152208'10^-31 kg and indifferent proton mass mpi= 1,67369371*10^-27kg.

8.Constants.Avogadro for protons NApi=1/(1000*mpi)= 5,974809*10^-27 kg

Elementary charge ei=sqrt(4*1000^2/(3*c^2))= 1,575748*10^-19 Ci

Faradays constant Fi =sqrt(ks)= 94147,9 Ci/molpi (i-protons/(1000*kg)

Coulomb constant for spheres ks=4/(3*mpi*c^2)= 8,863829*10^9 Nm/Ci2

Atomic Coulomb constant ka=7000/(6*mpi*c^2)=7,75585*10^12Nm/Ci2

Exact constants. Coulomb square/mass ratio ei^2/mpi=4*1000^2/(3*c^2) = 1,483533408*10^-11 Ci/kg

Planck constant hi=14*1000^3/(9*c^5)= 6,423652096*10^-34 Js

9.Further derivations. Magnetic permeability in free space (mu0)=ka*ei=hi*c/ei= 1,222126*10^-6 N/Ai2

If wanted (not needed) fine structure coefficient (alphai)=ei*c^2/2 =0,0070815663 Cim2/s2

From above Rydberg energy (i units) Ryi=mei*ei^2*c^6/8= mei*mpi*c^4*1000^2/6 =2,0538785*10^-18 kgm/s2 (Ci Joule)

Real physicians need go count their quants in Monday Timo Moilanen

Readable formulas:   2.

3. Atonic Coulomb constant needed change Ka=6*ks/(alpha) ,Alpha=fine structure constant. And proton mass coupled to electron mas mpi=mei^2*c^4/4.
Proton mass coupled charge unit and constants
Coupling: The elementary charge is between a proton and an electron .The electro motoric force F and electric field E is connected to physical objects and thereby mass via the proton, and are actuated or actuating with a force relative to the proton mass. (Newton/proton mass). Because of the inverse square law the force at distance r, F=f*Q1*Q2/r^2/proton mass. Here f is a factor (the relation), Q1andQ2 charges in a applicable unit that I call indifferent Coulomb Ci that is different from the SI coulomb (indexed i). Rewriting mass in nuclear units give F=f*Q1*Q2/(r^2*mpi*c^2) The proton mass mpi different from CODATA.
Spheres: For two identical spheres the electric fields meet at halfway their distance r/2. Using the radius of the speres as distance unit (for math reasons) and have proportional distance p=r/2R. A geometric integral over the sphere surface A from distance p, give f*A=INT 2*|R|sqrt(1-R^2)/(p+R)^2dR ó f*A=(4pi(sqrt(p^2-1)*(2p^2-1)*arcsin(1/p)-2p^2+2)/(p^2-1). To use r I divide by A/4=pi since(r/2)^2=4/r^2. This equation for sphere have a limes value 4/3 at infinite distance f=4/3. This give the full formula for coulombs constant (macroscopic spheres) F=ksQ^2/r^2 where ks= 4/(3*mpi*c^2)= 8,7*10^9 N/m2/Ci2.
1000 times 100 year: When mowing from weighed (kg) laboratory spheres to atomic scale, I realized that the ratio kg/g (kmol/mol) have been unnoticed. (The detail evaded me for a while even though I am a chemist) This mean macroscopic is N/kg (N/kmol) and atomic scale is N/g (N/mol). To get this on same magnitude for force and E, atomic is N/(kg/1000) =N*1000/kg. The force (field) is the same N but impacting a target of a 1/1000 units.
Atomic Coulomb constant: I introduce ka that is of class 1000 times bigger and rewrite e^2=2(alpha)*(epsilon)0 *h*c to ka*e^2=h*c. It can be derived ka=ks*6/(alpha) = 7,5210^12 Nm2/Ci2. The fine structure constant is derived ei*c^2/2= 0,007077. It is tough only a patch to the 1000mol/kmol ERROR.
The coupling: To keep this theory rigid the amount n of elementary charges need to match protons and kgs. Deploying a Avogadro type of number NApi=1kg/(1000*mpi). This give a Faraday constant Fi=NApi*ei=sqrt(ks)= 94000 Ci /mol protons. The correction is not about the coulomb being in mols, but having mpi kg:s as a common factor. This give ei=sqrt(4*1000^2*mpi/(3*c^2))= 1,57*10^-19 Ci. The charge mass coupling is exactly ei^2/mpi=4*1000^2/(3*c^2)=1,483533404*10^-11 Ci2/kg.
Planck: Further can be calculated Planck constant for Ci and kg compatible units hi=ei^2*ka/c=6,2*10^-34 Jis. This in classical (mechanical) Ji, not electric J
Proton mass: Elementary charge in square can be calculated ei^2=4mpi*1000^2/3c^2 and ei^2=mei^2*c^2*1000^2/3. From these proton mass mpi=mei^2*c^4/4. Ultimate value from iterating the formula sequence to Rydberg constant =10973731,56816 /m
19.June 2022 Timo Moilanen
Constants for mass based electrostatic theory
From iteration proton mass mpi=1,67170641445247*10^-27 kg and electron rest mass mei=9,09847475165718*10^-31 kg
Old formulas [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png[/IMG] in use [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png[/IMG] not i valid
New i (indifferent) charge / photon correlation [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png[/IMG]
Getting fine structure constant [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image008.png[/IMG] 0,007076851459316
Electric permittvity [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image010.png[/IMG]9,39034248*10^-12 Fi/m
Vacuum permeability [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image012.png[/IMG]1,1848876205*10^-6 N/Ai2
Exact ratio Q^2/M [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image014.png[/IMG] 1,483533408*10^-11 Ci2/kg
Planck constant [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image016.png[/IMG] 6,224222783457*10^-34 Jis[IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image018.png[/IMG]
Coulomb const. sphere [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image020.png[/IMG] 8,8743657095*10^9 Nm2/Ci2
Atomic Coulomb constant [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image022.png[/IMG]7,5239948956*10^12 Nm2/Ci Faradays constant [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image024.png[/IMG] 94203,8518823 Ci/molpi
Elementary charge [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image028.png[/IMG] 1,5748118345782*10^-19 Ci
Rydberg energy formula [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image030.png[/IMG]2,04767092830*10^-18 Ji can be written [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image032.png[/IMG] and [IMG]file:///C:/Users/tjmoi/AppData/Local/Temp/msohtmlclip1/01/clip_image034.png[/IMG]
1Ai ~= 0,971032239 A(SI) and 1,054436*10^-5mol (SI) /Ci
All new formulas and i-values are mathematically compatible.  4. Impossibly unreadable wall of text, but I note a 4-5% error in your fine structure constant. That is, your graphomanic string of calculations disagrees with experimentally determined values by many sigma. That would seem to imply that your work is wrong.  coulomb constant, fine structure constant, planck constant 