# 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. My theory has "evolved" to ka=ks*6/(alpha). "Fine structure constant" (patch) (alpha)=e*c^2/2 ​ 26.6 TiM

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

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.

This is a new structure for the constants that all are based on proton mass and are mathematically and arithmetically compatible. The only input is c speed of light making a flawless net of congruent formulas. In praxis the only value measured value is the Rydberg constant that I use as baseline for the whole system. The 4/3 in Coulomb constant come from a simple "geometric" integral. Because of the 1000time blunder over 100 years ago The so called fine structure constant is merely a arithmetic patch, and have a unit that I do not use to keep tings traditional in some aspect (for now, need to be corrected for several constants). The only visible way to explain all these new correlations is by my meaning math formulas (a few pages) and I'm not able to write an extensive book it is going to take for all details to be addressed, and therefore I need help because this is just the beginning of revising "everything". Hope I got some readable formulas picture address here at first.

6. Originally Posted by Timo Moilanen
This is a new structure for the constants that all are based on proton mass and are mathematically and arithmetically compatible. The only input is c speed of light making a flawless net of congruent formulas. In praxis the only value measured value is the Rydberg constant that I use as baseline for the whole system. The 4/3 in Coulomb constant come from a simple "geometric" integral. Because of the 1000time blunder over 100 years ago The so called fine structure constant is merely a arithmetic patch, and have a unit that I do not use to keep tings traditional in some aspect (for now, need to be corrected for several constants). The only visible way to explain all these new correlations is by my meaning math formulas (a few pages) and I'm not able to write an extensive book it is going to take for all details to be addressed, and therefore I need help because this is just the beginning of revising "everything". Hope I got some readable formulas picture address here at first.
it may be a novel scheme, but it fails to yield correct values. In a contest between novelty and correctness, novelty loses. Sorry.

7. it may be a novel scheme, but it fails to yield correct values. In a contest between novelty and correctness, novelty loses. Sorry.[/QUOTE]
It is not about novelty, it is about validity. The 1000 mol/kmol veritability must be regarded in all physics when describing atomic (subatomic) phenomenon measured in macroscopic world. This mean roughly that charge, electromotive force and derivatives have 1000 times higher values. This because the "force" is not distributed over kmols of particles. When on the other hand charge current and electromagnetic force is appearing in same magnitude in real (macroscopic) world. What is worth noticing is that this applies to atomic gravitation and subatomic phenomena measured in macroscopic units by "macroscopic" instruments. This means as an example that in a 2V lead battery cell the molecules experience a electric field in the magnitude of 2000V/m ( 2V/mm) minimum. This only directional since the E-field is very nonlinear (my f*A integral for example) due to microscopic topography and materials (atoms and valences).
So shortly "mainstream" is not only a little bit of, it is an impasse. And as you can see from my formulas they do not cover the electric field (yet), that is where the novelty is to be found, not in the minor fixes I have done.

These constants are in reality coupled features of particles not independent free entities. The biggest factor for the different "decimal" values is that these indexed "constants" is in units based on kg (via proton mass) not a random pair of 1A*1V*1s=1J, but units that directly ads up to classical mechanical units (SI-intent)

8. The fine structure constant is not a constant it is a myth born due to need. And my find of the 1000 time error excludes the need. The need to couple electric "structures" to classic kg based is here how I do it, and I'm very sure all alternative procedures will lead to the same results.

9. Originally Posted by Timo Moilanen
The fine structure constant is not a constant it is a myth born due to need. And my find of the 1000 time error excludes the need. The need to couple electric "structures" to classic kg based is here how I do it, and I'm very sure all alternative procedures will lead to the same results.
Myth or not, it is well defined and measured. Your derivation fails to reproduce the known value. Thus, your derivation is wrong. It’s really no more complicated than that.

10. [/QUOTE]

Myth or not, it is well defined and measured. Your derivation fails to reproduce the known value. Thus, your derivation is wrong. It’s really no more complicated than that.[/QUOTE]

As you probably see I have a new charge unit Ci, that is based on mass not SI C and is in percent scale different so the constant number values can not be same. The only measured Rydberg constant I use only as baseline as the last formula in the sting (network). The rest of all values come from my theories an the only parameter input c speed of light, and in beginning end proton mass and electron rest mass are also are also products of my math,
There is still a few places where mp+me is better than just mp.
For fine structure it has not been known exactly what it is. My formulas give it place origin and even units.
I did these to get a trustworthy Planck constant, now about 6,22*10^-34 Jis.to prove for myself (an some others)that the gravitational redshift need more mass than till today assumed.
I still try to paste a final collections of formulas
I'm also still looking for a writing scientist. (half the Nobel price)

11. It turned out that the electric permittivity E0=1/(12ks), this mathematically, and thinking of it the 4pi is only a logic input that do not work without putting it in separately. This leads to CODATA E0=12/4pi*E0i (close to) and vacuum permeability (mu)0 =4pi/12(mu)0i. The units for fine structure constant might be [ei*c^2]=s^2*m^-2*Ci^-1 (Yes that is upside down because it's how things work when assembling constants.)
Revised formulas to fit mp/me=1836,152673 and put in mp+me for accuracy since mpi+mei=mei*c^4/4.

9.7-22 The ampere comparison at the bottom should be 1 Ai= 0,971135 A (SI).
The integral over a spherical charge can be lim=1/3 , lim=4/3 for (r/2)^2 and integral over a round solid conductor lim=2/pi and 1/(2pi) resp. More over point to point values are are the basis of these constants and are probable to occur. Ex. ks/4 for r , 3ks/4 point to point , E0*4 and µ0/4 for r (field over total distance r).
Since these i-constant are calculated from lim. over a sphere at distant =(4*) 1/3 and the lim. value of a round conductor at dist.=2/pi resp1/(2pi). And mp/me ratio 1836,1526734311 and of course c=299792458 m/s, I can see no other way these constants could work than using the common charge unit Ci based on mass, to correlate exactly to mechanical units. The coulomb (ampere) today too much of for producing any scientifically correct numbers.

Today July 18. Final results of my research (for this nonquantum part)
Aug.3 added Josephson constant for comparison ( mass based electric units / Si units )KJ=505919,251215GHz/V