n=1 (DRAFT): A Physics Letter A (Mathematical Physics): Proton Radius, the Rydberg Equation, and Fundamental Physics Constants

Proton Radius, the Rydberg Equation, and Fundamental Physics Constants

Mark Rohrbaugh - MSEE, ΩIV ,  Lyz Starwalker - Mµ*    ©1991 - 2023 - ∞

n=1 Bohr_model

Highlights

• Complete solution to proton radius puzzle
• Correction to Rydberg Equation (extends with proton to electron mass ratio)
• Roots of Full Rydberg Equation define fundamental physics constants

Abstract

A mathematical solution for the proton radius has been derived which adds a term to the Rydberg equation.  By avoiding using the reduced mass approximation (as has been done in solid-state theory and the hydrogen atom's analytical solution to the Schrödinger Wave Equation) and including the proton to electron mass ratio which brings in the proton radius.  A proton to electron mass ratio of 1836.15267 is calculated with a proton radius of 0.8412fm.

Keywords

Proton radius; proton to electron mass ratio; Rydberg equation 

1.0 Introduction
This derivation makes use of, as a starting point,: $$R_M={R_\infty\over {1+{m_e\over M}}}[1]$$

[1] https://en.wikipedia.org/wiki/Rydberg_constant#Alternative_expressions

1.1 Governing model

Schrödinger Equation (and Full Wave Equation)

(At lowest energies, n=1, Bohr model and Schrödinger model are equivalent for 1H hydrogen)

2.0 Derivation:

$R_M={R_\infty\over {1+{m_e\over M}}}$

$R_M(1+{m_e\over M})=R_\infty$

$(1+{m_e\over M})={R_\infty\over R_M}$

$1={R_\infty\over R_M}-{m_e\over M}$

For hydrogen, 1H @ 0°K:, $M=m_p$

$1={R_\infty\over R_H}-{m_e\over m_p}$

For the electron to proton mass ratio (inverse of proton to electron mass ratio), the derivation of the proton to electron mass ratio:

$$\mu={m_p\over m_e}=1836.15267\dots$$

$$m_e={2R_{H}h\over c\alpha^2}$$

( $m_e$ for the electron mass: Derivation of Rydberg equation for electron mass, also see [1] above)

$$m_e{\alpha^2\over R_{H}}={2h\over c}$$

$$m_e{\alpha^2\over \pi R_{H}}={2h\over \pi c}$$

By substitution, let $r_e={\alpha^2\over\pi R_{H}}$, then:

$$m_er_e={2h\over\pi c}$$

Now, because for every action there is an equal and opposite reaction, for every force there is an equal and opposite force, for every torque, there is an equal and opposite torque, equate $m_pr_p$ to $m_er_e$ to balance torque/spin between proton and electron:

$$m_er_e={2h\over\pi c}=m_pr_p$$

$$\therefore {m_p\over m_e}={r_e\over r_p}={\alpha^2\over\pi r_pR_{H}}=1836.15267$$

Where:

$$m_pr_p={2h\over\pi c}=4\ell m_{\ell}$$

$$r_p=0.841235640(294664)\;fm$$(Google Calculator for r_p)

$\mu={m_p\over m_e}={\alpha^2\over\pi r_pR_H}=1836.15267$ (Google Calculator for μ)

$1={R_\infty\over R_H}-{\pi r_pR_H\over \alpha^2}$

$R_\infty={m_ee^4\over 8{\epsilon_0}^2h^3c}$

$$1={{m_ee^4\over 8{\epsilon_0}^2h^3cR_H}}-{\pi r_pR_H\over \alpha^2}\;[2]$$

$m_p=$ proton mass

$m_e=$ electron mass

$e=$ elementary charge

$\epsilon_0=$ permittivity of free space

$r_p=$ proton radius

$r_e=$ effective torque arm radius for electron

$\alpha=$ fine-structure constant

$h=$ Planck constant

$c=$ speed of light

$R_{H}=$ Rydberg constant for 1H hydrogen atom

$R_{\infty}=$ Rydberg constant for massive nucleus atom

$R_{M}=$ Rydberg constant for Multi-proton atom

$\ell=$ Planck length

$m_{\ell}=$ Planck mass

3. Other Solutions for proton mass (ratio)

Boundary Value Problem method of determining coefficients use with wave equation for both electron and proton; Geometrical assuming vacuum density and information theory of black hole event horizon - Haramein et al

4. Conclusions

This derivation provides a polynomial [2] that predicts future trends of fundamental physics constants coefficient values as the measurements are refined over the years to be more precise.  The polynomial [2] may also actually DEFINE the constants - ongoing work with the polynomial investigating stability and convergence continues.  

There are various algorithms one can envision setting some constants as known and iterating to find the others, and likely all constants in the equation.  A timebase reference is also needed and likely why c is defined in mainstream via decree rather than derivation. 

Q.E.D.

Credit authorship contribution statement

Mark's derivation with Lyz's input to equate/balance the proton and electron 

Declaration of Competing Interest

n/a

Data availability

n/a

References

[standard]

*Mµ - Master of the µniverse, Macro and micro, inner and outer-dimensional

The Surfer, OM-IV

©2023 Mark Eric Rohrbaugh & Lyz Starwalker ©2023

Ω

The Physics Constants as a Boundary Value Problem

A glaring incompleteness of current scientific theory is the complete and total lack of solving the constants as a boundary value problem.

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

There is a large body of literature on this subject and electrical engineers known it well.  Signals and System engineering requires it. 

The constants are coefficients of a boundary value problem. 

Boundary Conditions:

1. Single Hydrogen atom - full analytical solution to Schrödinger's Equation [1]
2. 0ºK - Absolute Zero, no phonons/vibrations
3. No applied EM fields
4. vacuum? (implied by 1.)
5. t = -∞, 0, +∞, t + 2πft
6. Extract the https://en.wikipedia.org/wiki/Characteristic_polynomial
7. Instrinsic/characteristic polynomial/solution?
8. 2 body problem, do not reduce to single body such as in Squalid-State
9. n=1, ?more?

Considering it is simply a second order wave equation, what is the reason mainstream science has ignored the fundamentals?

This is quite different than looking at the physics constants as "free" parameters.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydsch.html*

* DO NOT USE REDUCED MASS ASSUMPTION!

[1] - establishes 1H@0ºK as reference mass - the Hydrogen atom / proton is a reference for all other mass

https://en.wikipedia.org/wiki/Nearly_free_electron_model <~~ Works for Technology not Science!

The Surfer, OM-IV

Ω

Proton Mass Prediction - Proton should be Slightly Lighter - The Surfer was correct!

An earlier post I did on the trends of which way the constants should be varying over the years as they get more and more precise, and my proton prediction did not agree with the trend of the data 2010-2018.  However, there is a 2020 paper that in the most precise measurement of the proton to electron mass ratio and it indicates/hints at the proton should be slightly lighter (which agrees with my prediction):

*https://physicsworld.com/a/protons-could-be-lighter-than-we-thought/

“Intriguingly, the proton-electron mass ratio we have measured is in fact compatible with the recent measurements of the proton mass, which were unexpectedly smaller than previous reference values,” adds Koelemeij. “This means that the proton indeed seems to be lighter than we thought.”*

Here is a link to the post were the trend predictions based upon the polynomial (full Rydberg equation) were made:

https://phxmarker.blogspot.com/2022/05/trends-past-and-future-fundamental.html

The Surfer, OM-IV (Ω4)

Ω

Speed of Light Calculation and Error Comparison -- 1e-10 Accuracy (~10 digits), cont'd

Note: this is a work in progress to determine if the Full Rydberg equation has roots by numerical methods - the roots being the fundamental physics constants.

And the final constant the error can be minimized by iteration:

(6) Speed of Light, c

error, dx, c

-0.0005446185946568205, 10000000, 299792458

-0.0005446185946568205, 1000000, 299792458

-0.0005446185946568205, 100000, 299792458

-0.00021094319785108784, 100000, 299692458

0.00012295495182268468, 100000, 299592458

0.00012295495182268468, 10000, 299592458

0.0000895551066193434, 10000, 299602458

0.00005615749095255751, 10000, 299612458

0.000022762104598728072, 10000, 299622458

-0.000010631052664744622, 10000, 299632458

-0.000010631052664744622, 1000, 299632458

-0.000007291837241241161, 1000, 299631458

-0.000003952599528678213, 1000, 299630458

-6.133395268337338e-7, 1000, 299629458

-6.133395268337338e-7, 100, 299629458

-2.794123009630667e-7, 100, 299629358

5.451514817345071e-8, 100, 299629258

5.451514817345071e-8, 10, 299629258

2.1122393389916283e-8, 10, 299629268

-1.2270359506239004e-8, 10, 299629278

-1.2270359506239004e-8, 1, 299629278

-8.931084205521245e-9, 1, 299629277

-5.591809126848091e-9, 1, 299629276

-2.252533826130332e-9, 1, 299629275

1.0867413635651246e-9, 1, 299629274

1.0867413635651246e-9, 0.1, 299629274

7.528138112888882e-10, 0.1, 299629274.1

4.1888625901265186e-10, 0.1, 299629274.20000005

8.495870673641548e-11, 0.1, 299629274.3000001

Electron Mass - New Algorithm Discussion, continued

https://energywavetheory.com/subatomic-particles/electron/

(2) The electron mass:

error, dx, $e_m$

-0.0005446185946568205, 1e-34, 9.109383560899034e-31

-0.0004348416825593615, 1e-34, 9.110383560899034e-31

-0.0003250647704619025, 1e-34, 9.111383560899033e-31

-0.00021528785836444353, 1e-34, 9.112383560899032e-31

-0.0001055109462667625, 1e-34, 9.113383560899032e-31

0.0000042659658308075166, 1e-34, 9.114383560899031e-31

0.0000042659658308075166, 9.999999999999999e-36, 9.114383560899031e-31

0.0000042659658308075166, 1e-36, 9.114383560899031e-31

0.000003168196709646409, 1e-36, 9.11437356089903e-31

0.0000020704275887073464, 1e-36, 9.11436356089903e-31

9.726584677682837e-7, 1e-36, 9.11435356089903e-31

-1.2511065350384598e-7, 1e-36, 9.11434356089903e-31

-1.2511065350384598e-7, 9.999999999999999e-38, 9.11434356089903e-31

-1.5333741276712942e-8, 9.999999999999999e-38, 9.11434456089903e-31

-1.5333741276712942e-8, 9.999999999999998e-39, 9.11434456089903e-31

-4.356050076204099e-9, 9.999999999999998e-39, 9.11434466089903e-31

-4.356050076204099e-9, 9.999999999999998e-40, 9.11434466089903e-31

-3.2582810893799774e-9, 9.999999999999998e-40, 9.11434467089903e-31

-2.160511880511251e-9, 9.999999999999998e-40, 9.114344680899031e-31

-1.0627426716425248e-9, 9.999999999999998e-40, 9.114344690899031e-31

3.502664824850399e-11, 9.999999999999998e-40, 9.114344700899032e-31

(5) Permittivity of free space:

error, dx, $\epsilon_0$

-0.0005446185946568205, 1e-15, 8.854187817e-12

-0.0003186985089359551, 1e-15, 8.853187817e-12

-0.00009270185473797543, 1e-15, 8.852187817e-12

-0.00009270185473797543, 1.0000000000000001e-16, 8.852187817e-12

-0.00007009797671997386, 1.0000000000000001e-16, 8.852087817e-12

-0.00004749333263676103, 1.0000000000000001e-16, 8.851987817e-12

-0.00002488792245347593, 1.0000000000000001e-16, 8.851887817e-12

-0.0000022817461350355117, 1.0000000000000001e-16, 8.851787817000001e-12

-0.0000022817461350355117, 1e-17, 8.851787817000001e-12

-2.108636454334345e-8, 1e-17, 8.851777817000002e-12

-2.108636454334345e-8, 1e-18, 8.851777817000002e-12

-2.108636454334345e-8, 1.0000000000000001e-19, 8.851777817000002e-12

1.5202716863171872e-9, 1.0000000000000001e-19, 8.851777717000002e-12

1.5202716863171872e-9, 1.0000000000000001e-20, 8.851777717000002e-12

-7.403918589332648e-10, 1.0000000000000001e-20, 8.851777727000002e-12

-7.403918589332648e-10, 1.0000000000000001e-21, 8.851777727000002e-12

-5.143258041684362e-10, 1.0000000000000001e-21, 8.851777726000002e-12

-2.882593053143978e-10, 1.0000000000000001e-21, 8.851777725000002e-12

-6.219280646035941e-11, 1.0000000000000001e-21, 8.851777724000002e-12

(1) Planck's Constant:

error, dx, h

-0.0005446185946568205, 1e-37, 6.62607004e-34

-0.00009172484027375472, 1e-37, 6.62507004e-34

-0.00009172484027375472, 1.0000000000000001e-38, 6.62507004e-34

-0.00004642042436875382, 1.0000000000000001e-38, 6.62497004e-34

-0.0000011132730078911024, 1.0000000000000001e-38, 6.6248700400000005e-34

-0.0000011132730078911024, 1.0000000000000001e-39, 6.6248700400000005e-34

-0.0000011132730078911024, 1.0000000000000001e-40, 6.6248700400000005e-34

-6.601876793022043e-7, 1.0000000000000001e-40, 6.62486904e-34

-2.0710207759844224e-7, 1.0000000000000001e-40, 6.62486804e-34

-2.0710207759844224e-7, 1.0000000000000001e-41, 6.62486804e-34

-1.617935022624195e-7, 1.0000000000000001e-41, 6.62486794e-34

-1.1648492426186152e-7, 1.0000000000000001e-41, 6.62486784e-34

-7.117634359676828e-8, 1.0000000000000001e-41, 6.62486774e-34

-2.5867760267139772e-8, 1.0000000000000001e-41, 6.62486764e-34

1.9440826282135504e-8, 1.0000000000000001e-41, 6.62486754e-34

1.9440826282135504e-8, 1.0000000000000002e-42, 6.62486754e-34

1.4909967482878983e-8, 1.0000000000000002e-42, 6.62486755e-34

1.0379108905667067e-8, 1.0000000000000002e-42, 6.62486756e-34

5.848250106410546e-9, 1.0000000000000002e-42, 6.62486757e-34

1.3173915291986305e-9, 1.0000000000000002e-42, 6.62486758e-34

1.3173915291986305e-9, 1.0000000000000003e-43, 6.62486758e-34

8.643059601354253e-10, 1.0000000000000003e-43, 6.624867581e-34

4.1122016902761516e-10, 1.0000000000000003e-43, 6.624867581999999e-34

-4.1865733102497416e-11, 1.0000000000000003e-43, 6.624867582999999e-34

The fine-structure constant, $\alpha$ is squared, thus, like the proton radius going negative, $\alpha$  reduces the error towards ZERO (0) by increasing to a LARGE value.

Once a second set of constants is generated from the first step of the algorithm, the error will be compared to the original 0.000544 and comments/analysis made/continued.

Ongoing... ...note: these posts are investigative - will summarize findings after investigation.

BASIC code (simple) as of 5/20/2023:

10 PRINT "Hello World"

100 Rem New Algorith 1.1 5/15/2023 MR

102 count = 0

106 print "error, dx, q"

110 Dim x2(7),sign(7), dx(7)

120 Rem Init some vars

125 aminerr=1.0

132 res = 1e-10

200 xpi=3.14159265358979323846

250 rem 8 coefs here

255 Rem elementary charge (e)-0

260 x2(0)=1.60217662e-19

263 xorig(0)=x2(0)

265 Rem Planck's constant (h)-1

300 x2(1)=6.62607004e-34

325 xorig(1)=x2(1)

350 rem electron mass (Me)-2

400 x2(2)=9.109383560899034e-31

425 xorig(2)=x2(2)

450 Rem Proton radius (Rp)-3

500 x2(3)=8.41235640479985e-16

525 xorig(3)=x2(3)

550 Rem Rydberg Constant (R_H or R_{\infty})-4

600 x2(4)=10973731.5685083

605 xorig(4)=x2(4)

610 Rem Permittivity of free space (e0)-5

620 x2(5)=8.854187817e-12

650 xorig(5)=x2(5)

701 Rem Speed of Light (c)-6

702 x2(6)=299792458.0

704 xorig(6)=x2(6)

706 Rem fine-structure constant (\alpha)-7

708 x2(7)=0.00729735256

709 xorig(7)=x2(7)

710 For i = 0 to 7

720 sign(i)=0

730 next i

740 dx(0) = 0.001e-19

741 dx(1) = 0.001e-34

742 dx(2) = 0.001e-31

743 dx(3) = 1e-16

744 dx(4) = 10000000.0

745 dx(5) = 0.001e-12

746 dx(6) = 10000000.0

747 dx(7) = 0.001

750 Rem define bit to be twiddled here

1030 eold = err

1050 gosub 1600

1051 REM enter starting values here (temporary initial start)

1075 rem x2(0)=1.602e-19

1076 rem x2(1)=6.626e-34

1077 rem x2(2)=9.109e-31

1078 rem x2(3)=8.0e-16

1080 REM EDIT "i" to select constant 0,1,2... etc.

1090 i = 1 

1100 print err;", ";dx(i);", ";x2(i)

1150 rem Main Loop1 

1210 z1=x2(i)+dx(i)

1220 z2=x2(i)-dx(i)

1230 xsave=x2(i)

1240 x2(i)=z1

1250 eold = err

1260 gosub 1600

1270 e1=err

1280 x2(i)=z2

1290 gosub 1600

1300 e2=err

1310 x2(i)=xsave

1320 err = eold

1325 rem print x2(i),z1,z2

1327 rem print err,e1,e2

1330 if abs(e1) < abs(err) then x2(i)=z1

1332 if abs(e1) < abs(err) then aminerr=e1

1340 if abs(e2) < abs(err) then x2(i)=z2

1342 if abs(e2) < abs(err) then aminerr=e2

1350 if (abs(e1) >= abs(err)) and (abs(e2) >= abs(err)) then dx(i)=dx(i)/10.0

1360 if abs(aminerr) < res then goto 1500

1370 gosub 1600

1380 goto 1100

1500 gosub 1600

1510 print err;", ";dx(i);", ";x2(i)

1525 end

1550 REM Subroutines:

1600 rem starting error

1700 xerr1=x2(2)*x2(0)^4/(8*x2(6)*x2(5)^2*x2(1)^3*x2(4))

1800 yerr2=-xpi*x2(3)*x2(4)/(x2(7)^2)

1900 err = xerr1 + yerr2 - 1.0

2000 return

One slight modification to the polynomial is to use the $m_e\over m_p$ format, working with the proton mass, then calculating the radius afterwards...

New Algorithm Requires Modification - Crash & Burn 2.0

Looks like the algorithm will need some modification or the polynomial expanded/re-written.  The polynomial as written has the proton radius, and obviously, by inspection, if one tries to iterate for the proton radius, it comes out NEGATIVE due to the other constants being so far off:

error, dx, $r_p$

-0.0005446185946568205, 1e-16, 8.41235640479985e-16

-0.0009587998163527178, 9.999999999999999e-18, 8e-16

-0.0009523258036489013, 9.999999999999999e-18, 7.9e-16

-0.0009458517909451958, 9.999999999999999e-18, 7.800000000000001e-16

-0.0009393777782413792, 9.999999999999999e-18, 7.700000000000001e-16

-0.0009329037655375627, 9.999999999999999e-18, 7.600000000000001e-16

-0.0009264297528338572, 9.999999999999999e-18, 7.500000000000002e-16

-0.0009199557401300407, 9.999999999999999e-18, 7.400000000000002e-16

-0.0009134817274263352, 9.999999999999999e-18, 7.300000000000002e-16

-0.0009070077147225186, 9.999999999999999e-18, 7.200000000000003e-16

-0.0009005337020188131, 9.999999999999999e-18, 7.100000000000003e-16

-0.0008940596893149966, 9.999999999999999e-18, 7.000000000000003e-16

-0.0008875856766112911, 9.999999999999999e-18, 6.900000000000004e-16

-0.0008811116639074745, 9.999999999999999e-18, 6.800000000000004e-16

-0.000874637651203658, 9.999999999999999e-18, 6.700000000000004e-16

-0.0008681636384999525, 9.999999999999999e-18, 6.600000000000005e-16

-0.000861689625796136, 9.999999999999999e-18, 6.500000000000005e-16

-0.0008552156130924304, 9.999999999999999e-18, 6.400000000000005e-16

-0.0008487416003886139, 9.999999999999999e-18, 6.300000000000006e-16

-0.0008422675876849084, 9.999999999999999e-18, 6.200000000000006e-16

-0.0008357935749810919, 9.999999999999999e-18, 6.100000000000006e-16

-0.0008293195622773863, 9.999999999999999e-18, 6.000000000000007e-16

-0.0008228455495735698, 9.999999999999999e-18, 5.900000000000007e-16

-0.0008163715368697533, 9.999999999999999e-18, 5.800000000000007e-16

-0.0008098975241660478, 9.999999999999999e-18, 5.700000000000008e-16

-0.0008034235114622312, 9.999999999999999e-18, 5.600000000000008e-16

-0.0007969494987585257, 9.999999999999999e-18, 5.500000000000009e-16

-0.0007904754860547092, 9.999999999999999e-18, 5.400000000000009e-16

-0.0007840014733510037, 9.999999999999999e-18, 5.300000000000009e-16

-0.0007775274606471871, 9.999999999999999e-18, 5.20000000000001e-16

-0.0007710534479434816, 9.999999999999999e-18, 5.10000000000001e-16

-0.0007645794352396651, 9.999999999999999e-18, 5.00000000000001e-16

-0.0007581054225358486, 9.999999999999999e-18, 4.900000000000011e-16

-0.000751631409832143, 9.999999999999999e-18, 4.800000000000011e-16

-0.0007451573971283265, 9.999999999999999e-18, 4.700000000000011e-16

-0.000738683384424621, 9.999999999999999e-18, 4.600000000000012e-16

-0.0007322093717208045, 9.999999999999999e-18, 4.500000000000012e-16

-0.000725735359017099, 9.999999999999999e-18, 4.400000000000012e-16

-0.0007192613463132824, 9.999999999999999e-18, 4.3000000000000117e-16

-0.0007127873336094659, 9.999999999999999e-18, 4.2000000000000115e-16

-0.0007063133209057604, 9.999999999999999e-18, 4.1000000000000114e-16

-0.0006998393082019438, 9.999999999999999e-18, 4.0000000000000113e-16

-0.0006933652954982383, 9.999999999999999e-18, 3.900000000000011e-16

-0.0006868912827944218, 9.999999999999999e-18, 3.800000000000011e-16

-0.0006804172700907163, 9.999999999999999e-18, 3.700000000000011e-16

-0.0006739432573868998, 9.999999999999999e-18, 3.6000000000000107e-16

-0.0006674692446831942, 9.999999999999999e-18, 3.5000000000000105e-16

-0.0006609952319793777, 9.999999999999999e-18, 3.4000000000000104e-16

-0.0006545212192755612, 9.999999999999999e-18, 3.30000000000001e-16

-0.0006480472065718557, 9.999999999999999e-18, 3.20000000000001e-16

-0.0006415731938680391, 9.999999999999999e-18, 3.10000000000001e-16

-0.0006350991811643336, 9.999999999999999e-18, 3.00000000000001e-16

-0.0006286251684605171, 9.999999999999999e-18, 2.9000000000000097e-16

-0.0006221511557568116, 9.999999999999999e-18, 2.8000000000000095e-16

-0.000615677143052995, 9.999999999999999e-18, 2.7000000000000094e-16

-0.0006092031303492895, 9.999999999999999e-18, 2.600000000000009e-16

-0.000602729117645473, 9.999999999999999e-18, 2.500000000000009e-16

-0.0005962551049416565, 9.999999999999999e-18, 2.400000000000009e-16

-0.0005897810922379509, 9.999999999999999e-18, 2.300000000000009e-16

-0.0005833070795341344, 9.999999999999999e-18, 2.200000000000009e-16

-0.0005768330668304289, 9.999999999999999e-18, 2.100000000000009e-16

-0.0005703590541266124, 9.999999999999999e-18, 2.000000000000009e-16

-0.0005638850414229069, 9.999999999999999e-18, 1.9000000000000092e-16

-0.0005574110287190903, 9.999999999999999e-18, 1.8000000000000093e-16

-0.0005509370160153848, 9.999999999999999e-18, 1.7000000000000094e-16

-0.0005444630033115683, 9.999999999999999e-18, 1.6000000000000095e-16

-0.0005379889906077517, 9.999999999999999e-18, 1.5000000000000096e-16

-0.0005315149779040462, 9.999999999999999e-18, 1.4000000000000097e-16

-0.0005250409652002297, 9.999999999999999e-18, 1.3000000000000098e-16

-0.0005185669524965242, 9.999999999999999e-18, 1.20000000000001e-16

-0.0005120929397927076, 9.999999999999999e-18, 1.1000000000000099e-16

-0.0005056189270890021, 9.999999999999999e-18, 1.0000000000000098e-16

-0.0004991449143851856, 9.999999999999999e-18, 9.000000000000098e-17

-0.0004926709016813691, 9.999999999999999e-18, 8.000000000000098e-17

-0.00048619688897766355, 9.999999999999999e-18, 7.000000000000098e-17

-0.000479722876273847, 9.999999999999999e-18, 6.000000000000097e-17

-0.0004732488635701415, 9.999999999999999e-18, 5.000000000000097e-17

-0.000466774850866325, 9.999999999999999e-18, 4.000000000000097e-17

-0.00046030083816261946, 9.999999999999999e-18, 3.000000000000097e-17

-0.00045382682545880293, 9.999999999999999e-18, 2.000000000000097e-17

-0.0004473528127550974, 9.999999999999999e-18, 1.000000000000097e-17

-0.0004408788000512809, 9.999999999999999e-18, 9.706686919711669e-31

-0.00043440478734746435, 9.999999999999999e-18, -9.999999999999029e-18

-0.00042793077464375884, 9.999999999999999e-18, -1.9999999999999028e-17

-0.0004214567619399423, 9.999999999999999e-18, -2.9999999999999027e-17

-0.0004149827492362368, 9.999999999999999e-18, -3.999999999999902e-17

-0.00040850873653242026, 9.999999999999999e-18, -4.9999999999999025e-17

-0.00040203472382871475, 9.999999999999999e-18, -5.999999999999903e-17

-0.0003955607111248982, 9.999999999999999e-18, -6.999999999999903e-17

-0.0003890866984211927, 9.999999999999999e-18, -7.999999999999903e-17

-0.00038261268571737617, 9.999999999999999e-18, -8.999999999999903e-17

-0.00037613867301355963, 9.999999999999999e-18, -9.999999999999904e-17

-0.0003696646603098541, 9.999999999999999e-18, -1.0999999999999904e-16

-0.0003631906476060376, 9.999999999999999e-18, -1.1999999999999904e-16

-0.0003567166349023321, 9.999999999999999e-18, -1.2999999999999903e-16

-0.00035024262219851554, 9.999999999999999e-18, -1.3999999999999902e-16

-0.00034376860949481003, 9.999999999999999e-18, -1.49999999999999e-16

-0.0003372945967909935, 9.999999999999999e-18, -1.59999999999999e-16

-0.000330820584087288, 9.999999999999999e-18, -1.69999999999999e-16

-0.00032434657138347145, 9.999999999999999e-18, -1.7999999999999898e-16

-0.0003178725586796549, 9.999999999999999e-18, -1.8999999999999897e-16

-0.0003113985459759494, 9.999999999999999e-18, -1.9999999999999896e-16

-0.00030492453327213287, 9.999999999999999e-18, -2.0999999999999895e-16

-0.00029845052056842736, 9.999999999999999e-18, -2.1999999999999894e-16

-0.0002919765078646108, 9.999999999999999e-18, -2.2999999999999895e-16

-0.0002855024951609053, 9.999999999999999e-18, -2.3999999999999897e-16

-0.0002790284824570888, 9.999999999999999e-18, -2.49999999999999e-16

-0.00027255446975327224, 9.999999999999999e-18, -2.59999999999999e-16

-0.00026608045704956673, 9.999999999999999e-18, -2.69999999999999e-16

-0.0002596064443457502, 9.999999999999999e-18, -2.7999999999999903e-16

-0.0002531324316420447, 9.999999999999999e-18, -2.8999999999999904e-16

-0.00024665841893822815, 9.999999999999999e-18, -2.9999999999999906e-16

-0.00024018440623452264, 9.999999999999999e-18, -3.0999999999999907e-16

-0.0002337103935307061, 9.999999999999999e-18, -3.199999999999991e-16

-0.0002272363808270006, 9.999999999999999e-18, -3.299999999999991e-16

-0.00022076236812318406, 9.999999999999999e-18, -3.399999999999991e-16

-0.00021428835541936753, 9.999999999999999e-18, -3.4999999999999913e-16

-0.00020781434271566201, 9.999999999999999e-18, -3.5999999999999914e-16

-0.00020134033001184548, 9.999999999999999e-18, -3.6999999999999916e-16

-0.00019486631730813997, 9.999999999999999e-18, -3.7999999999999917e-16

-0.00018839230460432344, 9.999999999999999e-18, -3.899999999999992e-16

-0.00018191829190061792, 9.999999999999999e-18, -3.999999999999992e-16

-0.0001754442791968014, 9.999999999999999e-18, -4.099999999999992e-16

-0.00016897026649309588, 9.999999999999999e-18, -4.1999999999999923e-16

-0.00016249625378927934, 9.999999999999999e-18, -4.2999999999999925e-16

-0.0001560222410854628, 9.999999999999999e-18, -4.3999999999999926e-16

-0.0001495482283817573, 9.999999999999999e-18, -4.499999999999992e-16

-0.00014307421567794076, 9.999999999999999e-18, -4.599999999999992e-16

-0.00013660020297423525, 9.999999999999999e-18, -4.699999999999992e-16

-0.00013012619027041872, 9.999999999999999e-18, -4.799999999999991e-16

-0.0001236521775667132, 9.999999999999999e-18, -4.899999999999991e-16

-0.00011717816486289667, 9.999999999999999e-18, -4.999999999999991e-16

-0.00011070415215919116, 9.999999999999999e-18, -5.09999999999999e-16

-0.00010423013945537463, 9.999999999999999e-18, -5.19999999999999e-16

-0.00009775612675155809, 9.999999999999999e-18, -5.299999999999989e-16

-0.00009128211404785258, 9.999999999999999e-18, -5.399999999999989e-16

-0.00008480810134403605, 9.999999999999999e-18, -5.499999999999989e-16

-0.00007833408864033053, 9.999999999999999e-18, -5.599999999999988e-16

-0.000071860075936514, 9.999999999999999e-18, -5.699999999999988e-16

-0.00006538606323280849, 9.999999999999999e-18, -5.799999999999988e-16

-0.000058912050528991955, 9.999999999999999e-18, -5.899999999999987e-16

-0.00005243803782517542, 9.999999999999999e-18, -5.999999999999987e-16

-0.00004596402512146991, 9.999999999999999e-18, -6.099999999999987e-16

-0.000039490012417653375, 9.999999999999999e-18, -6.199999999999986e-16

-0.00003301599971394786, 9.999999999999999e-18, -6.299999999999986e-16

-0.00002654198701013133, 9.999999999999999e-18, -6.399999999999986e-16

-0.000020067974306425818, 9.999999999999999e-18, -6.499999999999985e-16

-0.000013593961602609284, 9.999999999999999e-18, -6.599999999999985e-16

-0.000007119948898903772, 9.999999999999999e-18, -6.699999999999985e-16

-6.459361950872378e-7, 9.999999999999999e-18, -6.799999999999984e-16

-6.459361950872378e-7, 9.999999999999999e-19, -6.799999999999984e-16

1.465075394335713e-9, 9.999999999999999e-19, -6.809999999999984e-16

1.465075394335713e-9, 9.999999999999999e-20, -6.809999999999984e-16

1.465075394335713e-9, 9.999999999999998e-21, -6.809999999999984e-16

1.465075394335713e-9, 9.999999999999997e-22, -6.809999999999984e-16

8.176739285659096e-10, 9.999999999999997e-22, -6.809989999999984e-16

1.70272684840711e-10, 9.999999999999997e-22, -6.809979999999984e-16

1.70272684840711e-10, 9.999999999999997e-23, -6.809979999999984e-16

1.055326936949541e-10, 9.999999999999997e-23, -6.809978999999984e-16

4.0792480504592277e-11, 9.999999999999997e-23, -6.809977999999984e-16

Likely will have to iterate ALL constants that are in the original limited Rydberg equation EXCEPT for proton radius until they are corrected enough to allow for the proton radius to be a positive number closer to expected value.  

updates incoming... 

For the Rydberg Constant $(R_H or R_{\infty})$

error, dx, $R_H$

-0.0005446185946568205, 10000000, 10973731.5685083

-0.0005446185946568205, 1000000, 10973731.5685083 -0.0005446185946568205, 100000, 10973731.5685083 -0.0005446185946568205, 10000, 10973731.5685083 0.0003679759110610803, 10000, 10963731.5685083 0.0003679759110610803, 1000, 10963731.5685083 0.0002766415942339062, 1000, 10964731.5685083 0.00018532392648995533, 1000, 10965731.5685083 0.00009402290327442664, 1000, 10966731.5685083 0.0000027385200349616667, 1000, 10967731.5685083 0.0000027385200349616667, 100, 10967731.5685083 0.0000027385200349616667, 10, 10967731.5685083 0.0000018257602190097089, 10, 10967741.5685083 9.130020666159311e-7, 10, 10967751.5685083 2.4557778033340583e-10, 10, 10967761.5685083 2.4557778033340583e-10, 1, 10967761.5685083 2.4557778033340583e-10, 0.1, 10967761.5685083 2.4557778033340583e-10, 0.01, 10967761.5685083 2.4557778033340583e-10, 0.001, 10967761.5685083 1.5430212663147813e-10, 0.001, 10967761.569508301 6.302669497415536e-11, 0.001, 10967761.570508301

Will continue to check all constants to uncover other issues and

reformulate approach.

The Surfer, OM-IV

Ω

Quantum Geometry - Dramatically Simplifies Calculations

https://www.science-astronomy.com/2022/09/scientists-discover-jewel-at-heart-of.html

Geometrical nature of physical reality allows for dramatically simplified calculations. This makes determining the "boundary problem" coefficients - or constants - possible.

The constants of physics are not "free variables" but boundary problem coefficients.

It is the intent of this blog to verify the roots/solution to the Full Rydberg equation converges to these constants.

https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html

It's simply a matter of time... ...more later.

The Surfer, OM-IV

©2023 Mark Eric Rohrbaugh & Lyz Starwalker © 2023

Ω

ECO - Electron Charge Only - Fixing Other Constants - Root Algorithm & Results

https://spark.iop.org/perrin-tube-sign-electron-charge

Solving for the electron charge only (part of step 2 of The Algorithm), here is a simple BASIC routine and results.  BASIC is being used so the algorithm is easily viewable and verifiable. 

Here is the BASIC code (online interpreter - https://www.calormen.com/jsbasic/):

1 REM variables only recognize first two characters thus xx1 and xx2 are same variable

10 PRINT "Hello World"

100 Rem New Algorithm 1.1 5/15/2023 MR

102 count = 0

106 print "error, dx, q"

110 Dim x2(7),sign(7), dx(7)

120 Rem Init some vars

125 aminerr=1.0

132 res = 1e-10

200 xpi=3.14159265358979323846

250 rem 8 coefs here

255 Rem elementary charge (e)-0

260 x2(0)=1.60217662e-19

263 xorig(0)=x2(0)

265 Rem Planck's constant (h)-1

300 x2(1)=6.62607004e-34

325 xorig(1)=x2(1)

350 rem eletron mass (Me)-2

400 x2(2)=9.109383560899034e-31

425 xorig(2)=x2(2)

450 Rem Proton radius (Rp)-3

500 x2(3)=8.41235640479985e-16

525 xorig(3)=x2(3)

550 Rem Rydberg Constant (R_H or R_{\infty})-4

600 x2(4)=10973731.5685083

605 xorig(4)=x2(4)

610 Rem Permittivity of free space (e0)-5

620 x2(5)=8.854187817e-12

650 xorig(5)=x2(5)

701 Rem Speed of Light (c)-6

702 x2(6)=299792458.0

704 xorig(6)=x2(6)

706 Rem fine-structure constant (\alpha)-7

708 x2(7)=0.00729735256

709 xorig(7)=x2(7)

710 For i = 0 to 7

720 sign(i)=0

730 dx(i) = 0.001e-19

740 next i

750 Rem define bit to be twiddled here

1030 eold = err

1050 gosub 1600

1075 x2(0)=1.602e-19

1100 print err;", ";dx(0);", ";x2(0)

1150 rem Main Loop1 

1210 z1=x2(0)+dx(0)

1220 z2=x2(0)-dx(0)

1230 xsave=x2(0)

1240 x2(0)=z1

1250 eold = err

1260 gosub 1600

1270 e1=err

1280 x2(0)=z2

1290 gosub 1600

1300 e2=err

1310 x2(0)=xsave

1320 err = eold

1325 rem print x2(0),z1,z2

1327 rem print err,e1,e2

1330 if abs(e1) < abs(err) then x2(0)=z1

1332 if abs(e1) < abs(err) then aminerr=e1

1340 if abs(e2) < abs(err) then x2(0)=z2

1342 if abs(e2) < abs(err) then aminerr=e2

1350 if (abs(e1) >= abs(err)) and (abs(e2) >= abs(err)) then dx(0)=dx(0)/10.0

1360 if abs(aminerr) < res then goto 1500

1370 gosub 1600

1380 goto 1100

1500 gosub 1600

1510 print err;", ";dx(0);", ";x2(0)

1525 end

1550 REM Subroutines:

1600 rem starting error

1700 xerr1=x2(2)*x2(0)^4/(8*x2(6)*x2(5)^2*x2(1)^3*x2(4))

1800 yerr2=-xpi*x2(3)*x2(4)/(x2(7)^2)

1900 err = xerr1 + yerr2 - 1.0

2000 return

Here are the results for a resolution of the error of the polynomial from ideal, res = 1e-10 case:

error, dx, q

-0.0005446185946568205, 1e-22, 1.60217662e-19*

-0.0009854958223842747, 1.0000000000000001e-23, 1.602e-19

-0.0007358946446630599, 1.0000000000000001e-23, 1.6021e-19

-0.0004862467236895762, 1.0000000000000001e-23, 1.6022e-19

-0.0002365520536283805, 1.0000000000000001e-23, 1.6023000000000001e-19

0.000013189371356858715, 1.0000000000000001e-23, 1.6024000000000002e-19

0.000013189371356858715, 1.0000000000000001e-24, 1.6024000000000002e-19

-0.000011786875279473641, 1.0000000000000001e-24, 1.6023900000000003e-19

-0.000011786875279473641, 1.0000000000000002e-25, 1.6023900000000003e-19

-0.000009289271657997311, 1.0000000000000002e-25, 1.6023910000000003e-19

-0.000006791663360261602, 1.0000000000000002e-25, 1.6023920000000003e-19

-0.000004294050386932646, 1.0000000000000002e-25, 1.6023930000000004e-19

-0.0000017964327371222666, 1.0000000000000002e-25, 1.6023940000000004e-19

7.011895886144259e-7, 1.0000000000000002e-25, 1.6023950000000005e-19

7.011895886144259e-7, 1.0000000000000002e-26, 1.6023950000000005e-19

4.5142714544255114e-7, 1.0000000000000002e-26, 1.6023949000000004e-19

2.0166474912208798e-7, 1.0000000000000002e-26, 1.6023948000000003e-19

-4.8097600902075044e-8, 1.0000000000000002e-26, 1.6023947000000002e-19

-4.8097600902075044e-8, 1.0000000000000002e-27, 1.6023947000000002e-19

-2.3121367820344574e-8, 1.0000000000000002e-27, 1.6023947100000003e-19

1.8548658164974086e-9, 1.0000000000000002e-27, 1.6023947200000003e-19

1.8548658164974086e-9, 1.0000000000000002e-28, 1.6023947200000003e-19

-6.427575138800989e-10, 1.0000000000000002e-28, 1.6023947190000004e-19

-6.427575138800989e-10, 1.0000000000000002e-29, 1.6023947190000004e-19

-3.92995080922276e-10, 1.0000000000000002e-29, 1.6023947191000005e-19

-1.43232647964453e-10, 1.0000000000000002e-29, 1.6023947192000005e-19

1.0653011806027735e-10, 1.0000000000000002e-29, 1.6023947193000006e-19

1.0653011806027735e-10, 1.0000000000000003e-30, 1.6023947193000006e-19

8.155409680909997e-11, 1.0000000000000003e-30, 1.6023947192900007e-19

The algorithm requires each constant to be solved for minimum error, using original NIST/CODATA as starting point.  The initial error is about -0.00054, so each constant is iterated until the error is zero to the specified res(olution), then a new error is calculated with the new set of constants.  Check to see if the error from the new set of constants is less than the starting error.  If it is, continue and check if converging.

Therefore, this is only 1 of 8 constants. 

*Also, note, some work for initial and final printing of the values is needed for completeness. Bold initial value is hand entered...

All bugs are not worked out as this is early code.  This code is being written with future consideration of iterating ALL 8 constants, however, to make progress, I will be blogging about each constant individually just like the electron charge here.

CSV, Comma Separated Variables, format is used for output for easy importing into Excel or most common spreadsheet tools.  Will be showing plots of error & vaules converging later. Soon, however, moar than 2 weeks...

The Surfer, OM-IV

Russell & RFKjr

Ω

New Polynomial Root Algorithm, continued

First column is the electron charge, it is iterated while the other constants are held to their original values and the LAST column is the ERROR.  The closer to zero the ERROR is the better the coefficients fit the theory. electron charge e = 1.602e-19 Coulombs, note the algorithm will compute to any desired number of decimal places. This is an intermediate step, all steps of the algorithm must be completed to verify that the overall error is going to zero. Ongoing…

Moar l8ter

This post is a continuation of:

https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html

https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html

For those new to the blog, here is a post with the "mainstream" derivation of the polynomial:

https://phxmarker.blogspot.com/2021/11/this-is-how-we-do-it-free-full-rydberg.html

©2023 Mark E Rohrbaugh & Lyz Starwalker 

The Surfer, OM-IV

Ω

Questioning Science Videos Link List

Joe Rogan - Eric Weinstein Podcast #1945

What's Going Wrong in Particle Physics? (This is why I lost faith in science.) Sabine Hossenfelder

Moar later. They're getting warmer...

¿Qué?¿Qué? Constants as FREE Parameters in Physics - What What? ¿Qué?¿Qué?

Constants as FREE parameters in physics may be incorrect. The constants may in fact be parameters of a boundary value problem in mathematics of the wave function...

Scientists consider the constants free parameters.  It seems like poor thinking and poor math. 

Some supporting links can be found here:

 https://freespoke.com/search/web?q=constants+as+free+parameters+in+physics

moar later...

Galois Theory - Roots of Polynomials

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

"In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand.

Galois introduced the subject for studying roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is solvable by radicals if its roots may be expressed by a formula involving only integers, nth roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals."

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

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

https://opensea.io/assets/matic/0x24A11e702CD90f034Ea44FaF1e180C0C654AC5d9/32033

Owned by Original Owner

0.08ETH ~= $100USD original price

4th Order Pimp Walk:

The Book - Paul Erdos -🥇📕

 

He had his own idiosyncratic vocabulary; although an agnostic atheist,[68][69] he spoke of "The Book", a visualization of a book in which God had written down the best and most elegant proofs for mathematical theorems.[70] Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF).[71][72] He accused SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from The Book!" This later inspired a book titled Proofs from the Book.

from:

https://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Personality

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

"The Book"

moar later...

The Surfer, OM-IV

https://www.linkedin.com/feed/update/urn:li:activity:7017704130341208064/

Ω