Friday, October 11, 2024

5x5: Polynomial Convergence of 5 Constants - Combined Newton-Raphson Iteration Technique - Standard Approach


The Algorithm of post 9/5/2022 new-algorithm-idea-multi-variate CONVERGES when holding the proton mass and electron mass (thus the $m_p\over m_e$ mass ratio) constant and iterating on these 5 constants:
$$e$$
$$\epsilon0$$
$$h$$
$$c$$
$$R_H$$

The initial values and tolerances need to be corrected and re-run the algorithm. Here is a table of the constants NIST/CODATA and what I used in the Newton_Raphson Iteration NRI method.
Image 1. Constants: NIST/CODATA & NRI



NRI method showing electron charge error getting smaller and smaller
(i.e., more negative on the log Y-scale)


This link is to the post that shows the color points on the graph with the inputs shown above in Image 1.

The algorithm is described in this post, only modification was to hold the proton and electron mass constant: https://phxmarker.blogspot.com/2022/09/new-algorithm-idea-multi-variate.html

A re-run is needed with the corrected inputs - I didn't use all the digits from NIST/CODATA.

The interesting thing is it appears to converge to a stable solution.  I need to investigate if it is UNIQUE by using different starting values and verfiy if it always converges to these same values.

Another interesting thing is a MAJOR NOTE: One does not need the proton radius solution to perform this NRI method of determining the constants. Simply don't drop the term, the reduced mass approximation (effective masses) when determining the constants. 

There may be some reason the $m_e\over m_p$ term was dropped from the polynomial - as I understand it, that assumption allows one to proceed with an analytic solution to Schrodinger's wave equations for solid-state theory. And that assumption does not have to interfere with determining the coefficients like anyone would do for their boundary value problems.

When you zoom in on the solutions, the last series of iterations, it curves back, very similar to the Lambert W function that is used to solve the iterative Widlar current source circuit.
Zoom in on last iterations of electron charge


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



The dream lives! The dream of solving for the constants. 

I'm looking into applying the constants to analyzing the "Island of Stability" - i.e., 
™Resonance & Harmony™ and MetaMaterials†™:
https://en.wikipedia.org/wiki/Island_of_stability



The Surfer, OM-IV

Sunday, October 6, 2024

Showing the 99 Iterations on the Plots: e, e0, h, c, r_h

9.1×10​−319.11×10​−319.12×10​−319.13×10​−31−0.002−0.00100.0010.002
trace 0trace 1trace 2y = ErrorElectronMass(x)
9.1×10​−319.11×10​−319.12×10​−319.13×10​−31−30−25−20−15−10−5
trace 0trace 1trace 2y = Math.log(Math.abs(ErrorElectronMass(x)))
1.6×10​−191.602×10​−191.604×10​−19−0.00500.005
trace 0trace 1trace 2y = ErrorElectronCharge(x)
1.6×10​−191.602×10​−191.604×10​−19−12−10−8−6
trace 0trace 1trace 2trace 3trace 4trace 5trace 6trace 7trace 8trace 9trace 10trace 11trace 12trace 13trace 14trace 15trace 16trace 17trace 18trace 19trace 20trace 21trace 22trace 23trace 24trace 25trace 26trace 27trace 28trace 29trace 30trace 31trace 32trace 33trace 34trace 35trace 36trace 37trace 38trace 39trace 40trace 41trace 42trace 43trace 44trace 45trace 46trace 47trace 48trace 49trace 50trace 51trace 52trace 53trace 54trace 55trace 56trace 57trace 58trace 59trace 60trace 61trace 62trace 63trace 64trace 65trace 66trace 67trace 68trace 69trace 70trace 71trace 72trace 73trace 74trace 75trace 76trace 77trace 78trace 79trace 80trace 81trace 82trace 83trace 84trace 85trace 86trace 87trace 88trace 89trace 90trace 91trace 92trace 93trace 94trace 95trace 96trace 97trace 98trace 99trace 100trace 101trace 102y = ErrorElectronCharge(x)
8.84p8.85p8.86p−14−12−10−8−6
trace 0trace 1trace 2trace 3trace 4trace 5trace 6trace 7trace 8trace 9trace 10trace 11trace 12trace 13trace 14trace 15trace 16trace 17trace 18trace 19trace 20trace 21trace 22trace 23trace 24trace 25trace 26trace 27trace 28trace 29trace 30trace 31trace 32trace 33trace 34trace 35trace 36trace 37trace 38trace 39trace 40trace 41trace 42trace 43trace 44trace 45trace 46trace 47trace 48trace 49trace 50trace 51trace 52trace 53trace 54trace 55trace 56trace 57trace 58trace 59trace 60trace 61trace 62trace 63trace 64trace 65trace 66trace 67trace 68trace 69trace 70trace 71trace 72trace 73trace 74trace 75trace 76trace 77trace 78trace 79trace 80trace 81trace 82trace 83trace 84trace 85trace 86trace 87trace 88trace 89trace 90trace 91trace 92trace 93trace 94trace 95trace 96trace 97trace 98trace 99trace 100trace 101trace 102y = Math.log(Math.abs(Error_e0(x)))
6.615×10​−346.62×10​−346.625×10​−346.63×10​−346.635×10​−34−12−10−8−6
trace 0trace 1trace 2trace 3trace 4trace 5trace 6trace 7trace 8trace 9trace 10trace 11trace 12trace 13trace 14trace 15trace 16trace 17trace 18trace 19trace 20trace 21trace 22trace 23trace 24trace 25trace 26trace 27trace 28trace 29trace 30trace 31trace 32trace 33trace 34trace 35trace 36trace 37trace 38trace 39trace 40trace 41trace 42trace 43trace 44trace 45trace 46trace 47trace 48trace 49trace 50trace 51trace 52trace 53trace 54trace 55trace 56trace 57trace 58trace 59trace 60trace 61trace 62trace 63trace 64trace 65trace 66trace 67trace 68trace 69trace 70trace 71trace 72trace 73trace 74trace 75trace 76trace 77trace 78trace 79trace 80trace 81trace 82trace 83trace 84trace 85trace 86trace 87trace 88trace 89trace 90trace 91trace 92trace 93trace 94trace 95trace 96trace 97trace 98trace 99trace 100trace 101trace 102y = Math.log(Math.abs(Error_h(x)))
299.5M300M−20−15−10
trace 0trace 1trace 2trace 3trace 4trace 5trace 6trace 7trace 8trace 9trace 10trace 11trace 12trace 13trace 14trace 15trace 16trace 17trace 18trace 19trace 20trace 21trace 22trace 23trace 24trace 25trace 26trace 27trace 28trace 29trace 30trace 31trace 32trace 33trace 34trace 35trace 36trace 37trace 38trace 39trace 40trace 41trace 42trace 43trace 44trace 45trace 46trace 47trace 48trace 49trace 50trace 51trace 52trace 53trace 54trace 55trace 56trace 57trace 58trace 59trace 60trace 61trace 62trace 63trace 64trace 65trace 66trace 67trace 68trace 69trace 70trace 71trace 72trace 73trace 74trace 75trace 76trace 77trace 78trace 79trace 80trace 81trace 82trace 83trace 84trace 85trace 86trace 87trace 88trace 89trace 90trace 91trace 92trace 93trace 94trace 95trace 96trace 97trace 98trace 99trace 100trace 101trace 102y = Math.log(Math.abs(Error_c(x)))
10.95M10.96M10.97M10.98M−20−18−16−14−12−10−8−6
trace 0trace 1trace 2trace 3trace 4trace 5trace 6trace 7trace 8trace 9trace 10trace 11trace 12trace 13trace 14trace 15trace 16trace 17trace 18trace 19trace 20trace 21trace 22trace 23trace 24trace 25trace 26trace 27trace 28trace 29trace 30trace 31trace 32trace 33trace 34trace 35trace 36trace 37trace 38trace 39trace 40trace 41trace 42trace 43trace 44trace 45trace 46trace 47trace 48trace 49trace 50trace 51trace 52trace 53trace 54trace 55trace 56trace 57trace 58trace 59trace 60trace 61trace 62trace 63trace 64trace 65trace 66trace 67trace 68trace 69trace 70trace 71trace 72trace 73trace 74trace 75trace 76trace 77trace 78trace 79trace 80trace 81trace 82trace 83trace 84trace 85trace 86trace 87trace 88trace 89trace 90trace 91trace 92trace 93trace 94trace 95trace 96trace 97trace 98trace 99trace 100trace 101trace 102y = Math.log(Math.abs(Error_Rh(x)))

-7.515424849397832 9.109383560899034e-31 1.60217662e-19 8.854187817e-12 6.62607004e-34 299792458 10973731.5685083 8.41235640479985e-16 0.00729735256 1.67262192e-27
-5.8971115321350664 9.114344700504225e-31 1.602397826809111e-19 8.851770688513177e-12 6.624858707417852e-34 299629212.0443415 10967687.245506773 8.41235640479985e-16 0.00729735256 1.67262192e-27
-6.591156369693428 9.111845836709579e-31 1.602309742441387e-19 8.852740414988349e-12 6.62534148348405e-34 299694988.7291945 10970102.535930475 8.41235640479985e-16 0.00729735256 1.67262192e-27
-7.284709727350453 9.110596847384763e-31 1.602265758472422e-19 8.853225392648997e-12 6.625582611107365e-34 299727912.9696378 10971309.500701131 8.41235640479985e-16 0.00729735256 1.67262192e-27
-7.97801579402642 9.1099724375462e-31 1.602243811617223e-19 8.853468120352604e-12 6.62570297634891e-34 299744419.52767915 10971912.61668511 8.41235640479985e-16 0.00729735256 1.67262192e-27
-8.67119482679135 9.10966024077092e-31 1.602232880496085e-19 8.853589749198316e-12 6.625762973460233e-34 299752719.03994274 10972213.874353414 8.41235640479985e-16 0.00729735256 1.67262192e-27
-9.364303531549092 9.109504137718674e-31 1.6022274567595068e-19 8.853650832615203e-12 6.625792788596846e-34 299756915.3062761 10972364.213263338 8.41235640479985e-16 0.00729735256 1.67262192e-27
-10.05736372449941 9.109426081507298e-31 1.6022247867054245e-19 8.853681643093567e-12 6.625807512722622e-34 299759059.9302607 10972439.092217313 8.41235640479985e-16 0.00729735256 1.67262192e-27
-10.750372327182195 9.10938705031312e-31 1.6022234935454027e-19 8.853697316349269e-12 6.625814691075618e-34 299760178.6810507 10972476.239443494 8.41235640479985e-16 0.00729735256 1.67262192e-27
-11.4433013879663 9.109367532815252e-31 1.6022228888717185e-19 8.853705420467896e-12 6.625818096394847e-34 299760784.45637333 10972494.51957189 8.41235640479985e-16 0.00729735256 1.67262192e-27
-12.136081470278663 9.109357772865622e-31 1.6022226284641456e-19 8.853709739679479e-12 6.625819615135135e-34 299761133.71854067 10972503.3653686 8.41235640479985e-16 0.00729735256 1.67262192e-27
-12.828572733572118 9.109352892058133e-31 1.602222540200534e-19 8.853712166254998e-12 6.62582019059723e-34 299761354.7075852 10972507.49361273 8.41235640479985e-16 0.00729735256 1.67262192e-27
-13.520484965634784 9.109350451019758e-31 1.6022225380139534e-19 8.853713646368718e-12 6.6258202944630686e-34 299761511.54791814 10972509.262776762 8.41235640479985e-16 0.00729735256 1.67262192e-27
-14.211250822894556 9.10934922996037e-31 1.6022225788670324e-19 8.853714653176257e-12 6.625820162595654e-34 299761636.3045279 10972509.852237057 8.41235640479985e-16 0.00729735256 1.67262192e-27
-14.899744031857105 9.109348618942479e-31 1.602222641240255e-19 8.853715423244395e-12 6.62581991293001e-34 299761745.01104605 10972509.851806756 8.41235640479985e-16 0.00729735256 1.67262192e-27
-15.583694188831462 9.109348312973724e-31 1.602222714372417e-19 8.853716074876568e-12 6.6258196044487e-34 299761845.68484235 10972509.556210736 8.41235640479985e-16 0.00729735256 1.67262192e-27
-16.258742074143946 9.109348159536807e-31 1.6022227928824812e-19 8.853716667245684e-12 6.625819266626412e-34 299761942.33524364 10972509.112990687 8.41235640479985e-16 0.00729735256 1.67262192e-27
-16.9168014810773 9.109348082369392e-31 1.60222287407967e-19 8.853717229916233e-12 6.62581891422315e-34 299762036.9669585 10972508.595925283 8.41235640479985e-16 0.00729735256 1.67262192e-27
-17.543255922926427 9.109348043343169e-31 1.6022229566185578e-19 8.85371777767176e-12 6.625818554605046e-34 299762130.5822397 10972508.041861711 8.41235640479985e-16 0.00729735256 1.67262192e-27
-18.115265483490322 9.109348023387396e-31 1.6022230398262955e-19 8.85371831793897e-12 6.6258181914670265e-34 299762223.68241507 10972507.469174068 8.41235640479985e-16 0.00729735256 1.67262192e-27
-18.603072324380214 9.109348012969658e-31 1.6022231233668707e-19 8.853718854391174e-12 6.625817826645557e-34 299762316.5181122 10972506.88716764 8.41235640479985e-16 0.00729735256 1.67262192e-27
-18.979252929055747 9.109348007322401e-31 1.6022232070719695e-19 8.853719388872119e-12 6.625817461064874e-34 299762409.2145673 10972506.300361784 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.23945440736334 9.10934800405397e-31 1.6022232908569844e-19 8.853719922351792e-12 6.625817095179777e-34 299762501.8347619 10972505.711117549 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.40045620187667 9.109348001978873e-31 1.6022233746802385e-19 8.853720455236135e-12 6.625816729234758e-34 299762594.4097372 10972505.12060659 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.489165444084975 9.109348000500927e-31 1.6022234585205159e-19 8.853720987778881e-12 6.625816363327577e-34 299762686.95525736 10972504.529322049 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.53831227093123 9.109347999313192e-31 1.602223542367377e-19 8.853721520116528e-12 6.6258159975327345e-34 299762779.4794007 10972503.937613187 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.56545163737693 9.109347998275518e-31 1.6022236262153316e-19 8.853722052280025e-12 6.6258156318746375e-34 299762871.9858189 10972503.345670715 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.576753638205577 9.109347997317615e-31 1.6022237100625662e-19 8.85372258430362e-12 6.625815266354521e-34 299762964.4763092 10972502.75348197 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58387524140449 9.10934799639233e-31 1.6022237939067522e-19 8.85372311620633e-12 6.625814900993366e-34 299763056.9521735 10972502.161148017 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585984172775937 9.109347995487432e-31 1.6022238777476815e-19 8.8537236479843e-12 6.625814535790523e-34 299763149.4136859 10972501.568625815 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.586336212868982 9.10934799458858e-31 1.6022239615850928e-19 8.853724179667337e-12 6.625814170748947e-34 299763241.86128265 10972500.975898989 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.588339851032643 9.109347993690769e-31 1.6022240454185293e-19 8.853724711234562e-12 6.625813805869681e-34 299763334.29505336 10972500.383108823 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58728248509197 9.109347992798687e-31 1.6022241292484085e-19 8.853725242682829e-12 6.625813441148428e-34 299763426.71488845 10972499.790144661 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.588922800488444 9.109347991903656e-31 1.602224213073961e-19 8.853725774039912e-12 6.62581307658993e-34 299763519.12103546 10972499.197070092 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58802213853708 9.109347991013313e-31 1.6022242968959805e-19 8.853726305279231e-12 6.625812712192384e-34 299763611.5132144 10972498.603822377 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.588851814558836 9.10934799012047e-31 1.6022243807139084e-19 8.853726836427892e-12 6.625812347963614e-34 299763703.89171195 10972498.01040674 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.586404099710833 9.109347989230023e-31 1.6022244645280846e-19 8.85372736742772e-12 6.625811983887544e-34 299763796.2563043 10972497.416899735 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.586310213357844 9.109347988332687e-31 1.6022245483376903e-19 8.853727898361236e-12 6.6258116199778465e-34 299763888.6073007 10972496.8231762 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585840201795452 9.10934798743513e-31 1.6022246321435253e-19 8.853728429163854e-12 6.625811256224035e-34 299763980.944554 10972496.229390427 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58643344990885 9.109347986536286e-31 1.6022247159455633e-19 8.853728959866536e-12 6.625810892641272e-34 299764073.26802903 10972495.635438839 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.586710110727836 9.109347985639178e-31 1.602224799743596e-19 8.853729490476923e-12 6.62581052921733e-34 299764165.5776964 10972495.04131506 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58675963703014 9.109347984742895e-31 1.602224883537648e-19 8.853730020964119e-12 6.625810165952051e-34 299764257.8734731 10972494.447102146 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585400584904235 9.109347983846802e-31 1.6022249673278322e-19 8.853730551343198e-12 6.625809802845237e-34 299764350.15547585 10972493.852721367 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585203759541564 9.109347982946896e-31 1.6022250511137656e-19 8.853731081616091e-12 6.625809439903736e-34 299764442.42380047 10972493.258203002 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585086010176465 9.109347982046485e-31 1.6022251348958498e-19 8.853731611789614e-12 6.625809077127126e-34 299764534.678312 10972492.663515134 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58469010403704 9.10934798114578e-31 1.602225218673963e-19 8.85373214184805e-12 6.625808714503221e-34 299764626.91907114 10972492.068739742 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58249072353875 9.109347980244004e-31 1.602225302447856e-19 8.853732671799201e-12 6.625808352043697e-34 299764719.1460152 10972491.473741688 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.583277614299398 9.109347979336017e-31 1.6022253862177059e-19 8.853733201645613e-12 6.62580798975011e-34 299764811.35939896 10972490.878660506 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.583000978419964 9.109347978430315e-31 1.6022254699835231e-19 8.853733731391689e-12 6.6258076276146225e-34 299764903.5589101 10972490.283407278 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.585704794003146 9.109347977523873e-31 1.602225553745457e-19 8.853734261039616e-12 6.625807265640688e-34 299764995.74461824 10972489.688095914 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58337547765411 9.109347976625168e-31 1.6022256375036773e-19 8.853734790561446e-12 6.625806903826248e-34 299765087.91629523 10972489.092554644 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.582524145817214 9.10934797571989e-31 1.6022257212576535e-19 8.853735319978565e-12 6.625806542171449e-34 299765180.07438517 10972488.496904656 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58215684591889 9.109347974812238e-31 1.602225805007613e-19 8.853735849297488e-12 6.6258061806813145e-34 299765272.218735 10972487.90108777 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.58331745446577 9.109347973903585e-31 1.6022258887533278e-19 8.853736378510252e-12 6.625805819355855e-34 299765364.3493024 10972487.30515645 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.581864847603274 9.109347972998285e-31 1.6022259724953921e-19 8.853736907614798e-12 6.625805458178795e-34 299765456.4659799 10972486.709080018 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.582836850797307 9.109347972088891e-31 1.6022260562331583e-19 8.853737436614573e-12 6.625805097169232e-34 299765548.56892747 10972486.112895366 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.580119672120123 9.109347971182318e-31 1.60222613996697e-19 8.853737965489957e-12 6.6258047363230814e-34 299765640.6580144 10972485.516484026 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.5813935179835 9.109347970268043e-31 1.6022262236967274e-19 8.853738494285442e-12 6.625804375636896e-34 299765732.7335056 10972484.919991583 8.41235640479985e-16 0.00729735256 1.67262192e-27
-19.579714900222736 9.10934796935745e-31 1.6022263074223546e-19 8.853739022957177e-12 6.625804015107775e-34 299765824.7950822 10972484.323325796 8.41235640479985e-16 0.00729735256 1.67262192e-27
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5 Constants Solved: Document Write Results On Page for first 99 Iterations

Saturday, October 5, 2024

5 Constants e, e0, h, c, r_h - Hold Electron Mass and Proton Mass, Iterate 5 Other Constants; See Console for Error (~=1e-9) & Constants

Friday, October 4, 2024

1st Iteration: Electron Mass(m_e), Charge(e), Permittivity (e0), Planck's Constant (h), Speed of Light (c), Rydberg Constant (Rh) - Plotly Polts with CODAT/NIST and Minimum Error 1st Iteration Values in Console