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

Error Calculation & Comments Below:

(0) error, dx, q

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

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

(1) Planck's Constant:

error, dx, h

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

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

(2) The electron mass:

error, dx, $e_m$

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

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

(4) Rydberg Constant ($R_H or R_∞$)

error, dx, $R_H$

-0.0005446185946568205, 10000000, 10973731.5685083

6.302669497415536e-11, 0.001, 10967761.570508301

(5) Permittivity of free space:

error, dx, $ϵ_0$

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

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

(6) Speed of Light, c

error, dx, c

-0.0005446185946568205, 10000000, 299792458

8.495870673641548e-11, 0.1, 299629274.3000001

Initial NIST/CODATA Error = -0.0005446185946568205  <~~~ That's Huge!

1st Iteration Error = 0.0027275446998467068

The good news is now the error is positive after 1st iteration, which is in the correct direction, however the magnitude of the error is greater.  More iterations can be done as well as an investigation into adjusting $r_p$ or $\alpha$.  Next, $R_H, r_p, \alpha$ iteration or another set of iterations need to be done to determine if the magnitude of the error is reducing and stable after more iterations.

Moar later...

The Surfer, OM-IV

Ω