Click the "Show output" button for more readable and total output log.
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| Full Rydberg Polynomial |
For now, the results for the roots for our most recent re-derivation:
(mks units)
elementary charge, e=1.6022514387454(393)e-19Planck's constant, h=6.6257738721130(28)e-34electron mass, m_e=9.1097907336274(77)e-31Proton radius, r_p=8.4119972191308(31)e-16Rydberg constant, R_H=10973241.071596(634)Permittivity of free space, epsilon_0=8.8537920581144(05)e-12Speed of Light, c=299779058.06636(304)Fine-structure constant, alpha=0.0072976787382677(79)
Digits resolution 14
Calc'd proton mass= 1.6726933172773(2)e-27
NIST proton mass= 1.67262192369(51) x 10-27 kg
Final fine-structure constant= 0.0072976787382677(79)
Input fine-structure constant= 0.00729735256 (compare to above line)
Proton/electron mass ratio=1836.1490029653(637)
The results are slightly different from The Oracle TOPPCG2 runs due to previously only solving for 7 of the 8 roots.
ReplyDeleteThe previous attempts used m_e in the "new" term (the term that is dropped by mainstream using the reduced mass approximation). Therefore, by adding this extra degree of freedom/variable, the final convergent result is different. This is similar to holding any of the constants to a desired or known GOLDEN value, and letting the algorith optimize the others based upon choice for a specific constant.
This can be done by setting the sign{?} = 0 instead of 1 or -1 (defaults to sign = 1).
When all of the constants are plotted versus iteration #, as well as the sign{?} variable, one can see if things converge smoothly or if there is random chaotic behavior. I've only zoomed into one or two, so once the MS Excel Spreadsheet is complete, all can be observed.
I could always program the loop using Python which is very BASIC like, so an easy port. Gives more more motivation to progress past the "Hello World!" stage.
ReplyDeleteFor Part 4 likely will simply compare the NIST/CODATA values to The Oracle TOPPCG 2.1, that'll save me wondering as well as readers. The NIST/CODATA is only accurate to 4-6 decimal places due to measurement errors and fitting to incomplete Rydberg constant equation (instead of the Full Rydberg Polynomial)
ReplyDelete