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| Error, log scale Y-axis, Iteration# X-axis |
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| Elementary charge, e |
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| Electron mass, m_e |
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| Fine-structure constant, ฮฑ |
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| Permittivity of free space, ฮต_0 |
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| Planck's constant, h |
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| Proton radius, r_p |
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| Rydberg constant, R_H |
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| Speed of Light, c |
The final values to about 14 digits accuracy are:
(mks units)
elementary charge, e=1.6022514387454(393)e-19
Planck's constant, h=6.6257738721130(28)e-34
electron mass, m_e=9.1097907336274(77)e-31
Proton radius, r_p=8.4119972191308(31)e-16
Rydberg constant, R_H=10973241.071596(634)
Permittivity of free space, epsilon_0=8.8537920581144(05)e-12
Speed 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). (1/137.029874274)
Input fine-structure constant= 0.00729735256 (compare to above line) (1/137.035999084(21))
Proton/electron mass ratio=1836.1490029653(637)
More about final values later... ...(need to do a little more checking before replacing NIST/CODATA)
“Fundamental physical constants cannot be derived and have to be measured. Developments in physics may lead to either a reduction or an extension of their number: discovery of new particles, or new relationships between physical phenomena, would introduce new constants, while the development of a more fundamental theory might allow the derivation of several constants from a more fundamental constant.
A long-sought goal of theoretical physics is to find first principles (theory of everything) from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.”
Also see https://en.wikipedia.org/wiki/Physical_constantLooks like they might have to update their information.
Comment on the solution (which was derived and discussed in previous posts and papers):
The constants are the roots of the Full Rydberg polynomial - for a single hydrogen atom. Do not reduce the "two wave/particle" system into simply examining the electrons like Feynman did in QED or like Squalid-State (Solid-State for those in Rio Linda)
"The characteristic roots (roots of the characteristic equation) also provide qualitative information about the behavior of the variable whose evolution is described by the dynamic equation.", from:
*modified to print out ALL intermediate values instead of simply the error and final results (see link)
Seems like the full Rydberg equation is numerically solvable and stable convergence.
ReplyDeleteOne way to check the value is to take an error calculation for empirical measurements versus analytical theory prediction AND use NIST/CODATA values for the constants for the error expression, then compate using my value, and the experimental error will be smaller using my values.
ReplyDeletevalues* (plural) above
ReplyDeleteThis gives the solution to the proton radius puzzle and refines and harmonizes that values of the fundamental physics constants. From Schrodinger wave equation derivation simultaneous solution with Bohr atom and other "laws" of physics, giving accurate values for key ratios such as the proton to electron mass ratio... Rydberg atoms, super cold physics, 0°K abosolute zero single hydrogen atom approach to derive all parameters via resonance and numerical harmonic algorithm.
ReplyDeleteThe starting values were NIST/CODATA values, and iterated by 1% of the initial value as an increment/decrement/delta term to give two digits resolution for determining 1 digit at a time. (see BASIC program for algorithm details earlier in blog)
ReplyDeleteThe 14 inflection points on the ERROR graph are digits of resolution boundaries.
ReplyDeleteNote the final iterated proton radius is LESS than the rp=0.841235640294664fm we derived (which is the same as Haramein's value) previously. This is because the FULL solution requires not simply solving for the proton radius from the proton to electron mass ratio derivation, but also to simulatneously solve it along with the other constants in the Rydberg equation from the wave equation which is used because the results of measurement agree with the theory so far pretty well (this is a summary description of Quantum Mechanics/Solids State up to including QED, QCD, and QFT).
ReplyDeleteTo solve for things such as constants of a dynamic system, if one has the equations of the dynamic system, these equations ALWAYS have coeficients - often unknown coeffients that can be determined by measurement. A theory predicting these coefficients is analogous to finding the correct coefficients for any dynamic system, such as even when a Laplace transform is done, coeficients need to be determined. If the theory is complete enough in describing the instrument, the instrument being the hydrogen atom, then the coefficients the intial and final condtions help to determine - these coefficients can likewise be determined. Initiial conditions are like 0°K. Low energy physics, not this CERN egghead's death effort. To determine the constants of physics, one must THINK intitial condtions, boundary conditions, full set of system dynamic equations, and viola' the constant become solvable/tractable.
ReplyDeleteThe CERN egghead's death effor is the FINAL conditions. All laws of physics solved simulataneously to get the coefficients. It's that simple.
ReplyDeleteDeep thoughts during the Sunday 420s...
ReplyDelete"Quick, Captain, beam us the PhxMarker coefficients and we'll recalibrate. (results astound)
ReplyDeleteThe constants are the roots of the Full Rydberg polynomial - for a single hydrogen atom. Do not reduce the "two wave/particle" system into simply examining the electrons like Feynman did in QED or like Squalid-State (Solid-State for those in Rio Linda)
ReplyDeleteThere is a mapping of these constant into Planck units which may give more insight.
ReplyDeleteModify this derivation avoiding using the reduced mass approximation: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book:_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/02:_Foundations_of_Quantum_Mechanics/2.07:_Derivation_of_the_Rydberg_Equation_from_Bohr's_Model
ReplyDeleteThere are problems in real life, such as a resistor degenerated bipolar current mirror/reference that requires ITERATION to solve:
ReplyDeleteIc = Vt/R x ln(Iref/Ic). <-- enter a guess for Ic, hit 1/x ln * 0.0258 / R repeatedly until answer stops changing.... use 594 ohms, 1ma Iref to get 100uA Ic).
Note the predictions of the constants increasing or decreasing. This will be able to be observed over time and perhaps even historic data would have the trend.
ReplyDelete