Ξ¨-The Limited Field being constants. Unknown constants, so they look like variables when they are unknown, however, as constant as Ο, Ρ, e, 1, or 0, when known.
(Leaving the previously coded algorithm(s*) aside momentarily to discuss this new idea. Again, this is a new idea, not even tested yet, however, it's just like the resistor degenerated (Widlar) bipolar current reference circuit that one iterates to get the value of the current)
Pepe the Frog is the Water Wave
(the energy is in the wave)
More than Global Thinking,
moar like Galactic Thinking
(be flexible and flow like water, go with it)
- Start with original NIST/CODATA constants' values.
- Pick one constant at a time and iterate it until the error** is zero up to the precision of the calculation (16 digits, need to check if more decimal precision is possible).
- Save that as the next new value of the constant.
- Chose the next constant, iterate until the error is again zero, save that value.
- Do this for all constants until a whole NEW set of values have been obtained, then REPEAT the whole process.
- Continue the process and check if the value are converging, diverging, oscillating or varying.
The concept is that the constants' inter-relationship IS defined by the polynomial, so using ALL the best measured values to calculate one, since that one we are interested in, say, the proton radius. We plug in ALL the NIST/CODATA values, including the one for the proton radius and see that the error is non-zero, so we tweak the proton radius until the error is zero. Then do it for each constant, repeatedly and IF the values converge to a new set of stable constants, then those are the precise theoretical values of the fundamental physics constants.
This likely will work because the value of one of the constants depends upon the value of ALL of the other constants (8 in this case), and using all of the other values to calculate one averages and uses the precision of the equation itself. (proposal)
So, the constant being calculated depends upon all the other constants. If we calculate what each one should be based upon all the others, we get a new value. This can be done for each constant, and the error plotted for each new set to verify the total error is decreasing. Each set of new constants is one iteration through the error calculation. With each new set of constants, the error should be getting smaller and smaller. And if repeated with different starting seed values should always converge to the same value independent of starting values (TBD). If so, then this algorithm is clear and clean.
Anyway, simply wanted to describe it since it is so simple. Then blog through it step by step and build a Goog-colab Python notebook solution old school like the good old days.
Maritime Law Pepe is watching the water agua AguA Ag|uA|Au πππΈππ¦...
*original early and mid 90s versions of the algorithm have been lost over time, and the recent version in this blog needs more work
** the full Rydberg polynomial is used for the error equation as when all constants are entered, it should equal 1.00000... and any deviation from unity is error. Zero error means when the constants are plugged into the Rydberg polynomial, it exactly gives 1.0. (or 0.0 if subtracting 1)
ΨΨΨ - another example of the field of constants: https://phxmarker.blogspot.com/2022/06/richard-feynman-on-fine-structure.html
The Limited Field being constants. Unknown constants, so they look like variables when they are unknown, however, as constant as Ο, e, 1, or 0, when known.
ReplyDeleteThese are the kind of problems that solve themselves given enough time and the better the problem is defined. Sometimes defining the problem VERY precisely also ends up creating the solution. So, not only are they self proving, they are self-solving. (sorta)
ReplyDeleteOne can see attempting the same algorithm with the original Rydberg Equation which does not include the electron to proton mass ratio which is a function of the proton radius and pi, fine-structure constant and the Rydberg constant, that the original equation can converge on ANY number of solutions since they are all ratioed. If one constrained some, it might help with convergence, however, the Full Rydberg equation includes the dropped term and since it is a Feedback type relationship, the polynomial may converge (TBD). Another thing to note is the Full Rydberg equation can be written as a second order polynomial for the R_H (Rydberg constant) term and then THEREFORE, significantly, one COULD solve for the Rydberg constant using the QUADRATIC equation, treating all other terms as "Known constants" to see if any insight can be gained. These notes are to keep track of idea for solutions and future blog posts.
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