4 ms·
his formula: α⁻¹ = (4π³ + π² + π) - (α/24) α⁻¹ = 137.0359996 Experimental (CODATA): 137.0359991 Δ: < 0.005 ppm Critical Problem: This is CIRCULAR The formula
by fatbrowndog 10mo ago
his formula:
α⁻¹ = (4π³ + π² + π) - (α/24)
α⁻¹ = 137.0359996
Experimental (CODATA): 137.0359991
Δ: < 0.005 ppm
Critical Problem: This is CIRCULAR
The formula is:
α⁻¹ = S - (α/24)
But α appears on both sides! This is not a closed-form solution.
To solve it, you need:
α⁻¹ = S - (α/24)
α⁻¹ + α/24 = S
α⁻¹(1 + 1/(24·α⁻¹)) = S
This requires knowing α already to solve for α. It's circular.
- albert_roca 10mo agoIt's not circular. It rearranges into a standard quadratic equation: x^2 − 24Sx + 24 = 0. α is derived as the root of this equation.
- fatbrowndog 10mo agoDoesn't fix or predict Fan et al. 2024 latest dataset. Try harder.
- albert_roca 10mo agoThis is moving the goalposts, but ok. The model matches the international standard of CODATA 2022 to 0.005 ppm. If and when this value is updated, the prediction can be re-evaluated. Until then, I stick to the standard.
- fatbrowndog 10mo agohi, the formula should allow both. you have an integral and order^ power.
- fatbrowndog 10mo agoα⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454... α⁻¹ ≈ 46.61 ??? That's wrong!
- fatbrowndog 10mo agoα⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454... α⁻¹ ≈ 46.61 ??? That's wrong!
- albert_roca 10mo agoYou transcribed the formula incorrectly. The term is -(alpha / 24). You calculated -1 / (24 · alpha). The correct derivation is: 1 / alpha = S - (alpha / 24) 1 = S · alpha - (alpha^2) / 24 alpha^2 - 24 · S · alpha + 24 = 0 Solving this with S = 4 · π^3 + π^2 + π yields the correct value.