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A comment on Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742439706e-11 (8 ppm). Parent comment
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
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The term is -(alpha / 24). You calculated -1 / (24 · alpha).
The correct derivation is:
Solving this with S = 4 · π^3 + π^2 + π yields the correct value.