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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

Re:Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742... by al2o3cr on Monday December 22, 2025 @09:45PM (#46361860) 

    You mention the "uncharged case", but ordinary matter is not mathematically neutral.
YOUR CODE assumes that it is, when it passes "q": 0 for four of the six objects.

For the other two, it passes "q": 1. Let's look at what it does then:

    L_src is much much smaller than Le, by roughly a factor of (mass / mPL)^2

    The calculation of lambda_a uses the electron mass even when calculating for a proton

    For the given objects, metric_factor is negligible.

    ai_unified = c^2 * (alpha * hbar / (me_kg * c)) / r^2 = alpha * (hbar * c) / (me_kg * r^2)

    but alpha = k*e^2 / (hbar * c)

    so ai_unified = k * e^2 / (me_kg * r^2) + small correction of O((mass / mPL)^2)
That's exactly the formula used for acc_coloumb in the code. Also interesting to note the "Coulomb acceleration" for a proton is calculated by dividing the electric force by the mass of the ELECTRON somehow.

As for "Phase 2"? The program's output doesn't even agree with the implementation about the formula being used.

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Re:Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742... by albert_roca on Tuesday December 23, 2025 @06:32AM (#46364457)
Hm. You are correct about m_p and m_e. That is indeed a sloppy mistake in the script. Bad code. However, the hypothesized closed value of G stays the same.
[ Parent | on HN ]
Re:Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742... by fatbrowndog on Tuesday December 23, 2025 @07:47AM (#46364918)
His G Formula (Section 14.6)

G = (ℏ·c·2·(1 + α/3)²) / (mp²·4⁶⁴)

His result:

G ≈ 6.6742439706 × 10⁻¹¹ m³·kg⁻¹·s⁻²

CODATA 2022: G = 6.67430(15) × 10⁻¹¹

Δ: 8 ppm

Critical Analysis

1. Where Does 4⁶⁴ Come From?

He claims it's from "holographic scaling at i=32":

mp = (√2 · mP / 4³²) · (1 + α/3)

Therefore:

mP = (mp · 4³²) / (√2 · (1 + α/3))

Since G = ℏc/mP²:

G = (ℏc · 2 · (1 + α/3)²) / (mp² · 4⁶⁴)

The logic:

Proton appears at "harmonic i=32" in binary scaling

Mass scales as m ~ 4ⁱ (surface area scaling)

Therefore mp ~ 4³² when normalized properly

Therefore 4⁶⁴ = (4³²)² appears in G

2. This is Pure Numerology

Why i=32 specifically?

Let me check the ratio:

mP / mp = 2.176434×10⁻⁸ / 1.672622×10⁻²⁷

        ≈ 1.301×10¹⁹
Now check powers of 4:

4³² = 2⁶⁴ = 1.844×10¹⁹

Close! But not exact. So he adds correction factors:

mp = (√2 · mP / 4³²) · (1 + α/3)

Let me verify:

(√2 · 2.176434×10⁻⁸ / 4³²) · (1 + 0.007297/3)

= (1.414 · 2.176434×10⁻⁸ / 1.844×10¹⁹) · 1.002432

= (3.076×10⁻⁸ / 1.844×10¹⁹) · 1.002432

= 1.668×10⁻²⁷ · 1.002432

≈ 1.672×10⁻²⁷

But this is circular! He's adjusting factors (√2, α/3) to make the formula work, then claiming it "derives" mp.

3. Why (1 + α/3)?

He claims:

"As a volumetric object in three-dimensional space, the proton carries a

distributed interaction cost (α/3)"

This makes no sense:

α is the electromagnetic coupling constant

Why divide by 3? "Because 3 dimensions"?

Why add to 1? "Because correction"?

This is parameter fitting, not derivation.

-----

A genuine derivation of G would:

1. *Start from dimensionless constants only*

2. *Derive mass ratios* from geometry (mp/me, mp/mP, etc.)

3. *Use dimensionful anchors* (ℏ, c) to get actual value of G

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