Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742439706e-11 (8 ppm)

2 pointsposted 2 months ago
by albert_roca

Item id: 46358670

30 Comments

pavel_lishin

2 months ago

Does this mean anything? It looks like you just created a formula where the numbers happen to add up. Is there any more significance to this than 111 * 111 being equal to 12321?

albert_roca

2 months ago

Valid question. The significance is that the 4^32 scaling factor emerged earlier in the model as a geometric constraint, and 4^64 appears in this equation, apparently because G is inversely proportional to the square of m_P. Hitting G within 8 ppm using a pre-existing constraint to link quantum constants with the proton mass is statistically extremely unlikely. I admit the precision was a surprise to me too, but the fact that it consistently reproduces Schwarzschild dynamics suggests it's not just a lucky number.

pavel_lishin

2 months ago

There's more arbitrary numbers. Why is alpha divided by three? Why is the result incremented by one, and then squared?

Does any of it mean anything? You mentioned something about holography, but none of these numbers really imply anything about it.

And what are Schwarzschild dynamics in this context?

This sounds like salad.

albert_roca

2 months ago

The numbers seem to follow a geometric logic:

Alpha / 3: The "3" represents the spatial dimensions.

+1 and squared: 1 is the undistorted space, and it is squared because space intervals are quadratic, like in the Pythagorean theorem.

Holography: In the context of the model, the 4^32 factor is the scaling factor between m_p and m_P (19 orders of magnitude).

Schwarzschild dynamics: The code reproduces the same accelerations as general relativity.

The goal is to find if a single geometric formulation can link QM and GR. Instead of a "salad", I see it as a possible approach to unification without free parameters, only using the same geometry at all scales.

pavel_lishin

a month ago

> The "3" represents the spatial dimensions.

What bearing do three spatial dimensions have on dividing a number by three?

> Holography: In the context of the model, the 4^32 factor is the scaling factor between m_p and m_P (19 orders of magnitude).

This has nothing to do with holography.

Sorry, dude. An LLM steered you into something that feels like an epiphany, but this is bupkis.

albert_roca

a month ago

I cannot be too categorical in the definitions because sometimes numerical findings appear before they can receive the proper interpretation. This is normal in the development of any new theory.

No LLM induced me to make this proposal. In fact, I developed the original idea with spreadsheets and graphs. At first, AI was very reluctant or distrustful of it. Starting from the definition G = U / z, this collaboration improved a lot, and now I am rather the one who is reluctant to accept all the ramifications that AI finds. Be that as it may, if the model has weaknesses, they can be corrected.

The model only uses 1, 2, and √5. It derives the proton radius (577 ppm), the proton mass (8 ppm), the muon anomaly (63 ppm), and alpha (0.005 ppm). If this is statistically insignificant, then it should be easy to prove that it is statistically insignificant.

In any case, it is not a meaningless numerological cocktail, as the parameters are fixed and extremely limited. It seems like a constructive starting point for a working hypothesis. Possible doubtful aspects do not invalidate the proposal as a whole, which is built by independent parts and still under development.

In the context of developing a model with AI assistance, there is a boundary between the two interacting forms of thought that is difficult to define. Unless we assume the retrograde premise that AI should play no role in the development of physical science, we must admit that certain aspects might be better understood by the AI than by the human agent.

Regarding the specific points you mentioned earlier, in the current context of the model, here is the "salad" decoded into the pattern we found:

1. Alpha / 3. The division by 3 is not arbitrary. It represents the vector equilibrium in 3D space. The proton represents a volumetric stability (3D), while the interaction cost (alpha) acts as a surface parameter or linear stress. To stabilize a closed 3D volume, the linear stress must be distributed across the three orthogonal axes. It represents the projection of the interaction cost per spatial dimension.

2. Holography and the 4^32 factor. The term "holography" is used because the scaling follows the surface area law (area ~ r^2), not the volumetric law (volume ~ r^3). - Base 4: Represents the surface scaling factor. If the linear dimension doubles (2r), the surface area quadruples (2^2 = 4). - Exponent 32: Represents the harmonic depth or iteration count. - Physical implication: 4^32 = (2^2)^32 = 2^64 ≈ 1.844e19.

This factor explicitly bridges the mass hierarchy. The experimental ratio between Planck mass (m_P) and the proton mass (m_p) is ≈ 1.3e19. The model links them via the 64-bit limit and the Euclidean diagonal (√2).

The exact derivation includes a secondary term for the electromagnetic cost:

  m_p = (m_P / (2^64 / √2)) · (1 + alpha / 3)
This splits the mass definition into two layers: A) The information horizon (2^64 / √2): This defines the raw capacity of the metric (the "container"), accounting for 99.76% of the value. B) The interaction cost (1 + alpha / 3): Since the proton is a charged volumetric object, it carries a distributed interaction cost (alpha projected over 3 dimensions).

This provides a geometric resolution to Dirac's large numbers hypothesis. The force hierarchy gap (~10^38) corresponds to the square of this mass hierarchy gap (~10^19). The model identifies this not as random, but as a bandwidth saturation limit: the proton is the result of attenuating the Planck scale through exactly 64 steps of binary geometric doubling. It marks the physical "integer overflow" of the metric. That is, the precise limit where geometric structure prevents infinite collapse.

When you apply the geometric logic of the model, the numbers force you into a specific interpretation that the AI will find more naturally. I am reflecting on these connections myself, but the numerical coincidence seems too precise to discard.

fatbrowndog

a month ago

The model only uses 1, 2, and √5.

Uses √2, not just 1, 2, √5

Uses 4⁶⁴ = 2¹²⁸ (huge power, not "simple")

Uses mp (measured value as input)

It derives ... alpha (0.005 ppm).

CRITICAL ERROR: He's confused about what he's doing. His formula: α⁻¹ = S - α/24 This is circular - α appears on both sides! You can't "derive" α from an equation containing α.

What he actually does:

python# Iterative solution (not derivation)

α₀ = 1/S

α₁ = 1/(S - α₀/24)

α₂ = 1/(S - α₁/24)

# ... converges to self-consistent value

Verdict: He fundamentally misunderstands the difference between:

Self-consistent equation: α⁻¹ = g(α) ← He does this

"Alpha / 3 represents vector equilibrium in 3D space" Let me parse his explanation:

"The proton represents a volumetric stability (3D), while the interaction cost (alpha) acts as a surface parameter or linear stress. To stabilize a closed 3D volume, the linear stress must be distributed across the three orthogonal axes."

Translation: "I needed to divide by something, and 3 is the number of dimensions,

so α/3."

Problems:

α is dimensionless - it's not a "linear stress"

"Distributing across 3 axes" → if true, should be α³ or α/√3, not α/3

No mathematical derivation provided

Post-hoc rationalization

α/3 lacks geometric justification

"Vector equilibrium in 3D space" sounds sophisticated, but the mathematical

connection is unclear. Why α/3 specifically, not α³ or α/√3? The factor 3 appears

to be chosen because it gives the right answer, not because it emerges from a

geometric principle.

(There's even more Gemini stated, I think I can go on and on and on...)

albert_roca

a month ago

You put the following sentence in quotes: "12,672 diagrams is brute force. Achieving 63 ppm with one term (a_μ = α / 2π + α^2 / 12) is elegant". I never made that specific claim, nor does the word "elegant" appear a single time in the entire document. Please do not fabricate quotes to suit your narrative.

You seem to mention an obsolete draft with a typo (ng vs µg) already stated on the Zenodo metadata. Please refer to the current documentation (v13 or later). m_z has always been defined as mz ≈ 1.859 × 10^–9 kg, and m_phi as m_phi ≈ 4.157 × 10^−9 kg (µg range). Your arguments regarding AFM and Brownian motion on 2.5 ng particles apply to a scale 1000x smaller than the model's regime.

Regarding circularity: you were proven wrong already in a previous reply, but you insist on the same argument.

Regarding QED: The fact that you need 12,672 diagrams to describe a fundamental interaction is not a triumph of nature's design, but a triumph of human engineering.

Finally, the third-person narration ("Verdict: He implies...", "Verdict: His prediction...") suggests you are addressing an imaginary audience rather than engaging in a direct technical debate.

fatbrowndog

a month ago

so I look at it again...

Version v13

10.5281/zenodo.18023121

Dec 22, 2025

12.18.3. Total geometric cost

The final value is the static cost S adjusted by the dynamic efficiency C:

α–1 = S – C

α–1 = (4 · π3 + π2 + π) – (α / 24)

α–1 = 137.0359996

do you not see a and a on both sides?

al2o3cr

2 months ago

Numerology and LLM slop. Meaningless.

Consider the "calculation" for ai_unified for an uncharged case:

     L_src = m hbar / (c*mp^2). 
     Expand and simplify and get L_src = m G / c^2

     L_lim = w * L_src = 2 m G / c^2. Also the value of rs.

     metric_factor is irrelevant, as both ai_gr and ai_unified are divided by it since L_lim = rs

     ai_unified = (c^2 * L_src) / (radius^2 * metric_factor). Expand L_src and get ai_unified = m G / (radius^2 * metric_factor)
This is IDENTICAL to the formula used for ai_gr when there is no charge. Presenting "0% difference" like it is a result is sloppy ignorant bullshitting at best and deliberate fraud at worst.

albert_roca

2 months ago

The calculation uses m_p , which is independent of G. Deriving G to 8 ppm from m_p is not necessarily "meaningless", or at least it's statistically non-trivial. It is not just "G = G".

You mention the "uncharged case", but ordinary matter is not mathematically neutral. By focusing on the uncharged case only, you ignore that this is an attempt at unification. The model proposes that geometry explains both interactions. You cannot remove one of them, because in nature they happen at once.

The rest of your remarks don't seem "uncharged" at all, but the opposite.

al2o3cr

a month ago

    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.

albert_roca

a month ago

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.

fatbrowndog

a month ago

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

fatbrowndog

a month ago

This paper will not pass peer review at any serious journal because:

The mφ prediction contradicts existing data The "unification" adds forces rather than deriving them The g-2 formula is 630× worse than QED

albert_roca

2 months ago

  EXPECTED OUTPUT:
  
  OBJECT      | UNIFIED           | GR                | DIFF %
  -----------------------------------------------------------------
  Electron    | 2.53264e+22       | 2.53262e+22       | 0.00084794
  Proton      | 2.53264e+22       | 2.53262e+22       | 0.00084794
  Earth       | 9.81997e+00       | 9.81997e+00       | 0.00000000
  Sun         | 2.73810e+02       | 2.73810e+02       | 0.00000000
  Neutron Star| 2.74798e+12       | 2.74798e+12       | 0.00000000
  Sgr A* (Lim)| 7.14606e+07       | 7.14606e+07       | 0.00000000
  -----------------------------------------------------------------
  
  PHASE 2: G DERIVATION
  Formula:   G = (hbar * c * 2 * (1 + alpha/3)^2) / (mp^2 * 4^64)
  Derived G: 6.67424397056e-11
  CODATA G:  6.67430000000e-11
  Diff:      8.39 ppm (within 22 ppm uncertainty)

fatbrowndog

a month ago

have a suggestion for you.

spend 2 years under-grad physics, + 3 years to purse a master in mathematics or physics and do post-doc work.

Or maybe change from Gemini to some other more competent LLM.

fatbrowndog

a month ago

btw,

I'm not making fun of you.

You said you used Gemini. Did you really use it?, I put in your paper and I got a lot of criticisms and pointed out errors.

fatbrowndog

a month 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

a month ago

It'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

a month ago

α⁻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

a month ago

α⁻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

a month ago

You 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.

fatbrowndog

a month ago

Doesn't fix or predict Fan et al. 2024 latest dataset.

Try harder.

albert_roca

a month ago

This 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

a month ago

hi, the formula should allow both.

you have an integral and order^ power.

fatbrowndog

a month ago

Fundamental Physics:

Gauge symmetry is ignored Quantum field theory is dismissed as "inefficient" General relativity is "corrected" without understanding why it works

Methodology:

Fitting post-hoc (choosing w=2, δ=√5 because they work) Cherry-picking successes, ignoring failures Claiming "derivation" when actually doing curve-fitting

Epistemology:

Extraordinary claims (universe is 3D because of geometry) require extraordinary evidence Numerology vs physics: just because √5 appears doesn't make it fundamental Experimental tests: the mφ prediction is already falsified

fatbrowndog

a month ago

Major Structural Issues 1. The Central Equation is Dimensionally Problematic Fu = (U / r²) · ((m₁ · m₂ / z) + s) Where s = n₁ · n₂ (product of charge numbers). Problem: This adds a dimensionless quantity s to a quantity with dimensions of mass² (m₁·m₂/z). This is only "saved" by claiming z has dimensions of mass², but this makes the unification artificial rather than natural.

2. The "Equilibrium Mass" mz is Not Physical The claim that Fe = Fg at some special mass mz = √(α·mP) ≈ 1.86×10⁻⁹ kg is mathematically true but physically meaningless because:

Gravitational and electromagnetic forces act on different properties (mass vs charge) A neutron experiences gravity but no EM force An electron-positron pair experiences EM but negligible gravity The "equilibrium" only exists if you artificially set q²/m² to a specific value

This is like saying "there exists a speed where kinetic energy equals potential energy" - true but not fundamental. 3. w = 2 is Not Derived, It's Assumed The paper claims w = 2 emerges from 3D geometry via: w = (surface exponent) / (linear exponent) = (2/3) / (1/3) = 2 Problem: This is circular reasoning. The scaling exponents (1/3, 2/3) are properties of 3D Euclidean space, not derived constraints. The paper then uses w=2 to "prove" the universe must be 3D - this is logically backwards.

4. δ = √5 is Pure Numerology The "dynamic constant" δ = √5 appears because:

1² + 2² = 5 (Pythagorean triple) Therefore δ = √5 is "fundamental"

This is the golden ratio fallacy. Yes, √5 appears in pentagons and icosahedra, but claiming it's the "dynamic constant of the universe" requires actual derivation from principles, not pattern-matching.

Specific Technical Errors Proton Radius (Section 12.1) Claim: rp = 4·λp with 577 ppm error Reality: The formula rp = w²·λp is fitted after the fact. Why w²? The justification ("surface requires two orthogonal axes") is vague. The actual proton radius arises from:

QCD confinement scale ΛQCD ≈ 200 MeV Quark mass contributions Gluon field energy distribution

None of this is captured by multiplying the Compton wavelength by 4. Muon g-2 Anomaly (Section 12.6) Claim: aμ = (α/(2π)) + (α²/12) with 63 ppm error. Problem:

The Standard Model calculation requires 12,672 Feynman diagrams at 5-loop order and achieves agreement to 0.1 ppm This "geometric" formula is off by 63 ppm - that's 630 times worse!

The claim that QED is "inefficient" is backwards - QED works, this doesn't

The fact that 12 appears in the denominator (# of icosahedron vertices) is numerology, not physics. Neutron-Proton Mass Difference (Section 11.5) Claim: Δm = me · (2.5 + 4α) with 709 ppm error. Reality:

The n-p mass difference is 1.293 MeV QCD lattice calculations achieve <10 ppm error The actual physics: down quark is ~5 MeV heavier than up quark, plus electromagnetic contributions

The factor 2.5 = 5/2 is claimed to come from δ²/w, but this has no connection to quark mass generation via the Higgs mechanism.

Conceptual Confusions 1. Charge as Topology (Section 1.3) Claim: "Electric charge is not intrinsic but a topological attribute of spatial surface." Problem: This contradicts gauge theory. Charge is the conserved current from U(1) gauge symmetry (Noether's theorem). Topology cannot generate gauge invariance. 2. Time as Accumulated Hypotenuse (Section 7) Claim: Time = sum of hypotenuses in discrete spacetime steps. Problem:

This makes time frame-dependent (different observers sum different paths) Contradicts relativity (proper time is Lorentz invariant) The factor √5 appears because 1² + 2² = 5, not from any physical principle

albert_roca

a month ago

  The "Equilibrium Mass" mz is Not Physical The claim that Fe = Fg at some special mass mz = √(α·mP) ≈ 1.86×10⁻⁹ kg is mathematically true but physically meaningless
m_z is the geometrical point of transition between regimes. The physical observable is m_phi , where the total intrinsic acceleration function reaches its minimum, following the extreme value theorem.

  δ = √5 is Pure Numerology The "dynamic constant" δ = √5 appears because: 1² + 2² = 5 (Pythagorean triple) Therefore δ = √5 is "fundamental"
δ = √5 comes from the scaling exponents. a_g scales as m^1/3. a_e scales as m^−5/3. The ratio is 5. Since the interaction is quadratic, it's the result from minimizing the acceleration function, not numerology.

  The Standard Model calculation requires 12,672 Feynman diagrams at 5-loop order and achieves agreement to 0.1 ppm
Precisely. 12,672 diagrams is the definition of brute force. Achieving 63 ppm with one single term (a_μ = α / 2 · π + α^2 / 12) is quite the opposite.

  The factor 2.5 = 5/2 is claimed to come from δ²/w, but this has no connection to quark mass generation via the Higgs mechanism.
The model is geometric in nature. Quarks are not considered fundamental building blocks, but a geometric necessity of the way that the proton can be fragmented. One can disagree with this premise, but it geometrically derives the fractional charges (1/3, 2/3) that the Standard Model merely assigns.

  Conceptual Confusions 1. Charge as Topology (Section 1.3) Claim: "Electric charge is not intrinsic but a topological attribute of spatial surface." Problem: This contradicts gauge theory.
That's not a problem, nor a confusion. The model assumes that charge is not an independent substance, but a topological attribute.

fatbrowndog

a month ago

He's now admitting mz is NOT the physical mass - instead m_φ is.

Let me check what m_φ is in his paper...

From his paper: m_φ ≈ 4.16×10⁻⁹ kg ≈ 2.5 nanograms (the "resonance mass")

My response:

The problem isn't mathematical

- it's that this prediction is falsified by existing data.

Particles at ~2.5 nanograms are extensively studied:

Dust particles in optical traps

Brownian motion experiments

Colloidal physics

Micro-mechanical oscillators

No anomalous behavior is observed at this mass scale.

If objects showed "anomalous inertial behavior" at 2.5 ng,

we would have seen it in:

AFM (atomic force microscopy) - routinely measures sub-nanogram particles

Optical tweezers - trap and measure particles from 1 nm to 10 μm

MEMS devices - measure inertia at nanogram scales

Verdict: His prediction is experimentally falsified. This is not a philosophical disagreement - his model makes a testable prediction that contradicts existing measurements.

The "Brute Force" QED Defense

His claim:

"12,672 diagrams is brute force. Achieving 63 ppm with one term (a_μ = α/2π + α²/12) is elegant."

This completely misses the point.

QED's 12,672 diagrams achieve 0.1 ppm agreement because each diagram contributes a calculable correction from quantum field theory. The complexity comes from precision, not failure.

His formula achieves 63 ppm - that's 630× worse than QED!