DOI: 10.5281/zenodo.15185126
title: Harmonic Unification Beyond Standard Model

description: The Standard Model of particle physics is incredibly successful, but it still leaves big questions unanswered—like why particles have the masses and charges they do, or why the forces between them are so different in strength. What if all of that could be explained using one simple idea?

 

The Harmonic Force Interaction (HFI) model suggests that everything in particle physics—mass, charge, decay behavior, and even force strength—comes from a particle’s "harmonic distance" from the Higgs boson. This distance isn’t spatial, but a logarithmic comparison of mass, converting it into something like a frequency. From there, the model uses sine, cosine, and tangent functions to explain particle properties as natural outcomes of harmonic resonance.

 

Instead of forcing the math to fit observations, this approach lets the math speak for itself. Discrete behaviors (like particle charges and decay patterns) just pop out naturally from the wave-like behavior of the system. It even shows how constants like the fine structure constant (1/137) emerge from harmonic balance, without needing to be inserted by hand.

 

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METHODOLOGY:

 

The core of the HFI model starts with a simple transformation: take the mass of a particle and compare it to the Higgs boson’s mass (125.1 GeV) using a binary logarithm. This gives you the harmonic distance, h:

 

h = log₂(MH / M)

 

From this one number, you can calculate all kinds of properties:

 

Lifetime: Particles with large mass (small h) decay quickly, while light particles (large h) are more stable. This is modeled using a formula that blends sine and tangent of 2πh.

 

Charge: Using sine and cosine of 2πh, the model accurately predicts the fractional charges of quarks and the whole-number charges of leptons, just from the math.

 

Force strengths: The electromagnetic, weak, and strong forces all emerge from different combinations of trigonometric functions of h—no extra tuning required.

 

Spin and helicity: Particle spin and handedness are described with simple cosine and sine expressions, tied directly to h.

 

Tuning with music theory: A correction called the Pythagorean comma, borrowed from tuning systems in music, ensures harmonic alignment remains precise over many steps—just like keeping a musical scale in tune.

 

Mixing and transitions: Even quark mixing (like what happens in the CKM matrix) is modeled as interference between harmonic states, using phase differences—just like wave interference in sound.

 

This model doesn’t rely on arbitrary constants or guesses. Everything is derived from basic math, using harmony as the guiding principle. It’s a physics framework that feels more like music—and that’s what makes it so powerful.

 

Here’s a quick breakdown of the core formulas behind the Harmonic Force Interaction (HFI) model. These aren’t random—they come straight from the relationship between a particle’s mass and the Higgs boson. Think of it like turning mass into music.

 

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1. Harmonic Distance (h)

This is the foundation. It compares a particle’s mass to the Higgs boson’s mass (125.1 GeV) using a base-2 logarithm:

 

h = log₂(MH / M)

 

This transforms mass into a “harmonic” value—like a frequency—that everything else is built on.

 

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2. Particle Lifetime (τ)

How long a particle lives is based on h. The formula looks like this:

 

τ(h) = τ₀ / [sin(2πh) - tan(2πh)]

 

Heavy particles (small h) decay fast. Light ones (large h) live longer or are stable. It’s all due to the sine and tangent behavior.

 

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3. Electric Charge (Q)

Charges aren't guessed—they come from:

 

Q(h) = (2/3)cos(2πh) - (1/3)sin(2πh)

 

This spits out +2/3 for up quarks, -1/3 for down quarks, -1 for electrons, and 0 for neutrinos. All from simple trig.

 

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4. Force Strengths (EM, Weak, Strong)

Each force is tied to a different trig combo of h:

 

Electromagnetic (EM):

F_EM ∝ sin(2πh)·cos(2πh) + csc(2πh)

 

Weak force:

F_Weak ∝ cos(2πh)·tan(2πh) + sec(2πh)

 

Strong force:

F_Strong ∝ sin(2πh)·tan(2πh) + cot(2πh)

 

This gives the correct strength hierarchy—EM is weak, strong is strongest.

 

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5. Spin (S) and Helicity

Spin comes from:

 

S(h) = ½[1 + cos(2πh)]

 

That means:

 

S = 0 → bosons (integer h)

 

S = ½ → fermions (half-integer h)

 

S = 1 → vector bosons (when cos = 1)

 

Helicity (left/right handedness) is:

 

Helicity = S(h) × sign[sin(2πh)]

 

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6. Pythagorean Correction (PC)

To stay in tune across many harmonic levels:

 

PC(h) = λ × (1.013643^⌊h/12⌋ - 1)

 

This corrects for tiny “detuning,” just like in musical scales. It keeps the math accurate over many steps.

 

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7. CKM Matrix (Flavor Mixing)

Quark flavor changes are modeled like wave interference:

 

|u⟩ = e^(i·2πh_u)

|d⟩ = e^(i·(2πh_d + δ))

V = ⟨u|d⟩ = e^(i·(h_u - h_d - δ))

 

The phase shift δ includes the Pythagorean comma. The matrix pops right out of harmonic phase differences.

 

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All of this comes from just one key parameter—h, the harmonic distance from the Higgs. No extra constants. Just harmony, waves, and trig.

 

Here's a link to python simulator that prompts you to input any mass in GeV and it will output all properties