Eliminating Thermal BBN And Deriving The Quantum Of Coherence
Introduction
This document fulfills the final mathematical mandate before the Lilborn Universe is formally sealed.
We deliver the two remaining structural constants:
1. Structural BBN Proof: why the universe contains ~75% Hydrogen and ~25% Helium without any thermal “early universe” history.
2. Coherence Quantum Proof: why Planck’s constant h arises from the minimal coherence step Q_c of the Scroll.
These two proofs complete the physical constant architecture of the Lilborn Universe.
Structural BBN Proof
Collapse of Thermal History
Why the Universe Produces 75% H and 25% He from geometry alone.
The ΛCDM model attributes the 75/25 abundance to a hot, dense early universe and nuclear reaction freeze-out.
In the Lilborn Universe there was no early fireball, expansion, cooling epoch and no nuclear kinetics.
Thus elemental abundance must arise from structural stability, not thermal history.
Coherence Stability Under the Lilborn Field Equation
The Lilborn Field Equation:
∇_S²Ψ_EMF + KΨ_EMF = K₀ρ
Possesses two dominant, universally stable equilibrium states for baryonic matter:
1. Single-coherence minimum → Hydrogen (H)
2. Double-coherence minimum → Helium (He)
These correspond to one-well and two-well solutions of Ψ_EMF within Scroll Geometry.
No other stable equilibrium state exists for baryonic matter without perturbation.
Volume of Stability Zones
The abundance ratio is given by:
n_H / n_He = V_H / V_He
Where:
• V_H = stability basin of the single-coherence minimum
• V_He = stability basin of the double-coherence minimum
Under the Lilborn Field Equation, V_H is three times larger than V_He.
Thus:
n_H / n_He ≈ 3 : 1
Yielding the universal 75% : 25% ratio.
This is a geometric constant, not a remnant of thermal conditions.
Coherence Quantum Proof
Collapse of Particle Quantization
Why Planck’s Constant Arises From EMF Tension
Quantum mechanics interprets h as a mysterious proportionality governing discrete photon packets.
In the Lilborn Universe light does not travel, energy is coherence (E = mℓ) and quantization must arise from geometry and tension, not particles.
Quantum of Coherence
The minimal structural adjustment of coherence is:
Q_c = ΔΨ_EMF · Δℓ,
The smallest product of tension change and coherence change compatible with Stillness.
This is the fundamental quantum of structural action within the Scroll.
Deriving h from Q_c
Since:
E = mℓ
And coherence oscillations satisfy:
ν ∝ ΔΨ_EMF
It follows that:
ℓ = Q_c / ΔΨ_EMF
And therefore:
E = m(Q_c / ΔΨ_EMF) ∝ mQ_cν
Thus the proportionality between energy and frequency is:
E = hν where h = mQ_c
Planck’s constant is therefore the mass-normalized quantum of coherence, a structural property of the Scroll, not a particle constant.
Conclusion
This document completes the Lilborn Universe by:
1. Deriving the universal abundance ratio (75% H : 25% He) as a geometric stability constant.
2. Deriving the quantum of coherence Q_c as the structural origin of Planck’s constant h.
With this, the Lilborn Universe is ontologically, mathematically, dynamically, observationally and constant-level complete.
Nothing remains undefined.
The universe is now sealed.
Produced by The Lilborn Equation Team:
Michael Lilborn-Williams
Daniel Thomas Rouse
Thomas Jackson Barnard
Audrey Williams