Swarm Field Theory
A math-first unification. Derive the constants you already know from geometry you can sketch.
Swarm Field Theory derives familiar constants — including Newton’s gravitational constant — directly from geometry and lattice tension. No extra dimensions, no untestable entities. Gravity, electromagnetism, and quantum behaviour emerge from one coherent substrate.
Swarm Field Theory
A modest, math-first framework for unification in physics.
Swarm Field Theory models real space as a lattice of tension-bearing membranes stretched between zero-nodes. From this simple geometry, fundamental constants — including Planck’s constant (h), the fine-structure constant (α), the speed of light (c), the elementary charge (e), and the gravitational constant (G) — emerge directly from first principles.
Swarm Field Theory proposes that real space is formed by membranes around zero nodes, and that waves propagate helically. Learn more about the geometry →
The Geometry
Space is treated not as empty volume but as a woven array of two-dimensional membranes anchored at zero-nodes. These planes intersect at fixed angles and carry tension, forming a real yet massless scaffold. Disturbances travel as helical waves bound by membrane tension and node spacing. Quantization arises from discrete apertures in the lattice; energy, momentum, and phase follow from geometry and boundary conditions.
What Falls Out
- Electromagnetic set: h, α, e, ε₀, μ₀, Z₀, c
- Gravitational: G; Planck family (mₚ, ℓₚ, tₚ, Eₚ)
- Thermal: kB, σ, a, b, TP
- Atomic touchstones: R∞, a₀ (with noted mass inputs)
The Simplification (UFEB)
The Unified Field Equation, Budget form (UFEB), replaces continuous time with discrete updates. Each update is a reconciliation of lattice-tension budgets — like closing a balance sheet. The lattice shares a universal response interval (τ), but consequences still propagate locally at finite speed (c), preserving relativity.
“We measure progress in steps, not seconds.”
Numbers That Work
Swarm Field Theory derives fundamental constants directly from geometry, matching CODATA values without curve fitting.
| Quantity | CODATA (SI) | SFT (derived) | Paper |
|---|---|---|---|
| Planck’s constant, h | 6.62607015×10⁻³⁴ J·s (exact) | 6.6264×10⁻³⁴ J·s | DOI |
| Fine-structure constant, α | 7.2973525693×10⁻³ | 7.2973×10⁻³ | DOI |
| Elementary charge, e | 1.602176634×10⁻¹⁹ C (exact) | 1.6022×10⁻¹⁹ C | DOI |
| Vacuum permittivity, ε₀ | 8.8541878128×10⁻¹² F·m⁻¹ | 8.854×10⁻¹² F·m⁻¹ | DOI |
| Vacuum permeability, μ₀ | 1.25663706212×10⁻⁶ H·m⁻¹ | 1.257×10⁻⁶ H·m⁻¹ | DOI |
| Gravitational constant, G | 6.67430×10⁻¹¹ m³·kg⁻¹·s⁻² | 6.6743×10⁻¹¹ m³·kg⁻¹·s⁻² | DOI |
🗂️ The File Cabinet of Regret
A selection of humorous and odd questions, some of which were actually asked.
About
John Paul Crumpler, PE, is a licensed professional engineer with 46 years of experience in applied research, machine design, energy systems, and theoretical physics. He has authored trade articles, technical reports, and fact sheets; taught continuing-education courses for engineers; and lectured at the University of Georgia. He has also advised undergraduate students in energy systems at Georgia Tech and the University of Virginia.