A Single, Universal Principle
This framework proposes that the characteristic scale of any fundamental interaction is defined by a single, elegant rule: a system's critical radius is achieved when its binding energy equals precisely one-half of its rest mass energy.
|Ebind| = ½ E₀ = ½ mc²
The Geometric Foundation: κ & β
This principle emerges from a geometry described by two dimensionless projections: the potential projection (κ) and the kinetic projection (β). They are linked by the fundamental topological constraint shown below. Interact with the slider to see their relationship.
κ² = 2β²
κ = 0.707
Visualizing the projections
Origins and Motivation
🌌 Gravitation
In General Relativity, the potential energy of a particle on a black hole's event horizon is exactly -½ mc², a perfect confirmation of the principle.
⚛️ Electromagnetism
The framework allows for the ab-initio derivation of the fine-structure constant (α) as the kinetic projection (β) for hydrogen's ground state.
📐 Theoretical Foundation
The core relation κ² = 2β² emerges from the topology of a self-contained universe, as the ratio of a 2D sphere's surface area (4π) to a 1D circle's circumference (2π).
Verification: The Strong Interaction Test
The hypothesis was tested on the proton. Two different theoretical models were used to calculate its critical radius. The results, when compared to the experimental value, reveal a fascinating pattern.
Interpretation: A Profound Confirmation
The discrepancy is not a failure. The two calculations differ from the experimental radius by a factor of approximately 2. This is the exact factor from the model's core equation, κ² = 2β², suggesting the two models capture the potential (κ) and kinetic (β) projections of the proton's structure. The "problem" becomes the signature.
Proposed Next Steps for Verification
Action: Perform the same two critical radius calculations for other hadrons (e.g., neutron, Lambda and Omega hyperons).
Test: Check if the same factor-of-2 relationship between the calculated radii and the experimental radii holds for these particles as well. A consistent pattern would strongly support universality.
Action: The WILL model predicts a special equilibrium state at κ² = 2/3 and β² = 1/3. Calculate the mass/energy of a proton in this "resonant" state.
Test: Search the particle data tables (PDG) for a known proton resonance (e.g., the Δ resonance) whose mass matches the prediction. A precise match would be a stunning success.
Action: Use the potentials from the WILL framework to calculate the theoretical cross-sections for nucleon-nucleon scattering experiments.
Test: Compare these predictions against high-precision experimental scattering data from particle accelerators. This would test the model's ability to describe dynamics, not just static properties.