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Energy Density vs Radius

Geometric Wave Theory prediction: vacuum pressure Pvac(r) ∝ ħc/r⁴ produces two parallel bands (slope = −4) on a log-log plot, separated by exactly 8/α = 8 × 137 = 1096. Hydrogen atom levels are the calibration — they lie exactly on the EM line by construction.

EM LINE — Coulomb-bound systems
E/V = 3αħc / (8π r⁴)
= 2.754×10⁻²⁹ / r⁴  [J/m³, r in m]
QCD LINE — Strong-bound hadrons
E/V = 3ħc / (π r⁴)
= 3.019×10⁻²⁶ / r⁴  [J/m³, r in m]
VERTICAL GAP between lines
8/α = 8 × 137 = 1096
= 103.04 decades on log axis
What the plot tests: H atom levels → lie exactly on EM line (Coulomb). Multi-electron atoms → slightly below EM line (electron screening). Molecules → below EM line (partial bonds, dipole interactions). Nuclei (binding E) → between lines (residual strong force ~1% of nucleon mass). Hadrons (rest mass) → on or near QCD line (full QCD confinement).

The key falsifiable prediction: All EM-bound systems should scatter along slope −4. All QCD-bound systems should scatter along slope −4, offset by exactly 1096×. Any deviation in slope would break the framework.

Interpretation

Finding: Two parallel bands, slope −4

The "ratio to EM line" column below shows each system's E/V divided by the EM line value at the same radius. Values near 1.0 = on EM line. Values near 1096 = on QCD line. Values between = intermediate forces (nuclear).
Proton: ratio ≈ 1096 = exactly 8/α. This is the key result.

Data Table

System r (m) E (eV or MeV) E/V (J/m³) Ratio to EM line Type