tau19

formal source

 126    τ₁₉ = τ₀ × φ¹⁹ ≈ 68 ps
 127
 128    The full ladder spans from t_P to cosmological times! -/
 129noncomputable def tau19 : ℝ := tau0 * phi^19
 130
 131/-! ## Quantum Gravity Predictions -/
 132
 133/-- RS predictions for quantum gravity:
 134
 135    1. **Minimum length = l_voxel**, not l_P
 136       - Below l_voxel, spacetime is discrete
 137       - l_P may be inaccessible
 138
 139    2. **φ-quantized energies** near Planck scale
 140       - Energies at φ^n × E_P
 141
 142    3. **No singularities**
 143       - Voxel structure prevents infinite densities
 144
 145    4. **Modified dispersion relations**
 146       - At high energy, E² = p²c² + m²c⁴ + corrections -/
 147def predictions : List String := [
 148  "Minimum length is l_voxel ≈ 10⁻¹⁹ m, not l_P",
 149  "Energies quantized in φ-ladder rungs",
 150  "Black hole singularities resolved by voxels",
 151  "Modified high-energy dispersion relations"
 152]
 153
 154/-! ## Experimental Signatures -/
 155
 156/-- Possible experimental tests:
 157
 158    1. **GRB time delays**: High-energy photons delayed by quantum gravity?
 159       - Fermi satellite data constrains quantum gravity scale