Sub-Planckian Discrete Spacetime Calibrated by Dirac's Large-Number Ratio
Year: 2026
Type: preprint
Abstract: We evaluate the continuum limit of a discrete spacetime substrate with fundamental spacing fixed by Dirac’s large-number ratio Q ≈ 4.17 × 10^(42) at the sub-Planckian scale δ_p ≡ ℓ_P / Q ≈ 3.88 × 10^(-78) m. On a hypercubic lattice, spatial symmetry eliminates odd-order finite-difference operators, excluding dimension-5 Lorentz-violating corrections. The leading residual effect is a dimension-6 operator at O(δ_p^2), governed by a cubic-harmonic angular prefactor g(θ, ϕ). Inserting δ_p produces a classical-level Q^(-2) ~ 10^(-85) suppression factor. For free photons, the resulting classical dispersion clears ultra-high-energy cosmic-ray bounds and predicts vanishing vacuum birefringence. Extending this suppression to interacting matter and preserving it against quantum radiative corrections are framed as open conditions, as do several broader limitations of the framework. In the electromagnetic sector, this substitution yields the scale-free identity α = Z_trans / Z_rot, treating the fine-structure constant as a calibration input. In the gravitational sector, it enforces the infrared identity G_N / G_raw = Q^2. Both serve as consistency conditions rather than parameter-free derivations. We formalize these results into a ten-condition falsifiability roadmap (BC1-BC10). Of the conditions evaluated, lattice isotropy, substrate stability, and parity protection are satisfied at the level of necessary lattice properties. Conversely, bulk volume counting, Newtonian coupling strength, fine-structure constant matching, and quantum loop radiative stability highlight concrete gaps, requiring microscopic vertex counting rules.
Author: LUH, Peter
Institution: Phi Beta Kappa Society
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204627950
Cites:
Cited by:
Related to: