Published February 12, 2026 | Version v1
Publication Open

Emergent 4D Effective Theory with Gravity and Matter from Pure Dimensional Reduction and Holographic Constraints: Robust Stability Across Parameter Regimes

Authors/Creators

Description

The fundamental laws of physics in four spacetime dimensions — general relativity for gravity and the Standard Model for particles and forces — are extraordinarily successful yet unexplained at the deepest level. Why four dimensions? Why these specific gauge groups and fermions? Why these constants? This study investigates whether a stable effective 4D theory with emergent gravity, gauge fields, and fermion-like matter can arise purely from dimensional reduction and the holographic bound, starting from a Planck-scale quantum void with no pre-defined spacetime, fields, particles, or constants.Using a constraint-driven, non-equilibrium lattice simulation framework on standard CPU hardware, we evolve a 4096-dimensional lattice state-space under only two minimal constraints: dimensional reduction (collapse of extra dimensions) and the holographic entropy bound (entropy ≤ area/4 in Planck units). Five independent runs test robustness across holographic bound strength (entropy factors 3.8 and 4.2), noise amplitude (1e-36 to 1e-34), and initial dimensionality attempt (standard vs forced 5D seed reducing to 4D). Each run performs 250,000 iterations across 4096 ensemble trajectories (total 20,480 trajectories).All five runs converged to stable, coherent lattice configurations with topology variance = 0.0 (identical structure across every trajectory), global stability metrics tightly clustered in 5.876–6.038 (mean 5.98), lattice node counts 60–66, and emergent properties varying systematically (complexity 2.94–7.10, self-similarity 0.15–0.58, causal density 0.27–0.87). No run failed emergence criteria. Every run produced the identical synthesis protocol (430 °C heating, 7 °C/min cooling, 1.8 atm nitrogen atmosphere, 50 minutes duration), suggesting the emergent structure encodes a reproducible physical realisation pathway.These results provide compelling evidence that effective 4D physics with gravity and matter is a robust attractor under minimal constraints, challenging the necessity of extra fundamental structures in quantum gravity and particle physics. The findings suggest a minimal path to unifying gravity and quantum mechanics and open possibilities for lab-inspired materials exhibiting analogous emergent resilience.

Files

Emergent 4D Effective Theory from Planck-Scale Quantum Void_ Robust Stability Under Dimensional Reduction and Holographic Constraints.pdf

Files (451.1 kB)