Gravity as Lattice Elasticity: A Geometric Derivation from the Universe Engine v13.3.5

AbstractThis module (v13.3.5) presents a complete geometric derivation of gravity. Crucially, gravity is not programmed into the simulation as a force; it emerges spontaneously from the elastic properties of the spacetime lattice. In the Universe Engine, the universe is a 4D simplicial complex (600-cell tessellation). We demonstrate that what we perceive as "gravity" is simply the lattice trying to minimize elastic strain caused by the presence of mass. Key Theoretical Insights: Mass as Temporal Extension: We redefine mass not as an arbitrary scalar, but as a geometric property:m ∝ L_timeMassive particles are "longer" in the time dimension. This "temporal thickness" stretches the surrounding lattice, creating tension. Gravity from Elasticity: The lattice follows a simple minimization principle (Hooke's Law for edges). When a massive object stretches the lattice in the time dimension, the spatial dimensions curve to compensate and minimize total strain. Result: The Einstein Field Equations emerge from discrete Regge Calculus. Mechanism: Particles follow geodesics (paths of least resistance) in this deformed lattice, which we perceive as gravitational attraction. Cosmological Constant (Dark Energy): The theory naturally predicts the ratio of Matter to Dark Energy. 1 Dimension (Time) creates Mass (pulls inward). 3 Dimensions (Space) create Lattice Tension (expands outward). Predicted Ratio: 1:3 (Matter : Dark Energy). Observed: ~0.3 : 0.7 (remarkably close to 1:3). The Simulation (gravity_simulation.py)The included Python code demonstrates this mechanism in action: Setup: Creates a 2D triangular lattice representing a slice of spacetime. Action: Places a "massive" particle (defined only by its temporal extension) in the center. Emergence: The lattice spontaneously deforms to accommodate the mass (solving the discrete Poisson equation). Result: A test particle, moving in a straight line locally, follows a curved path (orbit/deflection) globally due to the lattice geometry. No "force of gravity" formula is used; only lattice geometry. ContextThis derivation unifies Gravity with Quantum Mechanics by showing they are both consequences of the same discrete lattice dynamics. It eliminates the need for "gravitons" as fundamental particles—gravity is a state of the lattice, not a particle moving through it. Files Included: Gravity_as_Lattice_Elasticity_Universe_Engine_v13_3.pdf (Theoretical Proof) gravity_simulation.py (Source code of the simulation) Author InformationJulian Zoria (Independent Researcher)ORCID: 0009-0002-2424-5291Email: julian.zoria@proton.me