What question did this study set out to answer?

To present a geometric derivation of gravity as an emergent property of the spacetime lattice.

February 2, 2026Open Access

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

Key Points

To present a geometric derivation of gravity as an emergent property of the spacetime lattice.
Developed a geometric model using a 4D simplicial complex to represent the universe.
Demonstrated how mass affects the spacetime lattice through its elastic properties.
Utilized discrete Regge Calculus to derive the Einstein Field Equations.
Included a Python simulation to illustrate the lattice deformation around a massive particle.
Gravity emerges from the minimization of strain in the lattice due to mass presence.
Predicted ratio of Matter to Dark Energy (1:3) aligns closely with observed values (~0.3:0.7).
Particles follow geodesics in the deformed lattice, explaining gravitational attraction without traditional force concepts.

Abstract

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 ∝ LₜimeMassive 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 (gravityₛimulation. 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: GravityₐsLatticeElasticityUniverseEngineᵥ13₃. pdf (Theoretical Proof) gravityₛimulation. py (Source code of the simulation) Author InformationJulian Zoria (Independent Researcher) ORCID: 0009-0002-2424-5291Email: julian. zoria@proton. me

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

Key Points

Abstract

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