Geometric Origin of Time in Discrete Geometric Physics: Resolution of the Problem of Time in Quantum Gravity via the Bounce Mechanism of the 26 Vertex Cubic Lattice
Year: 2026
Type: article
Abstract: The problem of time in quantum gravity is one of the deepest mysteries of modern physics. Quantum mechanics treats time as an external parameter, while general relativity treats it as a dynamical variable tied to the geometry of spacetime. Attempts to unify these theories encounter fundamental contradictions: the Wheeler–DeWitt equation contains no time, time in GR has no preferred direction, and quantum theory cannot quantize time as an observable. In Discrete Geometric Physics (DGP), space is a 26‑vertex cubic lattice with the topological invariant Σw = 14. In this model, time is not postulated but derived from the bounce mechanism — an elementary act of irreversibility that occurs at critical deformation of the lattice. We show that time is discrete with a minimum quantum τ_Pl = ℓ_Pl / c; the arrow of time emerges from the irreversibility of the bounce; the Schrödinger equation is derived from discrete dynamics; relativistic effects (time dilation) arise naturally; the time operator and uncertainty relation are constructed; and gravitational waves modulate the tempo of time. All results are obtained from geometric invariants (Σw = 14, θ = arcsin(1/√3), φ = (1+√5)/2) and from numerical solution of minimization equations on the lattice. Specific values of parameters (τ_Pl, γ, η_crit, F_top, etc.) are fixed by geometry and not adjusted to fit any data. The theory provides verifiable predictions and resolves the problem of time in quantum gravity.
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166299845