Emergent Relativistic Kinematics and Inertia from the Relaxation Dynamics of a Discrete Space- Quantum Network

Abstract In this paper, we demonstrate that relativistic kinematics and the origin of inertia can emerge as macroscopic consequences of the relaxation dynamics of a discrete space-quantum network. Without presupposing any continuous spacetime metric, we model macroscopic motion as a non-equilibrium coherent relaxation process of the underlying network. We show that the maximum response rate of the network naturally imposes a causal delay (retarded geometry) on a moving topological defect. Through a purely geometric derivation, the Lorentz factor is rigorously obtained. By defining the energy-momentum tensor from the network's effective Lagrangian and requiring its conservation, we prove that the four-momentum behaves as a standard Lorentz four-vector. Consequently, the standard relativistic energy-momentum relations arise strictly as algebraic consequences of four-vector norm invariance. This work provides a first-principles dynamical mechanism showing that Minkowski spacetime is not a fundamental background, but an emergent effective geometry in the long-wavelength continuum limit.