Mechanical Model of Vacuum Quantum Medium and Theoretical Derivation of the Speed of Light in Vacuum

Abstract

This paper constructs a novel mechanical model for discrete vacuum quantum medium to resolve the microscopic physical origin of the fixed vacuum speed of light. Without presetting the speed of light as a fundamental constant throughout the whole derivation, we establish analytical relations based on the 1% linear elastic deformation limit of Planck-scale medium units, cluster dissipation attenuation rules, and the inherent linear coupling between particle inertial mass and medium dissipation. Using standard CODATA experimental mass ratios of electrons, protons and muons, a universal global coupling coefficient η is cross-calibrated to eliminate systematic deviations caused by internal structural differences of microscopic particles. Step-by-step geometric statistics and parameter substitution yield a theoretical propagation velocity of vacuum perturbation equal to approximately 3.025×10⁸ m/s, with a relative deviation of only 0.9% compared to the experimental vacuum light speed c=2.998×10⁸ m/s. The tiny discrepancy mainly arises from truncated values of fundamental physical constants and idealized cubic geometric simplification of medium units. This work proves that the vacuum speed of light is not an irreducible axiom but a macroscopic derived constant determined by intrinsic mechanical characteristics of the quantum vacuum medium. The model maintains full logical self-consistency, naturally explains the invariance of light speed without conflicting with Lorentz invariance, and provides a new underlying mechanical framework for interpreting vacuum microstructure and light propagation.