Can Spacetime Stiffness Generate Quantum Field Excitations? A Rigorous Theoretical and Computational Falsification Analysis

This paper examines the hypothesis that intrinsic mechanical-like stiffness in spacetime could generate quantum field excitations or effective particle masses. It derives the correspondence between a continuum wave equation and the Klein–Gordon equation for a neutral scalar field, then evaluates whether interpreting the model as a physical spacetime medium is consistent with established physics. The analysis considers Lorentz invariance and preferred frames, scalar versus photon degrees of freedom, gauge invariance and vector-field mass terms, and the origin of the Yang–Mills mass gap. Finite-difference time-domain simulations are presented alongside the analytical arguments. The paper concludes that the equation can serve as a consistent effective scalar-field model, while the interpretation of fundamental spacetime stiffness as its physical mechanism fails the consistency tests considered.