Quantum Geometry Regularization and the Emergence of Macroscopic Time. Part III: High-Energy Electromagnetic Fields as an Effective Probe of Non-Commutative Spacetime Foam and Lorentz Invariance Violation

This paper establishes a rigorous, self-consistent experimental protocol for testing the Relational KMS Interpretation of Quantum Mechanics and the discrete geometric regularizations formulated in Parts I & II of this triptych. We analyze the behavior of an emergent, macroscopic spacetime metric under extreme, coherent electromagnetic shear stress. Rather than evoking non-unitary transitions, we demonstrate that a high-intensity localized electromagnetic energy density induces a measurable perturbation in the Tomita–Takesaki modular flow of the underlying von Neumann factors of type III_1. This perturbation locally alters the Kubo–Martin–Schwinger (KMS) state, leading to a predictable shift in the non-commutative coordinate jitter. We outline the exact engineering specifications required to isolate this quantum-geometric anomaly while satisfying sub-critical QED and thermodynamics boundaries. The framework establishes Popperian falsification criteria via three independent diagnostic channels: cryogenic quantum optomechanics modeled via open-system Lindblad dynamics (QuTiP), high-precision laser polarimetry targeting vacuum birefringence (HEALPix), and picosecond time-of-flight spectrometry monitoring anomalous photon phase diffusion.