Vacuum Viscosity Saturation in High-Density Regimes: Resolving the Muon g-2 Anomaly via Magnetic Time Dilation

Notice: This document represents an early-stage conceptual draft. It has been deposited in this archive primarily to establish academic priority for the core physical hypotheses and experimental proposals (e.g., the local energy density framework). Readers should be aware that the mathematical formalism and numerical calculations herein are preliminary and are currently undergoing rigorous refinement. For the fully calibrated and peer-reviewed mathematical framework regarding the cosmological applications of this theory, please refer to the latest publications of the Primary Energy Research Group.

In our companion paper (Paygachkin, 2026, V2.0), we demonstrated that a vacuum viscosity of η ≈ 0.10 naturally resolves the Hubble Tension and explains the dispersion of Gravitational Waves (GW150914). However, microphysical experiments suggest that massive particles interact with the vacuum differently than massless waves.

In this study, we extend the Primary Energy framework to the "Matter Regime" of high energy densities. We postulate that vacuum viscosity is not a constant but saturates near massive particles. Analyzing the Muon g-2 anomaly, we derive a saturation limit of viscosity η_micro ≈ 0.14.

We calculate that this phase transition occurs when the local energy density exceeds a critical magnetic field threshold of B_crit ≈ 17.25 T.

Prediction: We propose a falsifiable experiment to verify this saturation. A stationary muon placed in a static magnetic field B > 20 T should exhibit a non-kinematic lifetime extension (Time Dilation) due to the local thickening of the vacuum. This "Static Time Dilation" is predicted to exceed standard relativistic calculations, confirming the material nature of the vacuum.