Intelligence Inertia: Physical Isomorphism and Applications

Classical frameworks like Fisher Information approximate the cost of neural adaptation only in low-density regimes, failing to explain the explosive computational overhead incurred during deep structural reconfiguration. To address this, we introduce $\mathbf{\text{Intelligence}}\mathbf{\text{Inertia}}$, a property derived from the fundamental non-commutativity between rules and states ($[\widehat{S},\widehat{R}]=i\mathcal{D}$). Rather than claiming a new fundamental physical law, we establish a $\mathbf{\text{heuristic}}\mathbf{\text{mathematical}}\mathbf{\text{isomorphism}}$ between deep learning dynamics and Minkowski spacetime. Acting as an $\mathit{\text{effective}}\mathit{\text{theory}}$ for high-dimensional tensor evolution, we derive a non-linear cost formula mirroring the Lorentz factor, predicting a relativistic $J$-shaped inflation curve – a computational wall where classical approximations fail. We validate this framework via three experiments: (1) adjudicating the $J$-curve divergence under high-entropy noise, (2) mapping the optimal geodesic for architecture evolution, and (3) deploying an $\mathbf{\text{inertia-aware}}\mathbf{\text{scheduler}}\mathbf{\text{wrapper}}$ that prevents catastrophic forgetting. Adopting this isomorphism yields an exact quantitative metric for structural resistance, advancing the stability and efficiency of intelligent agents.