Quantum Mechanics from Finite Observation: Born Rule, Interference, and Uncertainty as Consequences of Markov Blanket Geometry
Sloan Austermann
Paper 6 of 6 in the Metric Bundle Programme. We prove that the core axioms of quantum mechanics---the Born rule, superposition with interference, the uncertainty principle, and spectral quantisation---arise as necessary consequences when a finite agent with Fisher--Rao information geometry observes an infinite-dimensional geometric structure through a finite Markov blanket. The central result (\Cref{thm:born-uniqueness}) shows that among all power-law probability rules p_i \propto |\psi_i|^\alpha, only the Born rule \alpha = 2 yields a total Fisher information that is independent of the quantum state when summed over a complete set of mutually unbiased bases. This is verified analytically for qubits and numerically for higher dimensions. Combined with the metric bundle framework's derivation of gauge theory from \Met(M^4), these results suggest that both the Standard Model and quantum mechanics emerge from the geometry of the space of metrics, observed by agents of finite capacity. Shows that five axioms of quantum mechanics—the Born rule, complex Hilbert space structure, superposition, interference, and the uncertainty principle—emerge as necessary consequences when a finite agent (Markov blanket) observes infinite geometric structure (the metric bundle). The main result is the Born rule uniqueness theorem: among all power-law probability rules, only the Born rule (α=2) gives a state-independent Fisher information trace over mutually unbiased bases. v3 changes (March 2026): v3: Fixed 'eigenvalues {+1}^6 {-1}^4' to 'signature (6,4)' (actual eigenvalues are {2,2,2,1,1,1,-1,-2,-2,-2}). Fixed stale cross-reference to Paper 5 for Yukawa coupling claim. v4 changes (March 2026): v4: Recompiled with updated cross-references.
•Mar 6, 2026•0 citations