The Theory of Observerhood in Quantum Measurement: A Trial Formulation of Basis Selection Based on Informational-Geometric Consistency

Abstract This study proposes a reformulation of the observer’s role in quantum measurement by introducing an informational structural parameter ϕ, referred to as observerhood (SOP). Within this framework, the measurement problem is reframed not as a causal question—“why does collapse occur?”—but as a structural one: “why does this informational structure stabilize coherently?” The observer is modeled as an informational agent characterized by an exponential-family state ρ_ϕ defined over a set of measurable operators {A_i}. The informational consistency between the quantum state ρ and the observer’s structure ϕ is quantified by the quantum relative entropy C(ρ, ϕ) = −S(ρ || ρ_ϕ). The gradient flow of this function yields a non-unitary informational update process of the observer's structure. In a spin-½ system, the stationary distribution μ_eq(ϕ) reconstructs the Born rule in the low-informational-temperature limit. While this theory does not claim new empirical predictions, it reconstructs measurement as a dual process of external decoherence and internal consistency, providing a structural foundation that unifies decoherence theory, relational quantum mechanics, and informational structural realism.