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

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). Through 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‖ρϕ). 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 limit of low informational temperature. While the present theory does not claim novel empirical predictions, it reformulates measurement as a dual process of external decoherence and internal consistency. In doing so, it provides a structural foundation that unifies decoherence theory, relational quantum mechanics, and informational structural realism. The notion of observerhood is generalized beyond consciousness, encompassing devices, artificial agents, and biological systems, thus bridging quantum foundations, information geometry, and cognitive science through a common structural perspective.