Observer as a Physical System: A Causal Integration-Based Quantitative Model

Abstract The quantum measurement problem remains a foundational challenge due to the lack of an operable physical definition of the "observer." This paper addresses this gap by modeling the observer as a discrete dynamical system with a quantifiable causal structure, characterized by three hierarchical dimensions: Differentiation Degree, Interaction Degree, and Global Integration Degree. From these, we define the Effective Integrated Information Degree (Φ) as a single metric for the system’s information-processing capability. Based on the unitary evolution of quantum mechanics, we derive a testable core relationship: the uncertainty probability P of a measurement outcome decays exponentially with \Phi , i.e., P \propto e^{-\alpha \Phi} . This provides a mechanistic explanation for wave function collapse rooted in the internal dynamics of the observer system. We further establish a universal Mass-Energy-Information Equivalence framework by integrating Einstein’s mass-energy equivalence with Landauer’s principle, proving a rigid conversion between \Phi and the equivalent mass of the system. This work represents a paradigm shift: it transforms the "observer" from a philosophical concept into a calculable, verifiable physical system, and opens an empirically tractable path toward unifying quantum mechanics with fundamental physics. Regardless of experimental outcomes, the model provides a rigorous foundation for resolving the quantum measurement problem and advancing our understanding of the universe’s fundamental laws.