Real Space and Observed Space: An Energy-Efficiency Account of Measurement, Causality, and Cognition

This paper develops a foundational epistemology within Energy-Efficiency Theory (EET). It distinguishes real space—the ontological unfolding of energy distribution and constraints independent of any observer—from observed space—the projection accessible through measurement under finite signal speed, energy cost, and cognitive constraints. Starting from the three axioms of EET, we define the projection map Π mathematically, quantify information loss, and show that natural causality is the projection of energy gradients into observed space. Quantum measurement is interpreted as a free-to-bound energy transition, with the Born rule emerging from transition rates proportional to the squared overlap of quantum states. The framework explains why empirical knowledge is inherently probabilistic, why measurement has limits, why perception is constructive, and why science systematically approaches but never reaches absolute truth. Relation to the EET series: This paper aligns with the official EET specification 1 and integrates with Ben-Shi Dynamics—the kinetic core of EET—which comprises the Energy-Efficiency Regulator, the two fundamental energy rates (Ėᵣesp, Ėₘain), and Yang's Ben-Shi Sliding equation 2, 3. Together, these works form a complete dynamical and epistemological foundation for non-equilibrium systems. Version: V2. 2Keywords: non-equilibrium thermodynamics; quantum measurement; projection mapping; Energy-Efficiency Theory; scientific realism; cognitive constructionLicense: CC BY 4. 0Related identifiers: 1 Yang, H. (2026). Energy-Efficiency Theory (EET): Axioms and Core Concepts. Zenodo. DOI: 10. 5281/zenodo. 192824132 Yang, H. (2026). Yang's Ben-Shi Sliding: A Dynamical Framework for Conservation-Expansion Balance. Zenodo. DOI: 10. 5281/zenodo. 192847403 Yang, H. (2026). Response and Maintenance Energy Rates: The Driving Forces of Energy-Efficiency Regulation. Zenodo. DOI: 10. 5281/zenodo. 19284900