Physical Reality as a Hierarchical Emergent Structure from Information-Theoretic First Principles

This work presents a comprehensive, first-principles derivation of physical reality, positing that the universe is a hierarchical, emergent structure founded upon a minimal set of foundational postulates governing information, conservation, and logical inference. The argument proceeds in two stages: deconstruction and reconstruction. First, the traditional pillars of physics—dimensional constants, the Planck scale, and spacetime geometry—are critically analyzed and shown to be non-fundamental, derived concepts. Formal algebraic derivations are provided to show how constants like $G$, $c$, and $\hbar$ vanish when physical laws are expressed in dimensionless form. Second, a new foundation is established upon a tripartite basis: a definitional postulate (the physical nature of state), a dynamical postulate (unitarity), and an inferential postulate (the principle of maximum entropy). The precise, non-axiomatic status of these postulates is rigorously analyzed. From this nuanced foundation, the laws of physics are systematically re-derived as a series of emergent theorems and consequences. Level 1 provides formal mathematical derivations for the core framework of statistical mechanics and thermodynamics. Level 2 provides derivations of the Bekenstein Bound and the Holographic Principle, correctly identifying them as arguments from physical consistency. Level 3 presents the derivational framework for the emergence of Euclidean distance and Minkowski spacetime from the information-theoretic structure of the holographic boundary. A detailed explanation of the holographic projection is provided. Levels 4 and 5 then present the formal mathematical blueprints for the derivation of General Relativity and the Standard Model. The thesis then subjects its own logic to a series of rigorous critiques and provides formal rebuttals. The final synthesized conclusion concludes that physical laws are the thermodynamic and statistical consequences of information processing, redefining the task of a final theory as the completion of the explicit mathematical steps laid out in this blueprint.