Emergence of Physics from Quotient Structure: A Demonstration of SRDT's Meta-Theoretic Efficacy

Traditional approaches to a "Theory of Everything" (ToE) propose specific fundamental dynamics and attempt to derive observed physics from them, implicitly assuming physics is objective—a property of fundamental reality that observers merely discover. Scale-Relative Distinguishability Theory (SRDT) challenges this assumption by operating at the meta-theoretic level: rather than proposing specific content, SRDT specifies what any valid ToE must include. The central insight is that physics is not a property of fundamental dynamics (𝓕) alone, but emerges from the quotient 𝓕/𝓞—the equivalence classes of configurations that an observer 𝓞 with finite resolution cannot distinguish. This paper demonstrates SRDT's framework efficacy: its capacity to generate physics-like phenomena from a single mechanism without presupposing physical concepts. Using coupled Hénon maps as dynamics 𝓕 and a finite-resolution observer 𝓞, we show that twelve structural analogs of foundational physics concepts emerge from the quotient operation: space, time, matter, forces, wave-particle duality, entropy, quantization, superposition, locality, apparent randomness, measurement, and uncertainty. All twelve are classified as observer-created or observer-selective under SRDT's diagnostic taxonomy—none are intrinsic to 𝓕. This demonstration constitutes an existence proof: there exists at least one (𝓕, 𝓞) pair for which SRDT produces physics-like structure, validating the framework without claiming correspondence to human physics. The paper establishes that a complete Theory of Everything must specify not only fundamental dynamics but also observer characteristics—and for human physics, this means characterizing what we are as biological, embedded, finite-resolution observers.