On the Limits of Informational Physics

Building on the axiomatic foundations of On the Foundations of Informational Physics (hereafter Part I ), the dynamical derivations of On the Dynamics of Informational Physics (hereafter Part II ), and the variational unification of On the Unification of Informational Physics (hereafter Part III ), this paper investigates what the Representational Sufficiency Principle (RSP) implies about the nature of light, the structure of relativisticphenomena, and the meaning of the observer. The unifying theme is the concept of a limit — not as an obstacle but as a structural feature: the finite speed of distinguishability propagation defines causality; the finite informational granularity of the substrate defines thePlanck scale; the finite update budget of any recursive structure defines proper time and the asymmetry in the twin scenario; the finite representational capacity of the Bekenstein boundary defines collapse. Within the RSP framework, the speed of light c is proposed not as a postulated constant but as an emergent ratio between the minimal relational adjacency spacing ∆R and the minimal update interval ∆U of the informational substrate. Light is reinterpreted as zero – self-reference distinguishability propagation — pure update without recursion — which saturates this ratio because it carries no internal self-binding. Mass, by contrast, accumulates recursive constraint loops that consume update capacity and therefore propagates atsub-maximal rates. Time dilation and length contraction are recast as redistribution effects within a finite substrate update budget, and the twin scenario dissolves into an accounting asymmetry in accumulated internal recursion. Lorentz invariance is proposed to be emergent rather than fundamental: a necessary symmetry of the emergent 3+1 bulk arising from boundary combinatorics, exact in the infrared and subject to granularity-scale corrections at energies approaching the Planck regime. The apparent conflict between substrate discreteness and Lorentz invariance is resolved by the observation that the two properties belong todifferent ontological layers and are therefore not in competition. The paper further proposes a revised ontology of the observer: not a conscious agent but any recursively self-binding distinguishability structure that maintains internal coherence across updates. This redefinition connects directly to the collapse criterion established in Part III and dissolves several interpretational puzzles in quantum mechanics without introducing hidden variables. The paper closes by identifying the structural gaps that remain before the framework can be considered a candidate physical theory.