Special Relativity as an Emergent Symmetry of Entropy Geometry

We show that the relativistic symmetry structure familiar from Special Relativity—namely, Lorentz invariance, time dilation, and length contraction—emerges naturally from the Total Entropic Quantity (TEQ) framework, without requiring postulates about spacetime, light propagation, or inertial frames. In TEQ, physical structure is governed by entropy geometry: configurations evolve along trajectories that minimize instability under entropy-weighted dynamics. In regions of vanishing entropy curvature, this leads to a flat entropy metric that defines a resolution norm over infinitesimal variations. We identify the Lorentz group as the set of transformations that preserve this entropyresolved norm, and we show that time dilation and length contraction arise as resolution-induced effects—consequences of how motion through entropy geometry alters the system’s capacity to resolve distinguishable states. The invariant speed c appears as a derived structural constant, corresponding to the maximum rate of entropy-resolved resolution in flat regimes. In this formulation, Special Relativity is not a foundational framework but an emergent symmetry structure arising from deeper thermodynamic-geometric principles. Where Special Relativity assumes the structure of spacetime and derives consequences for measurement, TEQ inverts this logic: it derives the structure of spacetime-like symmetries as emergent features of entropy-resolved dynamics.