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 as a structural consequence of the Total Entropic Quantity (TEQ) framework. This derivation requires no 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 yields a flat entropy metric that defines a resolution norm over infinitesimal variations. We identify the Lorentz group as the class of transformations that preserve this entropy-resolved norm, and we derive time dilation and length contraction from entropy curvature effects—quantitatively equivalent to standard relativistic expressions, but interpreted as limits on resolvable structure. The invariant speed c appears as a derived structural constant, corresponding to the maximal rate of entropy-resolved evolution in flat regimes. 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. Lorentz contraction, in this formulation, is not a coordinate deformation but a structural suppression of resolution induced by motion.