Axiom Zero: The Entropic Genesis of Physical Law from Information

We propose a theoretical framework called Relational Information Theory (RIT),founded on a single postulate: the total entropy of a physical system equals the sumof its reference frame differentials. This axiom—which we call Axiom 0—representsa synthesis of Boltzmann’s statistical mechanics, Shannon’s information theory, andPlanck’s quantum hypothesis. From this starting point, we derive (rather than assume) Planck’s constant ℏ, Newton’s gravitational constant G, and the fine structureconstant α. The derivation of α−1 = π+π2+ 4π3−8π4α3 ≈ 137.036 achieves agreement with experiment at the level of 7 parts per billion, with no free parameters. Wealso present derivations of the weak mixing angle and nucleon-to-electron mass ratios. While significant open questions remain—particularly regarding higher-ordercorrections and independent experimental tests—these results suggest that the fundamental constants may emerge from information-geometric constraints rather thanbeing irreducible inputs to physics.