Constructing Physics from Measurements
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We reformulate fundamental physics from a list of axioms to the solution of a single optimization problem. Any experiment begins with a preparation, evolves, and ends with a measurement. We maximize the relative Shannon entropy of the final measurement with respect to its preparation, subject to a measurement constraint. Solving this for the natural constraint—the most permissive constraint admitting translations, boosts, rotations, and reorientations—yields a unified theory whose functional form contains general relativity (on spacetime) and Yang–Mills (on internal spaces). Mathematical consistency further restricts valid solutions to 3+1 dimensions, automatically selecting spacetime. Thus the forces, symmetries, and dimensionality of modern physics emerge as the unique solution to a single optimization posed over all experiments consistent with nature’s constraint.