Constructing Physics From Measurements

We present a reformulation of fundamental physics - from an enumeration of independent axioms to the solution of a single optimization problem. Any experiment begins with an initial state preparation, involves some physical operation, and ends with a final measurement. Working from this structure, we maximize the entropy of a final measurement relative to its initial preparation subject to a measurement constraint, the later defining the domain of the theory. Since we keep the structure of an experiment entirely general, solving this optimization problem identifies the unique optimal predictive theory that holds true for all realizable experiments within the domain. We then find that using the natural constraint -- which spawns the most general domain supported by this optimization problem -- points to a unification of fundamental physics. Rather than as separate postulates, we obtain quantum mechanics, general relativity, and the Standard Model gauge symmetries within a unified theory. Notably, mathematical consistency further restricts valid solutions to 3+1 dimensions only. This reformulation reveals that the apparent complexity of modern physics, with its various forces, symmetries, and dimensional constraints, emerges as the solution an optimization problem over all realizable experiments of nature.