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.
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.
We present a reformulation of fundamental physics from an enumeration of independent axioms into 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. Solving this optimization problem for the natural constraint --the most permissive constraint compatible with the problem-- identifies an optimal physical theory. Rather than existing as separate postulates, quantum mechanics, general relativity, and the Standard Model gauge symmetries emerge 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 to an optimization problem constructed over all realizable experiments in nature.
We present a reformulation of fundamental physics from an enumeration of independent axioms into 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. Solving this optimization problem for the natural constraint --the most permissive constraint compatible with said problem-- identifies an optimal physical theory. Rather than existing as a collection of postulates, quantum mechanics, general relativity, and the Standard Model gauge symmetries emerge 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 to an optimization problem constructed over all experiments realizable within the constraint of nature.
We present a reformulation of fundamental physics - from a collection 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 final measurements relative to their preparations subject to an appropriate physical constraint. This optimization problem considers all possible predictive theories over all possible experiments, whilst being constrained by all possible measurements, and then automatically selects the exact physics we observe as the optimal solution. As a consequence of this formulation, rather than as separate postulates, we obtain quantum mechanics, general relativity, and the Standard Model gauge symmetries within a unified theory. Mathematical consistency further restricts valid solutions to 3+1 dimensions, suggesting why our universe exhibits this specific dimensionality. This reformulation reveals that the apparent complexity of modern physics, with its various forces, symmetries, and dimensional constraints, emerges naturally when optimizing over all possible ways of predicting measurements from preparations.
We present a reformulation of fundamental physics from an enumeration of independent axioms into 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. Solving this optimization problem for the natural constraint --the most permissive constraint compatible with said problem-- identifies an optimal physical theory. Rather than existing as a collection of postulates, quantum mechanics, general relativity, and Yang-Mills emerge 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 to an optimization problem constructed over all experiments realizable within the constraint of nature.
We present a reformulation of fundamental physics from an enumeration of independent axioms into 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. Solving this optimization problem for the natural constraint --the most permissive constraint compatible with said problem-- identifies an optimal physical theory. Rather than existing as a collection of postulates, quantum mechanics, general relativity, and Yang-Mills emerge 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 to an optimization problem constructed over all experiments realizable within the constraint of nature.
We present a reformulation of fundamental physics from an enumeration of independent axioms into 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. Solving this optimization problem for the natural constraint --the most permissive measurement constraint compatible with said problem-- identifies a unified physical theory which contains quantum mechanics, general relativity (acting on spacetime) and Yang-Mills (acting on internal spaces). Notably, mathematical consistency further restricts valid solutions to 3+1 dimensions only, automatically yielding spacetime. This reformulation reveals that the apparent complexity of modern physics, with its various forces, symmetries, and dimensional constraints, emerges as the solution to an optimization problem constructed over all experiments realizable within the constraint of nature.