Constructing Physics from Measurements

We reformulate fundamental physics as the solution to an entropy optimization problem rather than an enumeration of axioms. Modeling the scientific method operationally—preparation, evolution, and measurement—we maximize the relative entropy of the final state relative to the initial preparation, subject to a measurement constraint. In the linear regime, the maximization of entropy yields the Dirac equation. Extending this to the most general non-linear constraint naturally reproduces the spectral action, leading to Einstein–Hilbert gravity and Yang–Mills gauge theory. Furthermore, imposing positivity and realness requirements on the partition function singles out (3{+}1) dimensions as the unique satisfying case. Thus, the apparent complexity of modern physics—forces, symmetries, and dimensionality—emerges not as a set of arbitrary postulates, but as the necessary solution to a single inference principle.