We present a unification of fundamental physical laws from a single principle: maximizing the Shannon entropy of all possible measurements relative to a system's initial state, under a universal measurement constraint. By solving this entropy maximization problem, we find that the most sophisticated solution involves 3+1-dimensional measurements encompassing both bivectors and complex numbers. This solution describes a relativistic quantum theory that naturally yields the metric tensor of general relativity via a double-copy mechanism applied to the Dirac current. Moreover, it inherently incorporates the SU(3)xSU(2)xU(1) gauge symmetries of the Standard Model. These findings expose deep connections between information theory and the mathematical structures underpinning fundamental physics, providing new insights into the emergence of 3+1 spacetime dimensions, gravity, and the fundamental symmetries of our universe.