Maximizing the Entropy of All Geometric Measurements Yields a Gravitized Standard Model

In modern theoretical physics, the laws of physics are directly represented with axioms (e.g., the Dirac--Von Neumann axioms, the Wightman axioms, and Newton's laws of motion). While axioms hold true merely by definition, the laws of physics are instead entailed by laboratory measurements. Motivated by this dissimilarity, this paper introduces a more suitable logical structure than axioms to represent the laws of physics, then makes the case for its supremacy. Specifically, we introduce an optimization problem on the entropy of all geometric measurements. Its 4 dimensional solution is a gravitized quantum theory with a ${\rm GL}^+(4,\mathbb{R})$ group symmetry. This symmetry is then found to break into a gravitational theory part and into a quantum theory of the SU(2)xU(1) and SU(3) groups. Remarkably, our optimization problem holds in a maximum of 4 dimensions, and becomes defective otherwise