Physics as an Optimization Problem over All Measurements
Alexandre Harvey-Tremblay · Preprints.org · 2024
We propose a novel approach to quantum theory construction that involves solving a maximization problem on the Shannon entropy of all possible measurements of a system, relative to its initial preparation. This maximization problem is additionally constrained by a phase condition that vanishes under measurements. Specifically, enforcing a vanishing U(1)-valued phase constraint leads to standard quantum mechanics, while a vanishing Spin^c(3,1)-valued phase constraint extends the theory to relativistic quantum mechanics and to quantum gravity. The latter scenario is found to incorporate the SU(3)xSU(2)xU(1) symmetries of the Standard Model as invariants of the probability measure itself, and to construct the metric tensor as an operator via a double-copy mechanism applied to Dirac currents. Significantly, this solution is consistent exclusively with a 3+1-dimensional spacetime configuration---all other dimensional settings are shown to lead to fundamental obstructions. This framework seamlessly integrates fundamental concepts from quantum mechanics, relativistic quantum mechanics, quantum gravity, the dimensional specificity of spacetime, and particle physics symmetries as the solution to a simple entropy maximization problem.