The boundary condition paradox: a limit to the university of differential equations

摘要

Laws of motion expressed as differential equations governing the behavior of a system of particles break down when applied to the universe as a whole. This is due to the fact that the boundary conditions should in principle be reducible to particle interactions; as a consequence a differential equation runs out of boundary conditions when applied to the whole universe. We formulate this pathology and consider whether it could be a portent of breakdown of existing theories in more local domains, such as those connected with the behavior of living systems.