Physical Systems as Objects: A Structural Correspondence for Computational Physics Education

Abstract

Physical systems and objects in the object-oriented programming (OOP) paradigm share a common organizational structure: identity, state, and governing laws. We argue that making this structural correspondence explicit, rather than leaving it as tacit knowledge embedded in scientific software, provides a natural and general basis for teaching computational physics. The correspondence is independent of both programming language and mathematical formalism, applying equally to differential equations, eigenvalue problems, and variational principles. To illustrate this idea, we present Ollin, an open-source Python framework for computational physics education organized around the correspondence principle. Four examples spanning mechanics, celestial mechanics, quantum mechanics, and variational optics demonstrate that the same representational structure can be preserved across diverse physical domains. In each case, the class definition serves as the physical model, its attributes encode the state and physical parameters of the system, and its methods encode the governing laws, regardless of whether those laws are integrated, diagonalized, or optimized. More broadly, the correspondence principle provides a conceptual framework for relating the organization of physical models to the organization of code.