Physics & Astronomy Professor Kaća Bradonjić, Hampshire College

"Mathematics as the Language of Physics: What is Lost in the Translation?"

The use of mathematics for codification of observations and the formulation of physical laws has been of such utility that it is easy to forget that mathematics as it is used by mathematicians is in many important ways different from mathematics as it is used by physicists. The former deals with purely abstract concepts, such as numbers and geometric shapes, while the latter is imbued with meaning which relates these concepts to the features of the physical world. Unlike the mathematician, the physicist is tasked with casting observations and physical laws into mathematical form and then interpreting the mathematical results as statements about the Nature. The big question is, what is lost in the translation? Given a mathematical formulation of a physical theory, where does its physics end and the pure math begin? After looking at some familiar examples from undergraduate physics, I will discuss these questions in the context of the general theory of relativity, examining how abstract concepts of a manifold, coordinates, metric tensor, and affine connection are used to model physical events, geometry of spacetime, and the gravitational field. Understanding the relation between math and physics in this context is essential for the development of new physical theories, such as modifications of general relativity and quantum theory of gravity.