Reforming The Math Language Of Physics (geometric Algebra) (oersted Medal Lecture)

Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics David Hestenes Department of Physics and Astronomy Arizona State University, Tempe, Arizona 85287-1504 The connection between physics teaching and research at its deepest level can be illuminated by Physics Education Research (PER). For students and scientists alike, what they know and learn about physics is profoundly shaped by the conceptual tools at their command. Physicists employ a miscellaneous assortment of mathematical tools in ways that contribute to a fragmentation of knowledge. We can do better! Research on the design and use of mathematical systems provides a guide for designing a unified mathematical language for the whole of physics that facilitates learning and enhances physical insight. This has produced a comprehensive language called Geometric Algebra, which I introduce with emphasis on how it simplifies and integrates classical and quantum physics. Introducing research-based reform into a conservative physics curriculum is a challenge for the emerging PER community. Join the fun! I. Introduction The relation between teaching and research has been a perennial theme in academia as well as the Oersted Lectures, with no apparent progress on resolving the issues. Physics Education Research (PER) puts the whole matter into new light, for PER makes teaching itself a subject of research. This shifts attention to the relation of education research to scientific research as the cent