Parallel Transport to Maxwell--A Detour on the Road to Reality

About this event

This meeting we are taking a slight detour on the road to reality The path to understanding is rarely a straight path. In this presentation we will follow a remarkable route through the history of mathematics and physics: from Ricci and Levi-Civita’s tensor calculus, through Einstein’s General Relativity and Levi-Civita’s idea of parallel transport, to Weyl’s more general theory of connections and the emergence of gauge theory. Then we will turn around and “ski back down the mountain,” using these more abstract ideas to recover familiar physics in Maxwell’s equations. Along the way, parallel transport will become quite literal—with parallel skiers illustrating how geometry, curvature, symmetry, and an action principle connect some of the deepest ideas of twentieth-century physics. To fully follow every step of the talk, it will help to have some familiarity with multivariable calculus, partial derivatives, vectors, and the basic idea of a differential equation. Some exposure to linear algebra, tensor notation, or electromagnetism will also help. But please don’t let that stop you from attending. There is real value in being exposed to advanced ideas before you completely understand them: today’s puzzling concept often becomes tomorrow’s research question. Many of us have had the experience of returning to a difficult idea again and again, understanding a little more each time. Richard Feynman reportedly did this with advanced quantum theory texts early in his life—reading material far beyond his immediate grasp, but letting it provoke questions and deepen his intuition. In that spirit, this talk is meant not only to explain, but also to inspire further exploration after the meeting—and in our era, continuing that exploration on your own has never been easier. This event is part of the Physics With Friends community, which hosts collaborative study groups in physics and mathematics. Other events: https://www.meetup.com/physicswithfriends/events/