# University of Michigan Math and Science Scholars

Relativity: A Journey through Warped Space and Time

Einstein forever altered our understanding of the nature of space and time with his theories of relativity. These theories tell us that the speed of light is a universal constant, declare that the fabric of space and time is warped by matter, and demand that matter moves through spacetime by following its curvature. Introduced 100 years ago, these concepts clash mightily with our everyday physical intuition, but are nevertheless cornerstones of modern-day physics. In this course we will explore the exciting world of relativity (both the special and general theories).After briefly reviewing classical mechanics (Newton’s laws), we will use thought experiments to understand the ideas behind relativity and see how they are actually ultimately simpler and more natural than classical mechanics. Along the way we will encounter strange paradoxes that push the limits of our understanding and learn powerful mathematics that will allow us to quantify our relativistic understanding of the universe. Using our new knowledge, we will delve into black holes, learn how GPS systems work, and debate the possibility of time machines and wormholes.

Prerequisites: basic concepts in geometry (e.g. coordinates, distance formulae) and physics (e.g. position, velocity, acceleration). A working knowledge of elementary calculus is recommended (e.g. what a derivative is and how to take one). We will introduce a little bit of multivariable calculus (e.g. partial differentiation) and integration techniques, so prior knowledge of those is a bonus. An open, curious and interested mind is absolutely necessary; you must be willing to think deeply about physics and the nature of our universe! Note: after the three weeks of the course have ended, if there is enough interest, there will be an optional extra week (July 5-9) where we can revisit some of the more advanced mathematical details that will be skipped over in the course (especially regarding curvature in general relativity).