Relativistic Dynamics

Abstract

Preface These notes assume that you have a knowledge of space and time in special relativity, and of force, energy, and momentum in classical mechanics (both at the college freshman level). They build on that knowledge to describe force, energy, and momentum in special relativity. These notes also use a few ideas from freshman-level electricity and magnetism, but not in an essential way. The intent is to present physical questions and their direct and straightforward (if laborious) solutions, rather than to show off how mathematically clever the author is. Teaching notes: I use these notes over five or six lectures to college sophomores. On the first day I ask students what they remember about space and time in special relativity. Students are often surprised and gratified that they remember anything about such a counterintuitive subject. Then I present " why we need relativistic dynamics " (section 2.1), followed by one of the two " momentum motivations " , either the collision motivation (sections 2.2, 2.3, and 2.4) or the four-vector motivation (sections 3.1, 3.2 and 3.3). I leave the other motivation for reading. I've tried it both ways and it doesn't seem to make any difference in how well the students learn. In either case I end up interpreting the " new quantity " mc 2 / 1 − (v/c) 2 (section 2.5) in class. In class I present chapters 4 and 6, leaving chapter 5 for reading. It is impossible to overemphasize the fact that mass is not conserved in relativity, which is why I make that point twice (once in section 4.1, again in section 4.2). I end with section 7.1, including working through problem 7.3 (Motion with constant force). This way we end by answering the question we started with, which ties the whole subject together. At this point, students are mentally exhausted: so many new and counterintuitive ideas, so close together. So I have never covered chapters 8 or 9. I just hope that when the students regain their footing they will look back at those two final chapters to learn some things wonderful and profound. Acknowledgment: The discussion of hard-sphere forces in section 9.2 arose from a question by David Carr, a Ph.D. student in computer science at Charles Sturt University in Australia, who was designing a game to teach relativity.