Physics in Spacetime
An introduction to Special Relativity

Benjamin Schumacher

 302 pages, 9x6 inches Feb 2005 Hardcover ISBN 1-58949-038-X US$56 Buy It This book is an introduction to special relativity for undergraduates in physics and mathematics. It is shaped by two convictions: (1) Relativity is not a "side issue" or "special topic". Rather, it is an essential unifying idea that illuminates every branch of physics. (2) The best way to teach relativity is to adopt a "spacetime" point of view from the start. A physical situation may appear different to different observers, but every observer must see the same four-dimensional spacetime. Beginning with an introduction to spacetime ideas and basic relativistic effects, the book moves on to four-vectors, frames of reference, energy and momentum, and the spacetime description of waves. The second half of the book, written at a somewhat higher mathematical level, discusses relativistic forces, tensors, the physics of continuous systems such as fluids, and the electromagnetic field. Three appendices give a review of vector algebra and calculus, provide an historical account of the development of relativity, and describe the "kernel-index" notation used in advanced texts on special and general relativity. The book should be accessible to students who have completed a calculus-based introductory physics course. It may be used as the main text for a semester-long course on special relativity, or as a supplemental text in courses on modern physics, mechanics, electromagnetism, or general relativity.  Preface Chapter 1 Spacetime 1.1 Joining space and time 1.2 Spacetime geometry 1.3 Spacetime interval 1.4 ProblemsChapter 2 Basic relativistic effects 2.1 The starship and the asteroid: a dialogue 2.2 Time dilation, length contraction 2.3 Moving clocks 2.4 The$\gamma\$ factor 2.5 A letter from Simplicio 2.6 Problems Chapter 3 four-vectors and the *-product 3.1 3-vectors in space 3.2 4-vectors in spacetime 3.3 Particle trajectories and the 4-velocity 3.4 4-acceleration 3.5 Problems Chapter 4 Frames of reference 4.1 Addition of velocities 4.2 The Lorentz transformation 4.3 Problems Chapter 5 Energy and momentum 5.1 Momentum and kinetic energy 5.2 4-momentum 5.3 Decays and collisions 5.4 Photons 5.5 The Compton effect 5.6 Local conservation 5.7 Extended objects 5.8 Problems Chapter 6 Waves 6.1 Describing waves 6.2 The wave 4-vector 6.3 The Doppler shift 6.5 Aberration 6.6 Waves and particles 6.7 Problems Chapter 7 Forces 7.1 Newtonian forces 7.2 4-force 7.3 Action and reaction? 7.4 Electromagnetic forces 7.5 Problems Chapter 8 Tensors and the electromagnetic field 8.1 Beyond 4-vectors 8.2 Tensors and their components 8.3 The electromagnetic field 8.4 Tensors in 3-space 8.5 Spacetime tensor anatomy 8.6 Problems Chapter 9 Conservation and continuity 9.1 Fields 9.2 The gradient 9.3 Regions and integrals 9.4 Divergence and curl 9.5 A proof of the divergence theorem 9.6 The delta function 9.7 ProblemsChapter 10 Conservation and continuity 10.1 The 4-gradient 10.2 Hypersurfaces and the 4-divergence 10.3 Counting particles 10.4 The flow of charge 10.5 Other quantities 10.6 Problems Chapter 11 Spacetime fluid mechanics 11.1 Newtonian continuum mechanics 11.2 The stress tensor 11.3 The flow of 4-momentum 11.4 Perfect fluids 11.5 Equations of motion 11.6 General continuous systems 11.7 Gases of particles and photons 11.8 Problems Chapter 12 Electromagnetism in spacetime 12.1 The Maxwell equations 12.2 Field and source in spacetime 12.3 Duality 12.4 More derivatives 12.5 The 4-potential 12.6 Electromagnetic waves 12.7 Radiation 12.8 Electromagnetic energy and momentum 12.9 Problems Appendix Historical outline

Benjamin Schumacher began his theoretical physics career as a student of relativity pioneer John Archibald Wheeler, doing research on black hole thermodynamics. He is best known for his fundamental contributions to quantum information theory, for which he received the 2002 Quantum Communications Award (the premier international prize in the field). He has been a Rosenbaum Fellow at the Isaac Newton Institute of Cambridge University and a Moore Distinguished Scholar at Caltech. At present he is Professor of Physics at Kenyon College, where he has been on the faculty since 1988.