Physics in Spacetime
An introduction to Special Relativity

Benjamin Schumacher

302 pages, 9x6 inches
Feb 2005 Hardcover
ISBN 1-58949-038-X


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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.


Chapter 1 Spacetime
1.1 Joining space and time
1.2 Spacetime geometry
1.3 Spacetime interval
1.4 Problems

Chapter 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 Problems

Chapter 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.