# Special Relativity

###### valerio Faraoni
Publisher:
Springer
Publication Date:
2013
Number of Pages:
304
Format:
Paperback
Series:
Price:
49.00
ISBN:
9783319011066
Category:
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
12/13/2013
]

The author's goal is to provide an account of Special Relativity that is more sophisticated than what is typically encountered by undergraduates in a "modern physics" course but still accessible to upper-level undergraduates. He assumes a good grounding in electromagnetic theory. The main mathematical technique is tensor calculus, done in the usual physicist's style. (I was amused to note that the section on "Index-free Description of Tensors" is starred as optional. Mathematicians and physicists just don't think alike!) Overall, a good second book on the subject for aspiring physicists.

1. Fundamentals of Special Relativity
Introduction
The Principle of Relativity
Groups—the Galilei group
Galileian law of addition of velocities
The lesson from electromagnetism
The postulates of Special Relativity
Consequences of the postulates
Conclusion
Problems

2. The Lorentz transformation
Introduction
The Lorentz transformation
Derivation of the Lorentz transformation
Mathematical properties of the Lorentz transformation
Absolute speed limit and causality
Length contraction from the Lorentz transformation
Time dilation from the Lorentz transformation
Transformation of velocities and accelerations in Special Relativity
Matrix representation of the Lorentz transformation
The Lorentz group
The Lorentz transformation as a rotation by an imaginary angle with imaginary time
The GPS system
Conclusion
Problems

3, The 4-dimensional world view
Introduction
The 4-dimensional world
Spacetime diagrams
Conclusion
Problems

4. The formalism of tensors
Introduction
Vectors and tensors
Contravariant and covariant vectors
Contravariant and covariant tensors
Tensor algebra
Tensor fields
Index-free description of tensors
The metric tensor
The Levi-Civita symbol and tensor densities
Conclusion
Problems

5. Tensors in Minkowski spacetime
Introduction
Vectors and tensors in Minkowski spacetime
The Minkowski metric
Scalar product and length of a vector in Minkowski spacetime
Raising and lowering tensor indices
Causal nature of 4-vectors
Hypersurfaces
Gauss’ theorem
Conclusion
Problems

6. Relativistic mechanics
Introduction
Relativistic dynamics of massive particles
The relativistic force
Angular momentum of a particle
Particle systems
Conservation of mass-energy
Conclusion
Problems

7. Relativistic optics
Introduction
Relativistic optics: null rays
The drag effect
The Doppler effect
Aberration
Relativistic beaming
Visual appearance of extended objects
Conclusion
Problems

8. Measurements in Minkowski spacetime
Introduction
Energy of a particle measured by an observer
Frequency measured by an observer
A more systematic treatment of measurement
The 3+1 splitting
Conclusion
Problems

9. Matter in Minkowski spacetime
Introduction
The energy-momentum tensor
Covariant conservation
Energy conditions
Angular momentum
Perfect fluids
The scalar field
The electromagnetic field
Conclusion
Problems

10. Special Relativity in arbitrary coordinates
Introduction
The covariant derivative
Spacetime curves and covariant derivative
Physics in Minkowski spacetime revisited
Conclusions
Problems

Solutions to selected problems

References

Index