Special Relativity

• Main Author: Faraoni, Valerio. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Series: Undergraduate Lecture Notes in Physics,
• Subjects: Physics.; Classical and Quantum Gravitation, Relativity Theory.; Mathematical Applications in the Physical Sciences.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-01107-3

This book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent c...

Table of Contents:

• Fundamentals of Special Relativity
• Introduction
• The Principle of Relativity.-�Groupsthe Galilei group.-�Galileian law of addition of velocities.-�The lesson from electromagnetism.-�The postulates of Special Relativity.-�Consequences of the postulates.-�Conclusion
• Problems.-�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.-�The 4-dimensional world view.-�Introduction.-�The 4-dimensional world.-�Spacetime diagrams.-�Conclusion
• Problems.-�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.-�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.-�Relativistic mechanics.-�Introduction.-�Relativistic dynamics of massive particles.-�The relativistic force.-�Angular momentum of a particle.-�Particle systems.-�Conservation of mass-energy.-�Conclusion
• Problems.-�Relativistic optics.-�Introduction.-�Relativistic optics: null rays.-�The drag effect.-�The Doppler effect.-�Aberration.-�Relativistic beaming.-�Visual appearance of extended objects.-�Conclusion
• Problems.-�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.-�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
• 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.