Special Relativity

The book is divided into two sections, an introductory text and a more advanced text. Both texts cover the same topics. Undergraduates might compare their curriculum with the text and study appropriately.

Introductory text

Introduction

• Historical Development

Principle of Relativity

• The principle of relativity
• Frames of reference, events and transformations
• Special relativity
• The postulates of special relativity

Spacetime

• The modern approach to special relativity
• Spacetime
• The lightcone
• The Lorentz transformation equations

Simultaneity, time dilation and length contraction

• The relativity of simultaneity and the Andromeda paradox
• The nature of length contraction
• Evidence for length contraction, the field of an infinite straight current
• De Broglie waves
• The twin paradox
• The pole barn paradox
• Addition of velocities

Dynamics

• Introduction
• Momentum
• Force
• Mass and energy

Aether

• Introduction
• The aether drag hypothesis
• The Michelson-Morley experiment
• Mathematical analysis of the Michelson Morley Experiment
• Lorentz-Fitzgerald contraction hypothesis

Faster than light signals, causality and Special Relativity

Advanced text

Mathematical transformations

• Introduction
• The Lorentz transformation
• The linearity and homogeneity of spacetime
• The Lorentz transformation
• Length contraction, time dilation and phase
• Hyperbolic geometry
• Addition of velocities
• Acceleration transformation

Waves

• Relativistic waves
• Principle of Relativity Applied
• Characteristics of Relativistic Waves
• The Doppler Effect

Relativistic dynamics

• Introduction
• Momentum
• Relativistic Mass

Mathematical approach

• Vectors
• Matrices
• Linear Transformations
• Indicial Notation
• Analysis of curved surfaces and transformations

• Four vectors

Problems

Appendices

• Mathematics of the Lorentz Transformation Equations

Further Information

• Modern Physics
• General Relativity