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In this chapter, I am going to introduce the two axioms of Special Relativity. These axioms are, to an extent, the only new physics introduced in this text: once I have introduced them and made them plausible, the rest of our work is devoted to examining their consequences, and the way in which they change the physics we are already familiar with.
This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates – length contraction and time dilation – are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.
Motion in curved spacetime, classical equations in covariant form, tidal forces, Einstein’s field equation in empty space, and weak (linearized) gravitation.
Introduction to vectors in curved spaces, the exterior calculus, tensor densities, affine connections and Christoffel symbols, parallel transport and covariant derivatives, metric spaces, and the theory of curvature.
The Schwarzschild solution and the classic tests of general relativity (precession of the perihelion of Mercury, the bending of starlight, and the gravitational redshift), horizons and singularities.