Introduction to Special Relativity

Part 1 The foundations of special relativity: schematic account of the Michelson - Morley experiment; inertial frames in special relativity; Einstein's two axioms for special relativity; coordinates - the relativity of time; derivation of the Lorentz transformation; properties of the Lorentz transformation. Part 2 Relativistic kinematics: length contraction; the length contraction paradox; time dilation; the twin paradox; velocity transformation. Part 3 Relativistic optics: the drag effect; the Doppler effect; aberration and the visual appearance of moving objects. Part 4 Spacetime: spacetime and 4-tensors; the Minkowski map of spacetime; rules for the manipulation of 4-tensors; 4-velocity and 4-acceleration; wave motion. Part 5 Relativistic particle mechanics: the conservation of 4-momentum; the equivalence of mass and energy; some 4-momentum identities; relativistic billiards; the centre of momentum frame; threshold energies; De Broglie waves; photons; the angular momentum 4-tensor; 3-force and 4-force; relativistic analytic mechanics. Part 6 Relativity and electromagnetism: the formal structure of Maxwell's theory; transformation of "e" and "b" - the deal field; potential and field of an arbitrarily moving charge; field of a uniformly moving charge; the electromagnetic energy tensor; electromagnetic waves. Part 7 Relativistic mechanics of continua: preliminaries external and internal forces; the augmented momentum and mass densities; the equations of continuity and of motion; the mechanical energy tensor; perfect fluids and incoherent fluids; integral conservation laws. Appendix - tensors for special relativity.