Course Overview: The unification of space and time into a four-dimensional space-time is essential to the modern understanding of physics. This course will build on first-year algebra, geometry, and applied mathematics to show how this unification is achieved. The results will be illustrated throughout by reference to the observed physical properties of light and elementary particles.
Learning Outcomes: Students will be able to describe the fundamental phenomena of relativistic physics within the algebraic formalism of four-vectors. They will be able to solve simple problems involving Lorentz transformations. They will acquire a basic understanding of how the four-dimensional picture completes and supersedes the physical theories studied in first-year work.
Course Synopsis: Constancy of the speed of light. Lorentz transformations; time dilation, length contraction, the relativistic Doppler effect.
Index notation, four-vectors, four-velocity and four-momentum; equivalence of mass and energy; particle collisions and four-momentum conservation; equivalence of mass and energy: \(E = mc^2\); four-acceleration and four-force, the example of the constant-acceleration world-line.
