Special Relativity Course

Lesson 1 • The Michelson-Morley Experiment

Analyzes the design and null result of the Michelson-Morley experiment. Demonstrates why this result demanded a fundamental revision of space-time concepts.

Lesson 2 • Galilean Relativity and Transformations

Derives the Galilean transformation equations and the principle of relativity for mechanics. Shows how classical physics treats observers in uniform relative motion.

Lesson 3 • Pre-Relativistic Attempts at Resolution

Surveys Lorentz-FitzGerald contraction and Poincaré's contributions before Einstein. Sets the stage for Einstein's radical reinterpretation of the problem.

Lesson 4 • Newtonian Space, Time, and Motion

Covers absolute space, absolute time, and inertial frames in classical mechanics. Provides the conceptual baseline against which relativistic ideas will be contrasted.

Lesson 1 • Time Dilation

Derives time dilation from the light-clock thought experiment and the two postulates. Students calculate dilated time intervals for moving clocks.

Lesson 2 • Length Contraction

Derives length contraction along the direction of motion using simultaneity arguments. Distinguishes proper length from contracted length in different frames.

Lesson 3 • The Two Postulates of Special Relativity

States and interprets the principle of relativity and the constancy of the speed of light. Establishes these as the axiomatic foundation for all subsequent derivations.

Lesson 4 • The Relativity of Velocity Addition

Derives the relativistic velocity addition formula and shows it preserves the light-speed limit. Contrasts results with Galilean addition for everyday and extreme speeds.

Lesson 1 • Deriving the Lorentz Transformation

Constructs the Lorentz transformation from linearity, the postulates, and symmetry arguments. Reveals how it reduces to the Galilean transformation at low speeds.

Lesson 2 • Relativistic Velocity Transformation

Derives the relativistic velocity addition law from the Lorentz transformation. Extends the result to velocities in all three spatial directions.

Lesson 3 • Recovering Time Dilation and Length Contraction

Re-derives time dilation and length contraction directly from the Lorentz transformation equations. Unifies earlier results within a single algebraic framework.

Lesson 4 • Structure of the Lorentz Boost

Analyzes the mathematical structure of boosts along one spatial axis and the role of the Lorentz factor. Introduces the parameter gamma as a central quantity.

Lesson 1 • Causal Structure and Light Cones

Classifies intervals as timelike, spacelike, and lightlike and defines the causal structure of spacetime. Shows how light cones determine which events can influence each other.

Lesson 2 • Four-Vectors and the Metric

Defines contravariant and covariant four-vectors and the operation of index raising and lowering. Introduces the Einstein summation convention for compact notation.

Lesson 3 • Four-Velocity and Four-Momentum

Constructs the four-velocity from proper time differentiation and the four-momentum from rest mass. Derives the energy-momentum relation as a four-vector identity.

Lesson 4 • Spacetime Diagrams

Teaches construction and interpretation of Minkowski diagrams for analysing relativistic scenarios. Uses diagrams to visualise simultaneity, time dilation, and length contraction.

Lesson 1 • Mass-Energy Equivalence

Establishes E = mc² as a consequence of four-momentum invariance and interprets rest mass as stored energy (physical energy). Discusses binding energy and mass defect in physical systems.

Lesson 2 • Relativistic Collisions and Decays

Applies four-momentum conservation to elastic collisions, inelastic collisions, and particle decays. Introduces the centre-of-momentum frame as a powerful problem-solving tool.

Lesson 3 • Energy-Momentum Invariant

Uses the four-momentum norm to derive the energy-momentum invariant E² = (pc)² + (mc²)². Applies the invariant to massless particles and photons.

Lesson 4 • Relativistic Kinetic Energy

Derives relativistic kinetic energy via work-energy theorem and identifies the rest energy term. Shows the classical limit emerges at low velocities.

Lesson 1 • Maxwell's Equations in Covariant Form

Rewrites all four Maxwell equations as two compact tensor equations. Demonstrates manifest Lorentz covariance of classical electromagnetism.

Lesson 2 • Transformation of Electric and Magnetic Fields

Derives explicit formulas for how E and B fields transform between inertial frames. Shows that a purely electric field in one frame has a magnetic component in another.

Lesson 3 • Four-Current and Four-Potential

Combines charge (electric charge) density and current density (electric current) into the four-current and scalar and vector potentials into the four-potential. Demonstrates their Lorentz transformation properties.

Lesson 4 • Covariant Lorentz Force and Four-Force

Expresses the Lorentz force law using the field tensor and four-velocity to obtain the four-force. Connects the covariant equation of motion to the classical limit.

Lesson 1 • Relativistic Beaming and Intensity

Analyses how relativistic motion concentrates radiation (electromagnetic radiation) into a forward cone and boosts intensity. Connects beaming to astrophysical jets and synchrotron sources.

Lesson 2 • Four-Wavevector and Photon Four-Momentum

Defines the four-wavevector for electromagnetic waves and links it to photon four-momentum. Establishes the covariant framework for analysing wave phenomena.

Lesson 3 • Aberration of Light

Derives the relativistic aberration formula for the direction of light in different frames. Applies the result to stellar aberration and headlight effect.

Lesson 4 • Radar and Optical Ranging in Relativity

Uses relativistic Doppler and signal travel time to analyse radar ranging between moving observers. Introduces the concept of radar coordinates as an operational definition of distance.

Lesson 1 • The Twin Paradox

Analyses the twin paradox using spacetime diagrams, proper time integration, and frame-switching. Resolves the apparent contradiction by identifying the asymmetry between the twins.

Lesson 2 • Rigid Bodies and Relativistic Rotation

Examines why perfectly rigid bodies are incompatible with special relativity and analyses Ehrenfest's paradox for rotating disks. Motivates the need for general relativity.

Lesson 3 • The Ladder and Barn Paradox

Examines the barn-pole paradox to deepen understanding of simultaneity and length contraction. Shows that both frames give consistent physical predictions despite apparent contradiction.

Lesson 4 • Limits of Special Relativity

Identifies the domain of validity of special relativity and the physical situations requiring general relativity. Summarises the conceptual achievements and open questions.