Special Relativity

From two postulates to the geometry of spacetime.

About this course

A twelve-lecture course that rebuilds mechanics on Einstein's two postulates. It opens with the cracks in classical physics, derives time dilation, length contraction and the Lorentz transformation, then recasts them geometrically as Minkowski spacetime — where the invariant interval, causality and the classic paradoxes all become statements about geometry rather than puzzles. The final module turns to dynamics: relativistic momentum and energy, four-vectors, and the closing result that electricity and magnetism are one field seen from different frames. Each module is paired with a problem set.

What you will be able to do

  • Derive time dilation, length contraction and the Lorentz transformation from the two postulates
  • Read and draw Minkowski diagrams, and use the invariant interval to classify causal relationships between events
  • Resolve the twin and ladder paradoxes by reasoning about simultaneity rather than memorising resolutions
  • Work with relativistic momentum and energy, and use four-vectors to write mechanics in covariant form
  • Explain how electric and magnetic fields transform into one another between inertial frames

What this course covers

  • Course Spine: The Speed of Light as the Rock
  • Galilean Relativity and Inertial Frames
  • Galilean Velocity Addition
  • Maxwell's Equations and the Fixed Speed of Light
  • The Luminiferous Aether and the Aether Wind Prediction
  • The Michelson–Morley Experiment
  • The Crisis: Maxwell vs. Galilean Addition
  • Einstein's Resolution and the Course Road Ahead
  • Module one recap and lecture roadmap
  • Setting up the two-frame dictionary
  • Deriving the Lorentz transformation from two demands
  • Why the transform must be linear
  • Historical context: Lorentz, Poincaré, and Einstein
  • Reading the Lorentz transformation: inverse, Newtonian limit, and space–time mixing
  • Lorentz transformation as a spacetime rotation
  • Three corollaries: time dilation, length contraction, simultaneity
  • Invariance of c is built into the transform, not a consequence
  • Speed of light as a spacetime conversion factor
  • Module roadmap: rebuilding relativistic mechanics
  • Failure of Newton's momentum across frames
  • Relativistic momentum: γmv
  • Experimental confirmation: Bertozzi's electron experiment
  • Total energy, rest energy, and E = mc²
  • Experimental confirmation: Cockcroft–Walton mass defect
  • Energy-momentum relation and the right-triangle geometry
  • The photon as the massless limit
  • Why c is unreachable: the energy-divergence argument
  • Clause Ten: mass and energy are one thing
  • Course spine and the invariant theme
  • Four-vector definition and the spacetime metric
  • Physical meaning of the metric's minus sign
  • Minkowski's geometric reformulation of relativity
  • Four-velocity and motion through spacetime at c
  • Four-momentum and mass as an invariant length
  • Conservation of four-momentum and the invariant mass
  • Four-force and covariance of relativistic dynamics
  • Collider vs fixed-target threshold energy
  • Clause eleven — covariance as the language of physics
  • Minkowski's geometric reframing of relativity
  • The spacetime diagram: axes, events, and world lines
  • The light cone and causal regions of spacetime
  • Tilted axes of a moving observer: the scissor effect
  • Hyperbola calibration of tilted axes
  • Reading all three relativistic effects off one diagram
  • The invariant interval and the minus sign
  • Clause six: the Lorentz transformation as spacetime geometry
  • Einstein's Two Postulates
  • Newton's Universal Time and Its Silent Assumption
  • The Train-and-Embankment Thought Experiment
  • Causality and the Limits of Relativity of Order
  • Quantifying the Disagreement: Δt = LV/C²
  • Defeating the Two Objections
  • Simultaneity as the First Domino: Chain to Time Dilation and Length Contraction
  • GPS as a Real-World Consequence
  • Course spine and the twelfth clause
  • Two motivating puzzles about magnetism
  • Magnetism as relativistic electricity — the wire argument
  • Charge invariance vs. charge-density non-invariance
  • Electromagnetic field transformation rules
  • Electromagnetic field invariants
  • The field tensor and four-vector sources
  • Quantitative verification of the wire argument
  • Maxwell's four equations as two covariant tensor lines
  • Course synthesis and the unification program
  • Course spine and lecture roadmap
  • The light clock and proper time
  • Derivation of time dilation and gamma
  • Meaning of gamma and proper time as shortest time
  • Reciprocity of time dilation and its resolution
  • Muon survival as experimental confirmation
  • All clocks slow equally — no preferred clock type
  • Time dilation as the second domino — preview of length contraction
  • The invariant interval: definition and convention
  • Proof of interval invariance under Lorentz transformation
  • Three causal classes: timelike, lightlike, and spacelike
  • Proper time as the interval along a world line
  • Causality and the absolute time-order of timelike pairs
  • The tachyon anti-telephone and why FTL breaks causality
  • The twin paradox preview: longest proper time on the straight world line
  • Clause seven: the interval as ruler, clock, and causal law
  • Course spine and lecture roadmap
  • Relativistic velocity addition derivation
  • Fizeau's 1851 experiment as historical validation
  • The speed of light as a fixed point
  • The cosmic speed cap
  • Relativistic Doppler effect: redshift and blueshift
  • Transverse Doppler effect and time dilation
  • Hubble expansion and cosmological redshift
  • Clause Eight: the Lorentz transformation as a crank
  • Course spine and lecture roadmap
  • Proper length and the simultaneity trap in measurement
  • Derivation of the length contraction formula
  • Reading the contraction formula: proper length is longest
  • Transverse lengths are unchanged
  • The muon retold from its own rest frame
  • Contraction is measurement, not physical compression
  • Pole-and-barn paradox preview and course outlook
  • Module spine and lecture thesis
  • The twin paradox setup
  • Space-time diagram resolution of the twin paradox
  • Experimental confirmation of time dilation
  • Proper time and the reverse triangle inequality
  • The ladder-and-barn paradox setup
  • Resolution via relativity of simultaneity
  • Acceleration as the symmetry-breaker
  • Clause Nine: no paradoxes in relativity

Syllabus

  1. The Kinematic Revolution

    1. The Cracks in Classical Physics
    2. Two Postulates & the Relativity of Simultaneity
    3. Time Dilation
    4. Length Contraction

  2. The Geometry of Spacetime

    1. The Lorentz Transformation
    2. Spacetime & Minkowski Diagrams
    3. The Invariant Interval & Causality
    4. Velocity Addition & the Doppler Effect
    5. The Great Paradoxes

  3. Relativistic Dynamics & Unification

    1. Relativistic Momentum & Energy
    2. Four-Vectors & Relativistic Dynamics
    3. Electromagnetism as Relativity