Two postulates
The constancy of the speed of light and the principle of relativity (the two postulates of special relativity)
The Michelson and Morley experiment: searching for the ether with an interferometer
Relativity of simultaneity, and which wall of a moving train the light reaches first
Time and length
Deriving time dilation with a light clock and the Pythagorean theorem
Why does Lorentz contraction happen? Deriving length contraction from time dilation
Resolving the pole and barn paradox with the relativity of simultaneity
Terrell rotation: a cube moving near light speed looks turned, not contracted
Why muons reach the ground, checked with time dilation and length contraction
Lorentz transformation
Deriving the Lorentz transformation from three conditions
Relativistic velocity addition, where 0.6c combined with 0.6c gives 0.88c
Rapidity and velocity addition: with β = tanh θ it becomes plain addition
How is the Doppler effect for light different from sound? The relativistic formula and redshift
Aberration and the headlight effect, or why the stars crowd forward at speed
Explaining magnetism with relativity: the charge in a wire and length contraction
Conservation of energy and momentum written with four-vectors
Spacetime diagrams
Reading world lines and moving axes on a spacetime (Minkowski) diagram
The light cone and the spacetime interval, the separation every frame agrees on
Faster-than-light signals and causality, or a reply that arrives before it is asked for
Why is the twin paradox not a contradiction? The jump in simultaneity at the turnaround
Hyperbolic motion and the Rindler horizon (a rocket accelerating at 1g)
Mechanics
Deriving relativistic momentum p = γmv from proper time
What does E = mc² mean? The rest energy of a body at rest
Particle collisions and centre of mass energy (fixed-target and colliding-beam accelerators)
General relativity
Treating gravity as acceleration with the equivalence principle
Gravitational time dilation, and why GPS clocks gain 38 microseconds a day
The bending of light and gravitational lensing: 1.75 arcseconds at the 1919 eclipse
The Shapiro delay (radio echoes held back by the Sun's gravity)
Curved spacetime and geodesics, or why things fall: time runs at different rates
What do the two sides of the Einstein equation mean? How the coefficient 8πG/c⁴ is fixed
Mercury's perihelion precession and the 43 arcseconds from general relativity
The event horizon of a black hole and the Schwarzschild radius
Frame dragging: the Lense-Thirring effect measured by Gravity Probe B
Gravitational waves, and the stretching of spacetime from a black hole merger