The weirdness that hides at the edges of speed.
Space bends. Time stretches. Mass and energy are the same thing. Einstein's special and general relativity rewrote geometry itself — and predicted everything from GPS corrections to black holes.
MODULE 1 · SR FOUNDATIONS
GALILEAN RELATIVITY AND THE FRAME PROBLEM
Why Newton's universe needed an observer who never moved.
MAXWELL AND THE SPEED OF LIGHT
The constant hiding in two SI numbers, and what it didn't depend on.
THE MICHELSON-MORLEY EXPERIMENT
An interferometer asks the wind which way it blows, and gets no answer.
EINSTEIN'S TWO POSTULATES
Drop one assumption, take one fact at face value, get a new universe.
THE RELATIVITY OF SIMULTANEITY
Two lightning bolts strike — and the train passenger disagrees with you about which came first.
MODULE 2 · SR KINEMATICS
TIME DILATION
Why a moving clock ticks slower — and why this is not an illusion.
LENGTH CONTRACTION
Why a moving rod is shorter — and why no one moving with it can tell.
THE LORENTZ TRANSFORMATION
The four lines of algebra that replaced Galileo.
RELATIVISTIC VELOCITY ADDITION
Why nothing made of matter ever crosses 299,792,458 m/s.
THE RELATIVISTIC DOPPLER EFFECT
What the source's color tells you about its motion through spacetime.
MODULE 3 · SPACETIME GEOMETRY
SPACETIME DIAGRAMS AND WORLDLINES
Draw a clock's life as a single line on a piece of paper.
THE INVARIANT INTERVAL
The one quantity every observer must agree on.
LIGHT CONES AND CAUSALITY
The shape spacetime gives "before" and "after" — and "neither."
FOUR-VECTORS AND PROPER TIME
The invariant heartbeat of every traveler in spacetime.
THE TWIN PARADOX
The longest worldline in spacetime is also the shortest in proper time.
MODULE 4 · RELATIVISTIC DYNAMICS
FOUR-MOMENTUM
Energy and momentum, packaged into one object that transforms as a vector.
MASS-ENERGY EQUIVALENCE
Why a hot cup of coffee weighs more than a cold one.
RELATIVISTIC COLLISIONS
Conservation of four-momentum, and what changes when speeds get high.
COMPTON SCATTERING
The 1923 experiment that finally made photons mechanical.
THRESHOLD ENERGY AND PAIR PRODUCTION
Why a 1.022 MeV gamma ray can become two electrons but a 511 keV one cannot.
MODULE 5 · SR APPLICATIONS AND PARADOXES
THE BARN-POLE PARADOX
Two observers, two answers, no contradiction.
BELL'S SPACESHIP PARADOX
A string between two synchronized rockets, and the geometry that snaps it.
GPS AS A WORKING RELATIVITY EXPERIMENT
Without two corrections, your position drifts ten kilometers a day.
PRECISION TESTS OF LORENTZ INVARIANCE
What happens when a theory survives a hundred years of being checked.
MODULE 6 · THE EQUIVALENCE PRINCIPLE
INERTIAL VS GRAVITATIONAL MASS
Why two completely different definitions give the same number to thirteen decimal places.
EINSTEIN'S ELEVATOR
A free-falling lab is a frame where gravity has been canceled.
GRAVITATIONAL REDSHIFT
Climb out of a gravity well and your photons get tired.
GRAVITY AS GEOMETRY
The equivalence principle's geometric implication: there is no force, only curvature.
MODULE 7 · CURVED SPACETIME AND TENSOR CALCULUS
MANIFOLDS AND TANGENT SPACES
Curved spaces and the flat ones that approximate them point by point.
TENSORS ON CURVED SPACE
Indexed objects that don't lie about which way they point.
THE METRIC TENSOR
The object that turns coordinate differences into actual distances.
CHRISTOFFELS AND PARALLEL TRANSPORT
The connection that says what "stays parallel" means on a curved surface.
GEODESICS
The straightest possible lines, and why falling apples follow them.
MODULE 8 · RIEMANN CURVATURE AND EINSTEIN'S EQUATIONS
THE RIEMANN CURVATURE TENSOR
Twenty independent numbers per point that say exactly how a space is bent.
RICCI, SCALAR CURVATURE, AND THE EINSTEIN TENSOR
The contractions that make a divergence-free curvature object.
THE STRESS-ENERGY TENSOR
Energy, momentum, pressure, and stress, all in one object.
EINSTEIN'S FIELD EQUATIONS
Spacetime tells matter how to move; matter tells spacetime how to curve.
THE NEWTONIAN LIMIT
Where GR gives back Newton, and where it refuses.
MODULE 9 · SCHWARZSCHILD AND THE CLASSICAL TESTS
THE SCHWARZSCHILD METRIC
The first exact solution to Einstein's equations, solved in a trench in 1915.
MERCURY'S PERIHELION
A 43-arcsecond-per-century mismatch that closed seventy years of guesswork.
LIGHT DEFLECTION AND GRAVITATIONAL LENSING
A May 1919 eclipse photograph, Einstein on the front page of every newspaper.
THE SHAPIRO TIME DELAY
Light slowed not by mass but by the geometry the mass produces.
THE CLASSICAL TESTS — A WHOLE THEORY ON TRIAL
Four independent predictions, four confirmed observations, one theory standing.
MODULE 10 · BLACK HOLES
THE EVENT HORIZON
The one-way membrane, what it looks like to the infaller, and what it doesn't.
KERR BLACK HOLES AND THE ERGOSPHERE
Spinning spacetime drags everything inside it along for the ride.
PENROSE DIAGRAMS AND CAUSAL STRUCTURE
Compactify infinity; learn what a black hole's interior actually looks like.
THE NO-HAIR THEOREM
Three numbers describe every black hole: mass, charge, spin.
BLACK-HOLE THERMODYNAMICS
The area theorem, Bekenstein entropy, and why a black hole is a thermal object.
HAWKING RADIATION
A semiclassical preview: even the blackest hole evaporates.
MODULE 11 · GRAVITATIONAL WAVES
LINEARIZED GRAVITY
Small ripples in a flat background, governed by a wave equation.
THE TWO POLARIZATIONS — PLUS AND CROSS
What a gravitational wave does to a ring of free-floating test masses.
BINARY INSPIRAL AND THE CHIRP
Two black holes spiraling in; the waveform's frequency rises like a chirp.
LIGO AND MULTI-MESSENGER ASTRONOMY
GW150914, GW170817, and what it means to hear the universe instead of seeing it.
MODULE 12 · COSMOLOGY
THE FLRW METRIC
The geometry the universe picked out for itself.
FRIEDMANN'S EQUATIONS
Two ODEs that govern the expansion of everything.
HUBBLE AND COSMOLOGICAL REDSHIFT
Why distant galaxies' light is stretched, and what is doing the stretching.
THE CMB AND BIG BANG NUCLEOSYNTHESIS
The leftover heat and the first three minutes' worth of helium.
DARK MATTER AND DARK ENERGY
What 95% of the universe's mass-energy budget is — and what we still don't know about it.
MODULE 13 · FRONTIERS
THE PENROSE-HAWKING SINGULARITY THEOREMS
When does GR predict its own breakdown?
THE INFORMATION PARADOX
Hawking radiation says yes, unitarity says no, and the answer is still being argued.
WHAT RELATIVITY DOESN'T SAY
A century of winning streak, and the wall it has not yet broken through.