Relativity
Explore the strange and beautiful world of special relativity, where space and time intertwine, simultaneity is relative, and the speed of light is the ultimate speed limit. These interactive simulations let you visualize spacetime diagrams, see length contraction and time dilation in action, and understand the resolution of famous relativity paradoxes.
Foundations of Spacetime
Build intuition for spacetime diagrams and the structure of special relativity. Place events, explore light cones, and watch how simultaneity changes between reference frames.
Minkowski Spacetime Explorer
Click to place events in spacetime, drag the β slider to change reference frames, and watch how simultaneity lines and light cones reveal the structure of special relativity
Light Cones & Causal Structure
Place events and explore their causal relationships through light cones—see which events can influence each other
Train & Platform Simultaneity
Watch two flashes that are simultaneous in the train frame occur at different times on the platform—adjust the train speed to see how simultaneity depends on motion
Twin Paradox: Differential Aging
Send one twin on a journey and watch their worldlines through spacetime—adjust speed and distance to see how acceleration creates differential aging
Time Dilation & Length Contraction
See the direct experimental evidence for relativistic effects. Watch moving clocks run slow and moving objects contract, just as Einstein predicted.
Atmospheric Muon Time Dilation
Simulate cosmic ray muons falling through the atmosphere and compare classical vs relativistic survival rates—see direct experimental evidence for time dilation
Length Contraction in Motion
Watch rods contract as they move past you—adjust velocity to see how Lorentz contraction shortens moving objects
Lattice of Clocks: Coordinate vs Optical Reality
See a grid of synchronized clocks from different reference frames—toggle between coordinate view and what you actually see with light delays
Accelerated Motion
Explore how constant acceleration creates event horizons in flat spacetime, revealing the deep connection between acceleration and gravity.
Classic Paradoxes
Resolve the famous paradoxes that puzzled early relativists. See how length contraction, simultaneity, and Born rigidity work together to eliminate apparent contradictions.
The Ladder-Barn Paradox
Fit a ladder into a shorter barn using relativity—explore how length contraction and simultaneity resolve the paradox from both frames
Bell's Spaceship Paradox
Watch two spaceships accelerate identically while a string between them snaps—see how Born rigidity works in special relativity
Ehrenfest Rotating Disk Paradox
Spin a disk and measure its circumference—discover how rotation creates non-Euclidean geometry even in flat spacetime
Velocity & Momentum
Discover how velocities combine in relativity, why nothing can exceed the speed of light, and how four-momentum conservation governs relativistic collisions.
Velocity Addition: The Speed Limit
Combine two velocities and watch how they add relativistically, never exceeding c—explore rapidities where addition is linear
4-Momentum & Relativistic Collisions
Collide particles and watch 4-momentum conservation—adjust energies to create new particles from kinetic energy
Thomas Precession from Sequential Boosts
Apply sequential velocity boosts in different directions and watch a vector precess—see how non-commutativity creates rotation
Optics & Radiation
Explore what you actually see when objects move at relativistic speeds. Watch aberration, Doppler shifts, and the headlight effect transform light and radiation.
Relativistic Optics: What You Actually See
Watch moving objects distort through aberration and Terrell rotation—this is what your eyes would actually see, not coordinate measurements
The Relativistic Headlight Effect
Watch radiation from a moving source concentrate into a forward beam—adjust velocity to see the headlight effect strengthen
Relativistic Doppler & Color Shifts
Watch light sources change color as they move—explore both longitudinal and transverse Doppler shifts
Electromagnetism & Relativity
See how electric and magnetic fields transform between frames, and discover that magnetism itself emerges from electrostatics and special relativity.
How E and B Fields Transform
Transform between reference frames and watch electric fields become magnetic—see the electromagnetic field tensor in action
Magnetism from Relativity
Watch a current-carrying wire from a moving frame—see how length contraction of charge density creates magnetic forces from purely electric interactions