Special Relativity Simulation

Controls

Simulation speed: 1.0×

Scenario

As the ship passes the station, each fires a flash of light and a probe straight ahead. The probes leave at the speed set here.

Probe speed from its craft: 0.50 c

Show

Light paths Newton’s prediction Measured lengths Clocks at each end (simultaneity)

FPS: 0

γ: 1.155

Station’s probe: 0.50 c

Ship’s probe: 0.80 c

Both flashes: 1.000 c

About this simulation

Light always travels at the same speed, c, whoever measures it and however fast they move. Everything else in special relativity follows from that.

What you're seeing

Six scenarios, in teaching order: the speed of light, lightning strikes (simultaneity), light clocks (time dilation), muons, a ship in a hangar (length contraction) and the twin paradox.
Everything is as measured from one frame, not as a camera would see it. Distances are in light-seconds (ls): light covers 1 ls in 1 s. Dots along a path are a strobe photo: equal spacing, equal speed.

Key idea

A moving clock’s light zig-zags further at the same speed, so it ticks slower: t = γt₀, where t₀ is the time on the moving clock and γ = 1/√(1 − v²/c²). Moving objects are shorter, L = L₀/γ, and clocks synchronised on one craft are not synchronised measured from the other. At 0.6c, γ = 1.25; at 0.8c, 1.67.

Things to try

Switch frames in each scenario. Both views are right, and they agree on what actually happens: which lamps light, which muons land, who comes home younger.
Turn on Newton’s prediction to see where the light would be if speeds simply added.
Go past 0.99c and the moving clock almost stops.

How to interact

Drag the speed slider and pick a frame under the simulation, or tap a craft to ride along with it. opens the settings (scenarios and extras), goes fullscreen, restarts and shows graphs. Press F to show the frame rate.