Modern · Experiment

Special Relativity

Because the speed of light is the same for everyone, a moving clock must tick slower and a moving object must shrink along its motion. Speed the ship toward light speed and watch both effects take hold.

light pulse (always travels at c) moving ship's clock stationary lab clock rest length outline

Controls

Speed v0.80 c
Lorentz factor γ1.667
Moving clock rate0.600×
Length L / L₀0.600
Lab clock0.0 s
Ship clock (proper)0.0 s
Relativistic Doppler3.00×
At v = 0.80c the ship's clock ticks at 60% of the lab's rate.
About this experiment ›

What you are looking at

Two identical light clocks: one sits still in the laboratory (lower, blue) and one rides a spaceship moving to the right (upper, green). A light clock ticks each time a pulse of light bounces between two mirrors. Because the bounce relies only on the speed of light — which Einstein took to be the same for every observer — comparing the two clocks reveals how time and space themselves must change.

Einstein's two postulates

Special relativity (1905) rests on two ideas: the laws of physics are the same in every inertial frame, and the speed of light c is the same for all observers, no matter how fast the source or observer moves. That second postulate is the strange one, and everything else follows from it.

Time dilation

In the ship's own frame the pulse goes straight up and down. But in the lab frame the ship is moving, so the same pulse must travel a longer diagonal path between bounces. Since its speed is still exactly c, a longer path means a longer time — the moving clock ticks slower. Working out the geometry gives the Lorentz factor:
γ = 1 / √(1 − v²/c²)  →  Δt_lab = γ · Δt_ship
The ship's clock runs at 1/γ of the lab rate. Watch the tick counters drift apart, and the two running clocks diverge — at 0.8c the ship ages only 60% as fast.

Length contraction

Distances along the direction of motion shrink by the same factor. The ship's length measured in the lab is
L = L₀ / γ = L₀ √(1 − v²/c²)
shown against the dashed rest-length outline. Heights (perpendicular to motion) are unchanged. This is why fast-moving muons created high in the atmosphere reach the ground — in their frame the atmosphere is contracted, in ours their clock is dilated; both pictures agree.

The cosmic speed limit

As v approaches c, γ shoots toward infinity (see the curve): clocks nearly freeze, lengths nearly vanish, and the energy needed to accelerate diverges. Nothing with mass can reach c. Push the speed slider toward 0.99c and watch γ climb steeply. The same factor governs relativistic energy, E = γmc², whose v = 0 limit is the famous E₀ = mc².