Special relativity simulator

Explore Einstein’s special relativity by changing the speed of a moving observer and watching the consequences happen. Three linked views cover the geometry of spacetime, time dilation and length contraction, all driven by one velocity slider and the Lorentz factor γ = 1/√(1 − β²).

This interactive simulation runs in your browser with WebGL. Free, no account needed.

What you can explore

Light cone

Drag an event around a three-dimensional light cone and the page tells you whether it is timelike, lightlike or spacelike relative to the origin. A dashed hyperbola shows every place the event can appear for a moving observer, which is why the spacetime interval s² is the same in every frame, while the tilted axes show how a moving observer slices spacetime differently.

Time dilation

Two light clocks tick side by side: one at rest, one moving. The moving photon zigzags along a longer diagonal path at the same speed c, so each of its ticks takes longer. Live tick counters converge on the ratio γ, turning the formula Δt = γΔt₀ into something you can count.

Length contraction

Two identical spaceships carry rulers along their hulls. As the moving ship speeds up it shortens along its direction of travel only, and a fixed lab ruler underneath lets you measure L = L₀/γ directly. At 0.8c the ship is 40% shorter.

Key equations

  • γ = 1 / √(1 − v²/c²)
  • Δt = γ Δt₀
  • L = L₀ / γ
  • s² = (ct)² − x²

Curriculum

AQA A-level physics (turning points), IB Physics A.5.

Common questions

Why do moving clocks run slow?

Light travels at the same speed for every observer. In a moving light clock the light has to cover a longer, diagonal path between the mirrors, so each tick takes longer by the factor γ.

What does it mean for an event to be spacelike?

It lies outside the light cone, so no signal travelling at or below the speed of light can connect it to the origin. Different observers can even disagree about which of the two events happened first.

More physics simulations