Time dilation light clock simulation
The light clock is the cleanest way to see why moving clocks run slow. A pulse of light bounces between two mirrors and each round trip is one tick. Put the clock on a moving platform and the light has to travel further per tick at the same speed c.
Interactive, free and runs in your browser. Part of the Special Relativity simulations.
What you will see
Two clocks sit side by side: one at rest, one moving. The moving photon leaves a zigzag trail. Tick counters run underneath, and the ratio between them settles on γ = 1/√(1 − v²/c²) for whatever speed you choose.
Try this
- Set β to 0.6 and check the tick ratio heads to 1.25.
- Set β to 0.87: the moving clock ticks about half as often (γ ≈ 2).
- Drop β towards 0 and watch both clocks fall back into step.
Common misconception
Time dilation is not the clock being damaged or slowed mechanically. Every process on the moving platform, including the people on it, runs slow in your frame, and from their frame it is your clocks that run slow.
Exam-style question
Muons have a mean lifetime of 2.2 μs at rest. How long do they live, measured in the lab, when moving at 0.98c?
γ = 1/√(1 − 0.98²) = 1/√0.0396 ≈ 5.03. Lab lifetime = γ × 2.2 μs ≈ 11 μs. That is why muons made high in the atmosphere reach the ground.
Key equations
Δt = γ Δt₀γ = 1 / √(1 − v²/c²)
Curriculum
AQA A-level physics (turning points), IB Physics A.5.