Einstein’s Light Clock: Time Dilation & Length Contraction

Use this free light clock simulation to explore why moving clocks record less time, derive the Lorentz factor and explain length contraction with a spaceship laser.

A light clock simulation for time dilation

Einstein’s Light Clock connects an animated light path with the mathematics of special relativity. Compare one light clock in its own rest frame and in a laboratory frame, then investigate a laser pulse travelling along a moving spaceship. This free resource supports A-Level Physics special relativity where required by your exam specification, extension study and introductory university learning.

Start with the same two events

A clock ticks when its photon returns to the lower mirror. Start at rest, then set the Lorentz factor to two. In the clock frame, light travels vertically between stationary mirrors. In the lab, the mirrors move sideways, so light follows a longer diagonal path. Both frames measure the same vacuum light speed c. The lab therefore measures a longer time between the same emission and return events.

The attached clock records proper time Δτ because these two events occur at the same place in its own frame. The laboratory interval is Δt = γΔτ, where γ = 1/√(1 − v²/c²). At γ = 2, a 2-second clock tick takes 4 seconds in the lab. The clock works normally for the observer travelling with it.

Connect the triangle to the equation

Select “Show triangle at first reflection” to pause the light clock simulation. The triangle labels the mirror spacing L, the sideways displacement vΔt/2 and the light path cΔt/2. Apply Pythagoras, then substitute the rest-frame round-trip time Δτ = 2L/c. The worked derivation beneath the animation connects these distances to time dilation.

Explain length contraction with the spaceship laser

The second tab sends a laser pulse from the ship’s tail to its nose and back. In the ship frame the two legs take equal times. Earth assigns a longer outward time because the nose moves away from the pulse, and a shorter return time because the tail moves towards it. The light speed remains c on both legs.

Add the Earth-frame journey times and compare the full round trip with the proper time recorded by the tail-mounted clock. Combining the journey calculation with time dilation gives length contraction: L = L₀/γ. L₀ is the ship’s rest length; L is its length measured in the Earth frame.

Select “Measure the ship’s length” to show rulers marking the nose and tail at one simultaneous instant in each frame. Length is a measurement of both endpoints at the same time in the chosen frame. The ship retains its normal rest length on board. The animation is a coordinate view, rather than a telescope image affected by light-travel delays.

What is a light-second?

A light-second is a unit of distance: exactly 299,792,458 metres, or approximately 300,000 kilometres. Light travels at one light-second per second. A 2-light-second path therefore takes light 2 seconds to cross. The introduction above includes a worked units calculation.

Explore the companion Worldline Lab

Explore these events on a spacetime diagram in Worldline Lab. Connect motion with worldlines, investigate light cones and compare coordinates in different inertial frames. You can also browse all free physics simulations or practise A-Level Physics questions by topic.

For further reading, see Einstein Online’s light-clock explanation from the Max Planck Institute for Gravitational Physics. If this light clock simulation helps, share it with a student, classmate or colleague.