Modern Physics
Light-clock time dilation
Raise β — watch the moving light clock tick slower (Δt = γ Δt₀) and the rod shorten.
Light-clock time dilation — interactive Modern Physics simulation. Raise β — watch the moving light clock tick slower (Δt = γ Δt₀) and the rod shorten. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Time dilation
Raise β — watch the moving light clock tick slower (Δt = γ Δt₀) and the rod shorten.
A light clock counts ticks by bouncing a photon between mirrors. Moving clocks measure longer round-trip times in the lab frame by factor γ = 1/√(1−β²). Simultaneous length contraction keeps c invariant—core of special relativity thought experiments.
- Δt = γΔt₀
- γ = 1/√(1−β²)
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A 'light clock' bounces a light pulse between two mirrors, ticking once per round trip. If the whole clock moves at high speed relative to you, do you observe it ticking slower, faster, or at the same rate as an identical clock at rest?
Predictions to weigh
- Slower — a moving clock's light pulse has to travel a longer diagonal path (from the observer's frame), so each tick takes longer.
- Faster — motion speeds up the clock.
- The same rate, since light always travels at c regardless of the clock's motion.
Variable roles
What you set:
- Speed fraction β = v/c
What you measure:
- Lorentz factor γ
- Dilated time Δt (µs)
How the investigation runs
- Open the light-clock-dilation preset and press Reset. The clock's proper time per tick is fixed at 1 µs.
- Enable the Lorentz factor and dilated-time readouts.
- Set the clock's speed (as a fraction of light speed, β = v/c) for each trial and record the dilated time observed.
Governing equation
Time Dilation — Δt = γ Δt₀
A clock moving at speed v = βc, observed from a stationary frame, appears to run slow by the Lorentz factor: Δt = γ·Δt_proper, where γ = 1/√(1 − β²) ≥ 1. The effect is negligible at everyday speeds but dramatic as β approaches 1.
What the printable worksheet asks students to work out
- For one trial, compute γ = 1/√(1 − β²), then Δt = γ·Δt_proper using the proper time 1 µs. Compare both to the table.
- Explain why γ stays close to 1 (barely any dilation) at low speeds but rises sharply as β approaches 1 — the light-clock's diagonal path only becomes dramatically longer once the clock's speed becomes a significant fraction of light speed.
Where this shows up beyond the lab
- From the perspective of someone traveling WITH the moving clock, it's their own clock that seems normal — and a clock on Earth that appears to be running slow instead. Explain why time dilation appears symmetric between two observers in relative motion, and why this isn't a contradiction (it's resolved by which observer actually changes reference frames).
- GPS satellites move fast enough that special-relativistic time dilation (plus a general-relativistic effect from weaker gravity at altitude) causes measurable clock drift, corrected for in the system's design. Why would ignoring this tiny effect eventually cause meaningful GPS positioning errors?
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — A.5 Galilean and special relativity
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Light Clock Dilation
- Select the relativity setup
- Press Play
- Moving clocks run slow
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Special Relativity: Time Dilation