Time Dilation: The Light-Clock Thought Experiment
1 · Predict
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?
- 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.
2 · Set Up
- 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.
3 · Collect Data
| Speed fraction β = v/c | Lorentz factor γ | Dilated time Δt (µs) |
|---|---|---|
| 0.3 | ||
| 0.6 | ||
| 0.9 |
Plot dilated time Δt (y-axis) against β (x-axis) for your three trials. Does the curve rise gently at first, then steeply?
4 · Analyze
- 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.
5 · Extend
- 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?
The Physics Behind This Experiment
Time Dilation
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.
Time Dilation
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.