1. Predict
Predict how doubling mirror separation affects proper period and the Lorentz factor.
Light clock and time dilation
The same light. Different time intervals.
Compare light bouncing between two mirrors in the clock’s rest frame and in the laboratory frame.
If light travels at c in both frames, why does one round trip take different amounts of time?
2. Run a controlled experiment
Set β = 0 and L = 1 m. Record Δτ and Δt for one round trip in ns. Explain their equality.
3. Compare and measure
At fixed L, test β = 0.6 and 0.8. Calculate Δt/Δτ and compare with the displayed γ.
4. Examine the relationship
At fixed β, increase L from 0.5 m to 1 m. How do the times and γ change? Use the fact that light has speed c in both frames.
5. Conclusions and limits
Compare accumulated proper and laboratory times after five cycles. Distinguish viewing time from physical nanoseconds in your explanation.
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Light clock and time dilation
ReadyClock’s rest frame
Laboratory frame
02 / LIVE MEASUREMENTS
Elapsed proper time τ—ns
Elapsed laboratory time t—ns
Lorentz factor γ—
Round-trip duration
Each square is 0.5 m; both panels share the same scale. One round trip takes 6 viewing seconds; physical times are in ns.
Scale and display notes
The laboratory grid and viewport stay fixed. The clock moves right; scroll horizontally yourself or use “Show the clock” when needed. There is no automatic tracking.
Both panels use the same fixed spatial scale: each square is 0.5 m. Scale stays fixed as mirror separation varies from 0.5 to 2 m.
Each round trip is played over 6 viewing seconds; physical times are in ns. Horizontal scrolling only changes the view, not physical position or times.
Ask. Test. Explain.
Ask a question
Does the speed of light change when a moving clock runs slow?
Test it
Compare round-trip times in the two frames at β = 0 and β = 0.6.
Interpret the result
How does the longer light path relate to time dilation?
Compare elapsed time, not different speeds of light.
In the clock’s rest frame, light travels vertically. In the laboratory, the mirrors move and light follows a longer diagonal path. Since light travels at c in both frames, the laboratory round-trip duration is longer.
Model and assumptions
Special-relativistic model: constant relative velocity, ideal mirrors and vacuum. No acceleration or gravity. The panels are coordinate views of the same photon events, not delayed optical images reaching a camera. Time is slowed for animation. Changing speed or separation starts a new experiment.
Symbols and derivatives: how to read them
| Notation | Meaning and unit |
|---|---|
| Time; s denotes seconds. The light clock uses ns = 10⁻⁹ s. | |
| L is mirror separation (m), c light speed in vacuum (m/s), v the clock’s horizontal laboratory velocity (m/s). β is dimensionless; here 0 ≤ β < 1. | |
| τ is proper time in the clock’s rest frame; t laboratory time; γ the dimensionless Lorentz factor. Δτ and Δt span the same round-trip events. Each panel is labelled with its own frame’s time. |
References and further reading
The books below offer further study of the relevant concepts. The simulation’s assumptions are stated separately above.
- Raymond A. Serway, John W. Jewett. Physics for Scientists and Engineers with Modern Physics. Edition 10 · Chapter(s) 38. Cengage. View source ↗
- Hugh D. Young, Roger A. Freedman. University Physics with Modern Physics. Edition 15 · Chapter(s) 37. Pearson. View source ↗
- David Halliday, Robert Resnick, Jearl Walker. Fundamentals of Physics. Edition 12 · Chapter(s) 37. Wiley. View source ↗