Time dilation and length contraction

Equipment

• “Speed β = v/c” slider driving the clock-and-rod figure
• “Model parameter” and second “Speed β” sliders for the relation plot
• “Pause” animation and “Reset view” buttons
• β and γ readout plus the 1/γ label on the figures

Procedure

1. Watch the moving clock run slow

   Sweep “Speed β = v/c” from 0 to 0.95: the moving clock's ticks stretch out compared with the lab clock. Read γ on the readout and check $\Delta t = \gamma\,\Delta\tau$; drag the canvas to rotate the scene if needed.

2. Measure the rod's contraction along the motion

   At the same β, look at the rod: its projected length along the motion shrinks while the transverse size stays fixed. Compare with $L = L_0/\gamma$ and stress that this is a measurement effect between frames, not a mechanical deformation.

3. Read the γ(β) plot and the non-relativistic limit

   In the “Quantitative relation” panel, sweep the second β slider: γ departs from 1 by only parts per thousand at small β but blows up as β → 1. Use $\gamma = 1/\sqrt{1-\beta^2}$ to estimate which β gives a 1% correction and explain why the effect is invisible at everyday speeds.

Simulation

Experiment history

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