Length Contraction: A Relativistic Rocket

1 · Predict

A 10-meter rocket flies past you at high speed. Do you measure its length as exactly 10 meters, longer, or shorter than that?

• Shorter — an object's length along its direction of motion appears contracted to an observer it's moving past.
• The same 10 meters — length doesn't depend on relative motion.
• Longer than 10 meters.

2 · Set Up

1. Open the length-contraction-rocket preset and press Reset. The rocket's proper (rest-frame) length is fixed at 10 m; its speed is β = 0.9.
2. Enable the Lorentz factor and contracted-length readouts.
3. Set the rocket's speed for each trial and record its contracted length as measured from your (stationary) frame.

3 · Collect Data

Plot contracted length L (y-axis) against β (x-axis) for your three trials. Does it drop off sharply as β approaches 1?

4 · Analyze

1. For one trial, compute γ = 1/√(1 − β²), then L = L_proper/γ using the proper length 10 m. Compare both to the table.
2. Explain why length contraction only affects the dimension ALONG the direction of motion — a rocket's width and height (perpendicular to its velocity) stay unchanged, only its length shortens.

5 · Extend

1. Just like time dilation, length contraction is symmetric: from the rocket pilot's own frame, it's Earth (and everything on it) that appears contracted along the direction of relative motion, while the rocket itself measures its normal 10 m length. Explain why this isn't a contradiction.
2. This experiment's rocket moving at β = 0.9 has γ ≈ 2.29 — meaning both its length is compressed by that factor AND, if it carried a clock, that clock would run correspondingly slow (time dilation) by the same factor. Explain why time dilation and length contraction are really two faces of the same underlying spacetime geometry.

The Physics Behind This Experiment

← Back to experiment