← Theory of RelativityPart 1 — Special Relativity · 10

The Shrinking Spaceship

▶ DRILL

Vika's 100 m ship is too long for George's 60 m tunnel — when it's parked. But send it flying and George measures it shorter along its direction of travel (and only that direction — it stays just as tall). Fast enough, the ship shrinks below 60 m and slides entirely inside the tunnel. It's the very same γ that slowed the moving clock, now squishing space. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words, names & pictures

SHIP'S SPEEDvery fast

now 80 m long (was 100)

SLOW-MOnormal

📏 HOW LONG IT LOOKS

was 100 m parked; now 80 m — shorter along its travel, but the same height.

🚇 THE 60 m TUNNEL

✗ too long — speed up until the ship shrinks under 60 m.

The big idea — a fast-moving thing is genuinely shorter along the direction it's zooming (and only that direction — it stays just as tall). It's the same squish, by the same amount γ, that slows a moving clock. That's why a too-long ship can fit a too-short tunnel at high speed. It's real — fast muons reach the ground because the air ahead of them is squished thin. (From Vika's seat it flips: she sees the tunnel as short, not her ship. Untangling that is the pole-and-barn puzzle — another drill.)

# formulaL = L₀/γ = L₀·√(1 − v²/c²) — contracted along the direction of motion only; transverse height unchanged

# setuprest length 100 m · tunnel 60 m · fits once v ≳ 0.8 c, where the ship contracts below 60 m

# reciprocalin the ship's frame it's the tunnel that's short — the pole-and-barn paradox, resolved by the relativity of simultaneity

# realfast muons reach the ground because the atmosphere is length-contracted in their frame; relativistic beams focus the same way