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The ladder paradox

A 12-metre ladder fits inside a 10-metre garage, if it's moving fast enough. Or does it?

A classic puzzle from Einstein's special relativity

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The story

The world's fastest delivery

Farhan works for a delivery company in a world where vans can travel close to the speed of light. Today he has to carry a 12-metre ladder into a garage only 10 metres long, with doors at both ends.

The garage owner, Mrs Bose, has read about relativity. "Moving objects get shorter in the direction they move," she says. "Run it through fast enough and, from where I'm standing, your ladder will shrink to less than 10 metres. For one instant I'll close both doors and the whole ladder will be inside."

Farhan, holding the ladder, frowns. "But from where I'm standing, I'm still and your garage is rushing at me. Your garage is the one that shrinks. It'll be even shorter than 10 metres. My ladder can't possibly fit."

They are both using correct physics. So does the ladder fit or not?

The puzzle

In the garage's view the ladder fits; in the ladder's view it can't. Both views can't be right… can they?

See it for yourself

Garage at rest, ladder rushing inDoors close at the same moment, for an instantnear doorfar doorBoth views are right. Who says “at the same time” depends on how you move.At rest: ladder 12 m, garage 10 m
γ (stretch factor)1.67Ladder, measured by garage7.2 mGarage, measured by ladder6.0 mIn the garage's viewFits: both doors shut at once

What's really going on

The key is that in relativity, two events that happen at the same time for one observer may not happen at the same time for another. Mrs Bose sees both doors close at the same instant with the ladder inside. Farhan sees the far door close and open again first, while the back of the ladder is still outside, and only then the near door shut behind it.

Nothing ever crashes into a closed door, and both observers agree on everything that physically happens; they just disagree on the order of events far apart. This is called the relativity of simultaneity, and it's what makes all of relativity's paradoxes fit together.

Think about it

What would happen if both doors stayed shut and the ladder had to stop inside the garage?

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