Vote 2020 graphic
Everything you need to know about and expect during
the most important election of our lifetimes

Discover the Ladder Paradox, relativity's greatest thought experiment

Illustration for article titled Discover the Ladder Paradox, relativitys greatest thought experiment

The Ladder Paradox is a famous thought experiment that shows you why you can fit objects into spaces that are too small for them. And also why you can't, depending on your perspective.


Relativity does a real number on our faith in reality. Although we can think of reality as objective, there are some special cases that prove it's nothing of the kind. Different people have their own reality, and these realities are, sometimes, incompatible. One particularly nagging problem is known as the Ladder Paradox, or the Barn-Pole Paradox.

Let's say you have a ladder and you have a garage. You've never put the ladder in the garage because the ladder is too long. You'd either have to open the front door and let the end of the ladder hang out into your driveway, or the back door, and let the other end of the ladder spill out into your back yard. One day, your friend Albert says that he can put your ladder inside your garage, albeit briefly. You see, as objects approach relativistic speeds, they undergo length contraction. So if you're sitting in your garage, and Albert - who's an old guy but has a good set of legs - runs through, the ladder will appear to be shorter than it is when it's standing still. If you have a garage door opener that closes both doors simultaneously (and quickly), the ladder will fit inside.


You think about it, and decide that there's a problem. If Albert's running right alongside the ladder, from his point of view, the ladder isn't moving, but the garage is. Since the garage is moving past him, it will be undergoing a length contraction, and be even shorter. The ladder won't fit at all.

Illustration for article titled Discover the Ladder Paradox, relativitys greatest thought experiment

You decide to test it out. You'll sit in the garage, and just as Albert runs through, you will shut both doors at the same time. Then you'll open them back up again at the same time, so Albert doesn't run into the door. This should allow you to see if the ladder fits. You go through the experiment and, amazingly, the ladder fits. When you meet up with Albert outside, he asks why you didn't close both doors simultaneously. You tell him that you did, and he says you didn't. You were right, he says, the garage was way too short. The only reason why the ladder didn't crash into the doors is they didn't close at the same time. The door to the back yard closed first, as he was approaching it. The ladder hung out into the driveway. Just as he was going to crash into the back door, it opened again. The ladder started moving out into the back yard, and just as it cleared the door to the driveway, that door closed and then opened again. At no point, says Albert, was the ladder completely in the garage with both doors closed.


As it turns out, both of you had a completely different experience, due to both length contraction and relative simultaneity. If you are standing equidistant from two light bulbs connected to the same switch, and someone flips that switch, you will see both light bulbs going on at the same time. Someone standing next to one light bulb, and far from the other, will see the one near them come on, and then, later, the other one come on. There's no way to say which one is first. Nothing travels faster than light - not even door molecules. (And they're fast. Who do you think coined the expression "don't let the door hit you on your way out"? Concerned physicists, that's who.) Which means that both you and Albert were right. The doors did and did not close simultaneously, and the ladder both did and did not fit in the garage.

My solution? Get a doggy door and let the ladder hang out of that. Problem solved. Why do you have to make everything so difficult?

[Via Hyperphysics, UNSW]


Share This Story

Get our newsletter


I feel stupid, so here's a rabbit with a pancake on it's head.