Fit a ladder into a shorter barn using relativity—explore how length contraction and simultaneity resolve the paradox from both frames
In barn frame:
• Ladder: 8.0 m (contracted)
• Barn: 8.0 m
In ladder frame:
• Ladder: 10.0 m
• Barn: 6.4 m (contracted)
A ladder is being carried through a barn at high speed. The ladder is longer than the barn in both of their rest frames. But due to length contraction:
Who's right? How can the ladder both fit and not fit inside the barn?
The key is that "simultaneously closing both doors" means different things in different frames. Events that are simultaneous in one frame are not simultaneous in another moving frame.
The ladder is contracted to L/γ. When it's completely inside, both doors close at the same time (in this frame). The ladder fits, and both doors are briefly closed together.
The barn is contracted to B/γ and too short for the ladder. The door closings are NOT simultaneous here:
The two doors are never closed at the same time in the ladder frame. The ladder passes through safely, one door opening before the other closes.
Δt' = γ(Δt - βΔx/c)
Two events simultaneous in the barn frame (Δt = 0) and separated in space (Δx ≠ 0) have a time difference in the ladder frame: Δt' = -γβΔx/c. The spatial separation causes temporal separation.
Both descriptions are equally valid. There's no "true" answer to whether the ladder fits. Each frame gives a self-consistent account of what happens, but they disagree on simultaneity.
While simultaneity is relative, causality is absolute. All observers agree on the causal order of events: which events can influence which. The door closings are spacelike separated, so they can't causally affect each other — that's why their order can flip between frames.
This isn't an optical illusion. In the barn frame, the ladder really is shorter than the barn. In the ladder frame, the barn really is shorter than the ladder. Both are true — reality itself depends on reference frame.
What if we tried to trap the ladder by closing both doors? Would it crash?
If you close the doors when the ladder is inside (in the barn frame), you're closing them at different times in the ladder frame. The ladder sees: rear door closes → front door opens → ladder exits → front door closes. No collision!
But if you tried to close both doors on the ladder keeping them closed (a spacelike simultaneous event in the barn frame), you'd need a mechanism to coordinate them. That mechanism would involve signals traveling at most at speed c, and those signals would arrive at different times in the ladder frame. The relativity of simultaneity prevents you from creating a genuine trap.
While we can't run actual ladder-barn experiments at relativistic speeds, the same physics appears in particle physics:
Watch the animation: See how the same physical process looks completely different in the two frames. Note when the doors close in each frame.
Adjust the velocity: At low β, the paradox weakens (less contraction). At high β, the effects are dramatic. At β = 0.6 with L = 10m and B = 8m, the ladder contracts to exactly 8m in the barn frame — a perfect fit!
Change the dimensions: Make the ladder much longer than the barn. Notice that even when the ladder is 1.5× the barn length, it can still "fit" at high enough velocity.
Simultaneity shift: Pay close attention to the timing of door closures. In the barn frame they're simultaneous. In the ladder frame, there's a clear time gap between them.
The ladder-barn paradox teaches us that space and time are not separate, absolute entities. They're woven together into spacetime, and different observers slice this 4D structure differently. What's simultaneous, what's the same length, even what's happening "now" — all depend on your state of motion.
This isn't a bug in nature. It's a feature of living in a universe with a maximum speed (c). The relativity of simultaneity is the price we pay for causality and the invariance of physical laws.