Pole Through the Barn: Two Frames Side by Side

Source

Collection: Wiki SR simulations (v1).
Concept: The pole-and-barn "paradox": a pole longer at rest than the barn can be momentarily enclosed with both doors shut in the barn frame, yet is never fully enclosed in its own frame — because simultaneity is relative.
Serves: Side-by-side barn-frame and pole-frame animations of the same events, so the disagreement over "both doors shut with the pole inside" is seen to come from the relativity of simultaneity, not a contradiction.
Inquiry: If the barn frame sees the pole enclosed with both doors shut, what does the pole frame see at that same moment? Why do the two frames disagree?
Misconception: That "simultaneous" is absolute, or that the pole also length-contracts in its own rest frame.

Pedagogy principles applied

ID	Principle	How it shows up here
H1	Misconception is structural, not a text card	The "fits in both frames" and "the pole shrinks too" errors are wrong prediction choices; the rebuttal appears only if the student picks one.
D6/D7	Guided inquiry reveals in stages	Five step-cards run predict → observe the barn frame → reveal the pole frame → verify at the freeze moment → resolve; the second frame and readouts appear only when the step needs them.
G4b/F8d	Second frame introduced deliberately	The pole-frame panel and full readouts stay hidden until the reveal step, so the barn frame is understood before the comparison is drawn.
A2	Fewest objects	Opens with a single barn-frame panel; the pole frame, timeline and readouts are added only as the inquiry calls for them.
C	Every number earns its place	γ, contracted lengths, Δt′ between closings and each frame's "inside?" verdict are each read or compared by a step.

Pole & Barn

Speed

pole fully enclosed not enclosed door flashing shut

Guided Inquiry

1 · Predict first

The pole is longer at rest than the barn, but fired through fast enough that in the barn frame both doors slam shut simultaneously with the whole pole inside. What does the pole frame show at that same moment?

2 · Watch it in the barn frame

Press ▶ (top bar) or drag the timeline. The contracted pole sweeps through; at t = 0 both doors flash shut together with the pole momentarily enclosed. Read the green "FULLY INSIDE" badge on the barn panel.

3 · Now the pole's own frame

The pole frame just appeared beside the barn frame — same events, re-described from the pole's rest frame. Here the pole keeps its full length L₀ and it is the barn that is contracted and moving. Scrub the timeline and watch each door close at its own pole-frame time.

4 · Freeze at "both doors shut"

The scene is frozen at the barn-frame moment t = 0 when both doors are shut. Compare the two "FULLY INSIDE" badges. In the pole frame, is the pole enclosed at this instant?

5 · Relativity of simultaneity

There is no contradiction: the barn frame's simultaneous door-closings are non-simultaneous in the pole frame. Each frame length-contracts the other object, never itself. Turn on ∑ Formal (top bar) for the Lorentz algebra, or drag the sliders to explore. Hit Finish to tuck this away.

Set up the experiment

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v = 0.80c

0.30c0.95c

L₀ = 12.0

620

D = 10.0

616

Show inside badge

Readouts

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Show details ▾

Lorentz factor

Length contraction (each frame contracts the other)

Lorentz transformation

The two door-closings in the pole frame

The two door-closings happen at the same barn-frame time but at different positions (x = 0 and x = D); the term in the Lorentz time transform makes them non-simultaneous in the pole frame. Here t′ is the coordinate time in the pole's rest frame (labelled τ on the clocks and readouts).