What happens when two length contracted ladders move through the same garage?

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kmarinas86
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kmarinas86 said:
Figure 4: Scenario in the garage frame: a length contracted ladder entering and exiting the garage
Five-panel sequence of a ladder passing through a garage drawn as a red roof with gray doors, showing the ladder shrinking and moving through the garage in successive frames.


Figure 5: Scenario in the ladder frame: a length contracted garage passing over the ladder
Sequence of six stacked frames showing a red-outlined ladder shape moving left past a row of brown rungs, illustrating a length contracted ladder passing through a garage.

So what happens if we have TWO ladders moving in opposite directions through the same garage?

Figure 4: Scenario in the garage frame: a length contracted ladder entering and exiting the garage

Five stacked diagrams of a ladder passing through a garage with a pitched roof, showing the ladder shortening and sliding along, with arrows indicating direction of motion.


Figure 5: Scenario in the ladder frame: a length contracted garage passing over the ladder

Six stacked diagrams of a ladder-shaped red triangle moving over a brown ladder-like row of rungs, each with a short arrow indicating motion and a gray bar beneath it, shown at successively shifted positions.


Something's amiss.

How, in the last diagram, does the second ladder (the one faster than garage) spend LESS time inside the garage so that (unlike as depicted in the last diagram) the faster ladder doesn't hit the doors of the garage.
 
Attachments
  • Five stacked frames of a ladder passing through a garage with a sloped roof and doors, showing the ladder shrinking and sliding through with arrows indicating motion direction.
    250px-(DOUBLE)Ladder_Paradox_GarageScenario.svg.png
    3.1 KB · Views: 643
  • Six stacked diagrams of a tent-shaped ladder sliding along a horizontal bar with arrows showing its motion, each frame shifted to show the ladder moving through a garage with its doors.
    250px-(DOUBLE)Ladder_Paradox_LadderScenario.svg.png
    4.4 KB · Views: 643
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Discussion

In Fig 5 you have both ladders entering simultaneously. That's incompatible with them entering simultaneously in Fig 4. (Ditto exiting.)
 
DrGreg said:
In Fig 5 you have both ladders entering simultaneously. That's incompatible with them entering simultaneously in Fig 4. (Ditto exiting.)

Thanks.