Solving the Paradox of Length Contraction on a Train

[Flexo]

There's one of the paradoxes with SR that I've never actually seen an answer for.

There is a man on a train traveling at a velocity where length contraction starts to matter. Say, .3c. There are some dirty bandits that have rigged up a trap door system in a mountain up ahead on the tracks. There are two(currently open) doors on either end of the mountain, which is the same length as the train. The dirty bandits know how fast the train is going, and they have made it so that at the appropriate time, both doors will shut while the train is inside.

The train will see the mountain as length contracted, and the bandits will see the train as length contracted. Does the train get stuck in the mountain or does the exit door crush it?

 

[granpa]

the bandits close the doors simultaneously from their point of view but not simultaneously from the point of view of the train.

no paradox at all.

 

[Flexo]

the bandits close the doors simultaneously from their point of view but not simultaneously from the point of view of the train.

no paradox at all.

Oh, that's way simpler than I was thinking it would be. Thanks.

 

[granpa]

its all way simpler than people think it is.

 

[Flexo]

its all way simpler than people think it is.

Actually...is it possible for them to have only one door, and have it rigged to shut immediately before the train would leave the tunnel? Simultaneity doesn't seem to apply.

 

[Flexo]

?

Alright, there is a guillotine type-contraption sitting at the end of a tunnel. The bandits have set it to fall immediately before the train reaches the end of the tunnel. The same length contraction effects occur, the train sees the tunnel is shorter and the bandits see the train as shorter. Does the guillotine crush the train or merely stop it?

 

[granpa]

the guillotine and the front of the train are at the same place at the same time. this will be true for all observers regardless of their velocity.

 

[Flexo]

the guillotine and the front of the train are at the same place at the same time. this will be true for all observers regardless of their velocity.

Oh, I suppose I'm making it more complicated than it needs to be. Thanks for the answers.

 

[AntigenX]

the bandits close the doors simultaneously from their point of view but not simultaneously from the point of view of the train.

no paradox at all.

I think when the train is in the tunnel (exactly between the two trapdoors), the event of closing the doors will be simultaneous from both point of views. No?

 

[Doc Al]

There's one of the paradoxes with SR that I've never actually seen an answer for.

A identical problem that is discussed everywhere is the "pole in the barn" paradox.

I think when the train is in the tunnel (exactly between the two trapdoors), the event of closing the doors will be simultaneous from both point of views. No?

No. Simultaneity is frame dependent.