Using length contraction to push a bomb trigger

[Jeronimus]

Inspired by Aziza's question i came up with a similar, seemingly puzzling question.

Imagine a space-platform with a big cylinder on it. The cylinder has a hole drilled in, with a bomb-button at the end of the hole, which would trigger a bomb destroying the whole galaxy.

A terrorist is on that space-platform with his rocket. He is too weak to push the trigger, so he decides to use his rocket nose to push it.
The nose of the rocket is only 10 meters long, while the cylinder hole is 20 meters.
The rocket is T shaped, so the tail of the rocket would hinder him from getting further inside once the nose is fully in. See picture.

http://www.lupiupload.de/images/2012/09/23/bf63b4dc89a421f8b0528116d43276dac3b53550.png

The terrorist is quite smart and knows SR quite well, so he decides to speed up his rocket to about 0.9c. The cylinder seen from his inertial reference frame at this speed would shrink to about 8.7m. The rocket nose within the terrorist's/rocket's inertial reference frame would be 10m still.
Enough for his rocket to fly in and push the button with it.

An observer on the cylinder is laughing at the terrorist, seeing the rocket coming in, which from his inertial frame of reference has a nose length of only ~4.36m. Knowing the cylinder is of some super strong material, just like the rocket, he is convinced that the terrorist won't succeed since even in the rest frame, the rocket nose was only 10m long, not enough to push the button.Will the terrorist succeed in blowing up the galaxy or not?

 

[Aziza]

Inspired by Aziza's question i came up with a similar, seemingly puzzling question.

Imagine a space-platform with a big cylinder on it. The cylinder has a hole drilled in, with a bomb-button at the end of the hole, which would trigger a bomb destroying the whole galaxy.

A terrorist is on that space-platform with his rocket. He is too weak to push the trigger, so he decides to use his rocket nose to push it.
The nose of the rocket is only 10 meters long, while the cylinder hole is 20 meters.
The rocket is T shaped, so the tail of the rocket would hinder him from getting further inside once the nose is fully in. See picture.

http://www.lupiupload.de/images/2012/09/23/bf63b4dc89a421f8b0528116d43276dac3b53550.png

The terrorist is quite smart and knows SR quite well, so he decides to speed up his rocket to about 0.9c. The cylinder seen from his inertial reference frame at this speed would shrink to about 8.7m. The rocket nose within the terrorist's/rocket's inertial reference frame would be 10m still.
Enough for his rocket to fly in and push the button with it.

An observer on the cylinder is laughing at the terrorist, seeing the rocket coming in, which from his inertial frame of reference has a nose length of only ~4.36m. Knowing the cylinder is of some super strong material, just like the rocket, he is convinced that the terrorist won't succeed since even in the rest frame, the rocket nose was only 10m long, not enough to push the button.


Will the terrorist succeed in blowing up the galaxy or not?

haha I feel so inspirational.

according to me (and I am no expert), he will succeed. If you read the replies by Fredrik and harrylin to my question, they give nice explanation that can be applied here as well. Basically the rear of the rocket will get stopped by crashing into the sides of cylinder, but the front end of the rocket doesn't know what happened at the rear end, so the front just keeps flying at full speed. So the rocket gets ripped apart but the nose makes it to the end of the cylinder to touch the trigger, since it never got the message that it has to stop.

The only thing that is confusing me about this explanation is that it seems that in one frame, the rocket gets ripped apart, but in another frame (say, the rocket frame), it won't get ripped apart...

 

[A.T.]

This is known as bug-rivet-paradox:
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/bugrivet.html

If not elastic enough, the rivet/rocket will be torn appart in both frames, but it is harder to explain in the rivet frame. In particular because there is no distinct rest frame of the whole rivet, as soon as contact occurs. And because the rest frames of the rivet parts become noninertial at some point.

 

[sweet springs]

Hi.

Knowing the cylinder is of some super strong material, just like the rocket, he is convinced that the terrorist won't succeed since even in the rest frame, the rocket nose was only 10m long, not enough to push the button. Will the terrorist succeed in blowing up the galaxy or not?

He or she will succeed it.

 

[sweet springs]

Hi.

The only thing that is confusing me about this explanation is that it seems that in one frame, the rocket gets ripped apart, but in another frame (say, the rocket frame), it won't get ripped apart...

The two collisions at head and tail are independent events that do not have causal relationship. Regards.

 

[sweet springs]

Hi. Here is a similar paradoxical tale concerning transmitting information on crash.

Train bridge explosion

A train is running on the bridge. Terrorists explode the bombs set at all the feet of bridge AT THE SAME TIME on earth. The bridge goes into pieces and the train begins falling KEEPING ITS HORIZONTAL SHAPE as it was running on the railway. Bottoms of all the cars crash to the river surface at the same time.

In the frame of the train, the bombs do not explode simultaneously. Bombs in front of them explode first and the back last. So the first car drops first and the last car falls last. The train DOES NOT KEEP ITS HORIZONTAL SHAPE LINE but perpendicular. The first car smashes on the river first.

So the damage of crash are same among the cars or the first car is damaged most severely because of the angle crash?

Regards.

 

[Dale]

Will the terrorist succeed in blowing up the galaxy or not?

Unfortunately, yes, the terrorist succeeds. This is equivalent to the bug rivet paradox discussed in the other thread and the explanation is the same.

 

[Jeronimus]

Hi.
The two collisions at head and tail are independent events that do not have causal relationship. Regards.

This is quite to the point after thinking about it. Even though the rocket nose is a little bit over 4m seen from the cylinder's rest frame point of view, the nose of the spaceship "sees" no reason to stop going at v=0.9c inside the cylinder once the tail hits the cylinder.

The information from the tail to the nose about it having crashed on the cylinder can reach the nose at lightspeed at best (assuming we send a laser pulse from the tail towards a detector installed at the nose, informing it that the tail crashed).

That laser pulse will never reach the detector, because by the time it does, the nose will already be on the button and the galaxy blown up.

Otherwise said. If the rocket had no thick tail, and we assume a huge laser cannon shoots it from behind just when the back of the rocket which now fits in the cylinder properly, enters, the laser would not be able to make it in time to the nose, before it hits the button.The material of the rocket/cylinder used here is completely irrelevant. Even with the strongest possible material even an infinite strong which does not exist, the nose would keep going because it simply doesn't know what is going on back there. As you said rightly. There is no causal relationship between the two events, tail and nose crashing.

It's almost like saying that in order for a causal relationship to build up between two events, information which can travel at c max has to be transferred first between the two events.

 

[Jeronimus]

thanks everyone for the good replies. Each of has helped to wrap my mind around this now solved paradox.

 

[harrylin]

[..] The only thing that is confusing me about this explanation is that it seems that in one frame, the rocket gets ripped apart, but in another frame (say, the rocket frame), it won't get ripped apart...

We explained that in "your" thread.